Work & Machines — Print · Physical Science: Matter, Forces & Energy, Grade 8

Explain how machines transfer energy, trade force for distance, and improve useful output.

Printable chapter lessons and review.

Work: Transferring Energy with a Force

Learning goals

Readings for this unit

Before this unit

Multiply force by distance and identify movement direction.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in work: transferring energy with a force?

Illustrative evidence case. A supplied object moves 3 m horizontally while a 4 N force acts in that direction. In another case a person holds the object still with an upward force.

Force and displacement must be distinguishedForce and displacement must be distinguishedDisplacement: 3 m rightApplied force: 4 N rightAligned constant force: work = 4 × 3 = 12 JHolding still: displacement 0 → ideal work on object 0.Illustrative model • use the labels and stated assumptions
The supplied aligned force and displacement give 12 J of mechanical work. The distance arrow is not a force arrow, and a person can expend metabolic energy even while the held object has no displacement. This simple formula assumes the constant force is along the movement.

Notice and wonder

Would the same horizontal displacement give work by a vertical force? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Find the work in the first case and explain the ideal mechanical work in the second. Clarify the everyday meaning of effort. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

work
Energy transferred by a force acting through a displacement.
joule
The unit of energy and work; 1 J = 1 N·m.
displacement
Change in position, with direction.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In science, work is energy transferred by a force acting through a displacement. A push on a moving box can transfer energy to it. Pushing a wall that does not move does no mechanical work on the wall, even though your muscles use energy. State which object you are analyzing.

When a constant force acts in the same direction as displacement, work = force × distance. Force is measured in newtons and distance in meters, so work is measured in newton-meters, called joules (J). The simple multiplication applies to the component of force along the movement.

When a force does workWork needs force and movement in the same directionPushing a box alongforcemovementforce and motion aligned — work doneHolding a box stillforceno movementforce but no movement — no work doneWork = force × distance moved in the direction of the force
The everyday sense of work and the physics sense part company here. Holding something heavy is tiring and transfers no energy to the object, because the scientific definition requires movement along the line of the force.

A force opposite the direction of motion, such as sliding friction, does negative work on the moving object. A force perpendicular to movement does zero work in that direction. Lifting a book slowly transfers energy to the Earth–book system, increasing gravitational potential energy. Work transfers energy; it does not create it.

Opposite forces make different contributions to workOpposite forces make different contributions to workmoving boxDisplacement: 3 m rightPush: 10 NResistance: 4 NPush work: +30 J. Resistance work: −12 J. Net work: +18 J.Forces and displacement are distinct arrows with distinct units.
For the stated constant aligned forces over 3 m rightward displacement, the push does +30 J of work and resistance does −12 J on the box. Their net contribution is +18 J. A red force arrow is not the same quantity as the blue displacement arrow. The diagram omits vertical interactions that do no work in this horizontal idealization.

Work transfers energy when a force acts through a displacement. If a constant force acts along the movement, work=force×distance. A force opposing movement does negative work on the object, reducing its mechanical energy.

Supporting a stationary bag can be tiring, yet the supporting force does no mechanical work on the bag because the bag does not move. A force perpendicular to movement also does no work in this simple model. Your body can still use chemical energy internally.

Draw the movement and force before substituting numbers. State whether you calculate work by one force or net work by all forces. Friction's work can reduce an object's kinetic energy while increasing thermal energy in the object and surroundings.

Build your understanding

Where this fits

This unit helps answer the chapter question: How can a machine make a task easier without creating energy? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Specify the object receiving energy

In mechanics, work is energy transfer when a force acts through displacement. Name the object and the displacement caused or accompanied by the force. Effort in ordinary language is broader than mechanical work on that object. Holding a bag still can require bodily energy without doing mechanical work on the stationary bag.

Force and displacement must be distinguishedForce and displacement must be distinguishedDisplacement: 3 m rightApplied force: 4 N rightAligned constant force: work = 4 × 3 = 12 JHolding still: displacement 0 → ideal work on object 0.Illustrative model • use the labels and stated assumptions
The supplied aligned force and displacement give 12 J of mechanical work. The distance arrow is not a force arrow, and a person can expend metabolic energy even while the held object has no displacement. This simple formula assumes the constant force is along the movement.

Read the visual model

Why can holding a bag feel tiring while work on the stationary bag is zero?

Visual reasoning — after your attempt

The bag has no displacement in the simple mechanical calculation. The person’s muscles still use energy through internal processes, which is a different system.

If a bag has no displacement, the simple work-by-that-holding-force calculation is zero. Muscles still consume energy internally. The conclusion concerns the selected bag and force, not a claim that the person used no energy at all.

Pause and explain

Why can holding a bag feel tiring while work on the stationary bag is zero?

Check your reasoning after answering

The bag has no displacement in the simple mechanical calculation. The person’s muscles still use energy through internal processes, which is a different system.

Part 2 · Use the aligned-force relationship carefully

For a constant force parallel to displacement, work=force×distance in that direction. A newton-meter equals a joule. If the force is perpendicular, its mechanical work is zero in the ideal model. Do not multiply total path length by an unrelated force magnitude without considering direction.

When a force does workWork needs force and movement in the same directionPushing a box alongforcemovementforce and motion aligned — work doneHolding a box stillforceno movementforce but no movement — no work doneWork = force × distance moved in the direction of the force
The everyday sense of work and the physics sense part company here. Holding something heavy is tiring and transfers no energy to the object, because the scientific definition requires movement along the line of the force.

Read the visual model

Which condition is needed for simply using W=Fd?

Visual reasoning — after your attempt

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

A 15 N horizontal push over 2 m in the same direction transfers 30 J by work. An upward supporting force on a bag carried horizontally does zero work on the bag in the ideal level-motion model, because the displacement is perpendicular.

Pause and explain

Which condition is needed for simply using W=Fd?

Check your reasoning after answering

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

Part 3 · Trace positive and negative contributions

A force in the displacement direction does positive work; an opposing force does negative work. The net work reflects the combined contribution. At constant speed, an applied force can do positive work while friction does equal negative work, leaving no change in kinetic energy.

Opposite forces make different contributions to workOpposite forces make different contributions to workmoving boxDisplacement: 3 m rightPush: 10 NResistance: 4 NPush work: +30 J. Resistance work: −12 J. Net work: +18 J.Forces and displacement are distinct arrows with distinct units.
For the stated constant aligned forces over 3 m rightward displacement, the push does +30 J of work and resistance does −12 J on the box. Their net contribution is +18 J. A red force arrow is not the same quantity as the blue displacement arrow. The diagram omits vertical interactions that do no work in this horizontal idealization.

Read the visual model

Positive work transfers energy into the chosen object through that force; negative work transfers energy out through that force in this account. Add contributions only after their directions and common displacement are clear.

If resistance becomes 6 N over the same 3 m, what happens to its work and to the net work?

Visual reasoning — after your attempt

Resistance work becomes −18 J; the push remains +30 J, so net work is +12 J. Work signs depend on the force direction relative to displacement.

A box moves 3 m under a steady 5 N pull and 5 N opposing resistance. The pull does +15 J and resistance −15 J. Mechanical energy is transferred to thermal stores through resistance even though the box’s speed stays constant.

Pause and explain

Does constant speed mean every individual force does zero work?

Check your reasoning after answering

No. Individual forces can do positive and negative work that sum to zero. The net work, rather than each contribution, determines the kinetic-energy change.

Part 4 · Connect lifting to an energy store

Lifting an object steadily against gravity increases the gravitational potential energy of the object-Earth system. In the simple model, lifting work equals weight×vertical height when other effects are neglected. The height gained matters for this energy change even when a ramp makes the route longer.

Lifting connects force through distance to gravitational energyLifting connects force through distance to gravitational energyHeight increase 2 mMass: 3 kg; g ≈ 10 N/kgWeight ≈ 30 N. Ideal steady lift: work = 30 × 2 = 60 J.Gravitational energy gain belongs to the object–Earth arrangement.
A supplied 3 kg object rises 2 m near Earth with g rounded to 10 N/kg. For a steady ideal lift its upward supporting force equals the 30 N weight, transferring 60 J into the object–Earth gravitational arrangement. The drawing is schematic; extra acceleration, resistance or the lifter’s own energy changes would need a fuller account.

Read the visual model

The height change compares two positions relative to a chosen reference. It is not the total walking path of the lifter. State the receiving system and the steady-lift assumptions before equating force×height with gravitational energy change.

Would holding the object at the final height continue to add mechanical work to it through the stationary support force?

Visual reasoning — after your attempt

No. With no displacement, that support force does no additional mechanical work on the stationary object. The person can still expend biological energy.

A 20 N load raised 0.5 m gains 10 J of gravitational potential energy. A longer ideal ramp can reduce input force while increasing travel distance, preserving the necessary energy transfer. Real resistance adds extra input work.

Pause and explain

Why can a ramp reduce force without eliminating the energy needed to lift?

Check your reasoning after answering

The smaller force acts over a longer distance. The load’s height gain still requires the same gravitational energy increase in the ideal model.

Apply the whole unit · Account for work on a moving box

Illustrative case: a box moves 4 m horizontally at constant speed under a 12 N pull and 12 N opposing resistance. Separately, a 30 N load is lifted steadily through 0.6 m.

Your task

Calculate work by each horizontal force and net work; then calculate the lifting energy transfer. Explain why a zero horizontal net work does not mean no energy use, and state the assumptions behind the lifting result.

What your response should show

  • Use the supplied observations and measurements accurately; include units where needed.
  • Explain the science behind your answer, rather than giving only a number or label.
  • Show a labeled model, calculation, or evidence comparison as requested.
  • State an assumption or limitation and suggest a useful next measurement.
Response guidance — after your attempt

Pull work=+48 J; resistance work=−48 J; net work=0 J, consistent with unchanged kinetic energy. Energy still transfers to thermal stores through resistance. Lifting transfers 30×0.6=18 J to gravitational potential energy under steady aligned-force conditions with other losses neglected. The calculation concerns specified forces and objects.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Ask on which object before asking how much work. Start with aligned arrows, then discuss perpendicular and opposing examples. Do not use lifting tasks that require heavy loads. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Work transfers energy when a force acts through a displacement. For aligned force and motion, W = F × d.

Worked examples

Example 1

A constant 12 N force pulls a box 3 m in the same direction. Find the work done by that force.
  1. Use W = F × d because force and displacement align.
  2. W = 12 × 3.
Answer: 36 J

Example 2 · Worked application

A 15 N horizontal force moves a box 4 m in the same direction. Find work by that force.
  1. Work for aligned force and displacement is W=Fd.
  2. Substitute 15 N×4 m.
  3. The unit N·m is a joule.
Answer: 60 J.
Check the reasoning

A force without displacement transfers no mechanical work to the object in this simple model.

Example 3

A horizontal 15 N force moves a box 4 m in the same direction. Find the work; compare with holding it still.
  1. Use W=Fd=15×4=60 J.
  2. With zero displacement, mechanical work on the stationary box is zero.
Answer: 60 J while moving; 0 J on the stationary box by the supporting force.

Example 4 · Find and fix the mistake

Context: A 15 N horizontal force moves a box 4 m in the same direction. Find work by that force. A student claims: “Holding a heavy bag still means doing positive mechanical work on the bag.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: A force without displacement transfers no mechanical work to the object in this simple model.
  2. The bag's displacement is zero, so mechanical work on it is zero. The person's muscles can still use metabolic energy.
Answer: The bag's displacement is zero, so mechanical work on it is zero. The person's muscles can still use metabolic energy.
Check the reasoning

A force without displacement transfers no mechanical work to the object in this simple model.

Example 5 · Interpret the visual model

Opposite forces make different contributions to workOpposite forces make different contributions to workmoving boxDisplacement: 3 m rightPush: 10 NResistance: 4 NPush work: +30 J. Resistance work: −12 J. Net work: +18 J.Forces and displacement are distinct arrows with distinct units.
For the stated constant aligned forces over 3 m rightward displacement, the push does +30 J of work and resistance does −12 J on the box. Their net contribution is +18 J. A red force arrow is not the same quantity as the blue displacement arrow. The diagram omits vertical interactions that do no work in this horizontal idealization.
If resistance becomes 6 N over the same 3 m, what happens to its work and to the net work?
  1. Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
  2. Positive work transfers energy into the chosen object through that force; negative work transfers energy out through that force in this account. Add contributions only after their directions and common displacement are clear.
  3. Resistance work becomes −18 J; the push remains +30 J, so net work is +12 J. Work signs depend on the force direction relative to displacement.
Answer: Resistance work becomes −18 J; the push remains +30 J, so net work is +12 J. Work signs depend on the force direction relative to displacement.
Check the reasoning

Keep the model’s stated limits explicit: For the stated constant aligned forces over 3 m rightward displacement, the push does +30 J of work and resistance does −12 J on the box. Their net contribution is +18 J. A red force arrow is not the same quantity as the blue displacement arrow. The diagram omits vertical interactions that do no work in this horizontal idealization.

Avoid these mistakes

Check your understanding

A horizontal 15 N force moves a box 4 m in the same direction. Find the work; compare with holding it still.

Discuss the answer

60 J while moving; 0 J on the stationary box by the supporting force.

Why must a work calculation include direction as well as distance?

Discuss the answer

Work transfers energy when a force acts through a displacement. If a constant force acts along the movement, work=force×distance. A force opposing movement does negative work on the object, reducing its mechanical energy. Supporting a stationary bag can be tiring, yet the supporting force does no mechanical work on the bag because the bag does not move. A force perpendicular to movement also does no work in this simple model. Your body can still use chemical energy internally.

Return to the phenomenon

A supplied object moves 3 m horizontally while a 4 N force acts in that direction. In another case a person holds the object still with an upward force. Find the work in the first case and explain the ideal mechanical work in the second. Clarify the everyday meaning of effort. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

The first force transfers 4×3=12 J through the aligned displacement. For the chosen held object, no displacement means zero ideal mechanical work by the holding force. The person may still use metabolic energy to maintain muscle activity. Everyday effort and the technical force–displacement quantity answer different questions.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

A supplied object moves 3 m horizontally while a 4 N force acts in that direction. In another case a person holds the object still with an upward force. Find the work in the first case and explain the ideal mechanical work in the second. Clarify the everyday meaning of effort. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

  • Use two relevant stated records or conditions.
  • Explain the mechanism rather than only repeat a definition.
  • Label observation and inference.
  • Name a changed model feature or a remaining uncertainty.
Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

The first force transfers 4×3=12 J through the aligned displacement. For the chosen held object, no displacement means zero ideal mechanical work by the holding force. The person may still use metabolic energy to maintain muscle activity. Everyday effort and the technical force–displacement quantity answer different questions.

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

Would the same horizontal displacement give work by a vertical force? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

  • Answer the figure question with its stated labels.
  • Connect the visual representation to the scientific idea.
  • Identify a specific limitation from the caption.
  • Propose a useful change without misrepresenting supplied evidence.
Hint

The supplied aligned force and displacement give 12 J of mechanical work. The distance arrow is not a force arrow, and a person can expend metabolic energy even while the held object has no displacement. This simple formula assumes the constant force is along the movement.

Response guidance — discuss after your attempt

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work. The supplied aligned force and displacement give 12 J of mechanical work. The distance arrow is not a force arrow, and a person can expend metabolic energy even while the held object has no displacement. This simple formula assumes the constant force is along the movement.

Words to know

work
Energy transferred by a force acting through a displacement.
joule
The unit of energy and work; 1 J = 1 N·m.
displacement
Change in position, with direction.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Exit check

Would the same horizontal displacement give work by a vertical force? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work. The supplied aligned force and displacement give 12 J of mechanical work. The distance arrow is not a force arrow, and a person can expend metabolic energy even while the held object has no displacement. This simple formula assumes the constant force is along the movement.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Levers, Ramps & Pulleys

Learning goals

Readings for this unit

Before this unit

Understand that useful work requires both force and distance.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in levers, ramps & pulleys?

Illustrative evidence case. Illustrative ideal ramps raise the same load by 0.5 m. Ramp A is 1 m long and B 2 m long; measured input forces are 20 and 10 N under the simplified no-loss model.

A longer ramp trades distance for forceA longer ramp trades distance for forceRamp A: 1 m; 20 NRamp B: 2 m; 10 NSame load rises 0.5 m • ideal input work: 20 J each.Illustrative model • use the labels and stated assumptions
The labeled lengths and forces, rather than the schematic slopes, define the ideal comparison. Both raise the same load by 0.5 m, with 20 J input work in this no-loss model. A longer path reduces required force but does not make energy; real friction changes the input.

Notice and wonder

Why are these ramps not a scale drawing? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Compare input work and explain the force–distance trade-off. State why actual friction would change the required input. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

simple machine
A device that changes the size or direction of an applied force.
fulcrum
The pivot about which a lever turns.
ideal machine
A model with no dissipative energy losses.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

A simple machine changes how a force is applied. A lever turns around a pivot, called a fulcrum. A ramp lets a load rise along a sloping path. A pulley redirects a rope; some pulley arrangements also reduce the input force. Machines help us complete tasks, but they do not make energy from nothing.

Three simple machinesThree ways to trade force against distanceLevereffortloadRamppush alongheightPulley4 supporting segmentsEach reduces the force needed and increases the distance moved — energy in is never less than out
All three make a job feel easier by the same bargain: less force over a greater distance. None of them reduces the energy required, which is the point the efficiency unit then quantifies.

An ideal machine can reduce the force needed by increasing the distance through which you apply it. A long, gently sloping ramp requires less force than a steep one to raise the same load slowly to the same height, ignoring friction. The gentler ramp requires a longer trip.

A fixed pulley can change the direction of a force without reducing its size. A movable pulley supported by more rope segments can reduce the pulling force, but more rope must be pulled. Real machines also transfer some energy to thermal energy and sound, so their input work exceeds their useful output work.

Count strands supporting the moving loadCount strands supporting the moving loadFixed pulley: one supporting strandMovable pulley: two supporting strands100 NPull 100 N; direction changes100 NPull 50 NEach supporting strand: 50 N
The fixed ideal pulley changes pulling direction but leaves a 100 N effort for a 100 N load. The movable ideal pulley is lifted by two rope strands with equal tension; 50 N in each supports the 100 N load. The model assumes negligible pulley/rope mass and friction, and the sketches are reasoning tools rather than construction instructions.

A machine can reduce the input force by increasing the input distance. An ideal ramp spreads the work of raising a load over a longer path. It does not reduce the required gain in gravitational potential energy.

For a lever, turning effect depends on force and its perpendicular distance from the pivot. A long effort arm can balance a larger load on a short arm. For a pulley system, count the rope segments actually supporting the moving load; a fixed pulley may change direction without reducing effort.

Real machines have friction and can bend or slip, so input work usually exceeds useful output work. Compare designs for the same load and height, measure both effort and travel, and keep fingers clear of pinch points. A smaller force does not by itself show a smaller energy requirement.

Build your understanding

Where this fits

This unit helps answer the chapter question: How can a machine make a task easier without creating energy? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Use a machine to change a task

Simple machines can change force magnitude, force direction, or where a force is applied. They do not create energy. An ideal machine trades force against movement distance; real machines also transfer some input energy to less useful stores. Identify the input action and useful output before comparing designs.

Three simple machinesThree ways to trade force against distanceLevereffortloadRamppush alongheightPulley4 supporting segmentsEach reduces the force needed and increases the distance moved — energy in is never less than out
All three make a job feel easier by the same bargain: less force over a greater distance. None of them reduces the energy required, which is the point the efficiency unit then quantifies.

Read the visual model

Must every simple machine reduce force?

Visual reasoning — after your attempt

No. Some primarily change direction or trade increased force for a movement or speed advantage. Describe the actual input and output rather than assuming a force reduction.

An ideal ramp raises a load with a smaller force acting over a longer distance than a vertical lift. A fixed pulley may mainly change pulling direction. Being called a machine does not automatically mean the input force is reduced.

Pause and explain

Must every simple machine reduce force?

Check your reasoning after answering

No. Some primarily change direction or trade increased force for a movement or speed advantage. Describe the actual input and output rather than assuming a force reduction.

Part 2 · Explain a lever with turning effects

A lever turns about a pivot or fulcrum. The turning effect depends on the force and its perpendicular distance from the pivot. A longer input arm can balance a larger output force in a simple ideal static lever. Distances measured along an angled lever are not always the perpendicular moment arms.

A lever trades force against its distance from the pivotA lever trades force against its distance from the pivotEffort: 75 N downLoad on lever: 300 N downPivot support upArm: 4 m1 mTurning effects: 75×4 = 300×1. Forces shown act on the lever.
The ideal lever is balanced when the 75 N effort acts 4 m from the pivot and the 300 N load force acts 1 m from it. The turning effects match even though the forces differ. Both downward red arrows are forces on the lever; its upward force on the load is a different receiver’s force. Arrow lengths are qualitative here, while the arm distances and force labels supply the calculation.

Read the visual model

The pivot is the turning point. A force’s perpendicular distance from it affects turning. The lever does not create energy; during a small movement the long effort end travels farther than the short load end.

Why can the smaller effort balance the larger load force? Would moving the effort closer to the pivot keep the same balance?

Visual reasoning — after your attempt

Its arm is four times as long: 75×4 = 300×1. Moving the effort closer reduces its turning effect, so a larger effort would be needed under the same ideal conditions.

With a 0.4 m input arm and 0.1 m output arm, a 10 N perpendicular input can balance a 40 N output load. Both turning effects are 4 N·m. This is a balance model; acceleration and friction require more information.

Lever model compares a 10 newton input over a 0.4 meter arm with a 40 newton output over a 0.1 meter arm.Input 10 NLoad 40 NInput arm 0.4 m0.1 mPivotEqual turning effects: 10 × 0.4 = 40 × 0.1 = 4 N·m
Ideal static lever model. The input and load both act downward on the lever, on opposite sides of the pivot. Their perpendicular moment arms are 0.4 m and 0.1 m. The lever in turn pushes upward on the load with 40 N. Read the labels rather than measuring the sketch.

Pause and explain

Why can pushing farther from the pivot reduce the needed force?

Check your reasoning after answering

A larger perpendicular distance gives a larger turning effect for the same force. A smaller force can then balance the same load turning effect.

Part 3 · Compare ramps by height and path

An ideal frictionless ramp of length L and height h requires a parallel input force equal to load weight×h/L for steady motion. Increasing length while keeping height fixed reduces the ideal input force. The required gravitational energy change still depends on the same height gain.

A longer ramp trades distance for forceA longer ramp trades distance for forceRamp A: 1 m; 20 NRamp B: 2 m; 10 NSame load rises 0.5 m • ideal input work: 20 J each.Illustrative model • use the labels and stated assumptions
The labeled lengths and forces, rather than the schematic slopes, define the ideal comparison. Both raise the same load by 0.5 m, with 20 J input work in this no-loss model. A longer path reduces required force but does not make energy; real friction changes the input.

Read the visual model

What changes when the ramp gets longer but the rise stays the same?

Visual reasoning — after your attempt

The ideal input force becomes smaller and input distance larger. The gravitational energy increase remains the same for the same load and height.

For a 60 N load and 1 m rise, a 3 m ideal ramp requires 20 N parallel pull. Input work=20×3=60 J, equal to 60×1 J for the vertical lift. A rough ramp needs extra input for resistance.

Pause and explain

What changes when the ramp gets longer but the rise stays the same?

Check your reasoning after answering

The ideal input force becomes smaller and input distance larger. The gravitational energy increase remains the same for the same load and height.

Part 4 · Count supporting rope segments in a pulley model

An ideal movable pulley can distribute a load across supporting rope segments with equal tension. A fixed pulley changes direction without the same force advantage. Rope movement increases as more supporting segments lift the load. Friction, rope mass, and changing geometry can reduce the real advantage.

Count strands supporting the moving loadCount strands supporting the moving loadFixed pulley: one supporting strandMovable pulley: two supporting strands100 NPull 100 N; direction changes100 NPull 50 NEach supporting strand: 50 N
The fixed ideal pulley changes pulling direction but leaves a 100 N effort for a 100 N load. The movable ideal pulley is lifted by two rope strands with equal tension; 50 N in each supports the 100 N load. The model assumes negligible pulley/rope mass and friction, and the sketches are reasoning tools rather than construction instructions.

Read the visual model

Tension is the pull transmitted along a rope. Count strands that act on the moving load/pulley assembly, not every segment visible in the picture. A fixed pulley alone does not automatically double force advantage.

For the movable case, how much rope must be pulled to raise the load 0.5 m ideally?

Visual reasoning — after your attempt

1 m: both supporting strands shorten by 0.5 m as the load rises. The force reduction trades for greater effort travel, leaving ideal work unchanged.

Two vertical rope segments supporting a 40 N load each carry 20 N in the ideal balanced model. Lifting the load 0.5 m requires taking in 1 m of rope. Count segments actually supporting the moving load, not every visible rope piece.

Pause and explain

Why does a two-supporting-segment pulley require more rope movement?

Check your reasoning after answering

Both supporting segments shorten when the load rises. The input rope must supply twice the load’s upward distance in the ideal arrangement.

Apply the whole unit · Choose a lifting method

Illustrative ideal choices for raising a 60 N load through 0.5 m: vertical lift; a frictionless 2 m ramp; a pulley with two vertical supporting rope segments. Ignore machine weight and friction.

Your task

Calculate input force and input distance for each method, compare input work, and explain a practical constraint that could favor one method. Sketch the ramp or pulley with labels.

What your response should show

  • Use the supplied observations and measurements accurately; include units where needed.
  • Explain the science behind your answer, rather than giving only a number or label.
  • Show a labeled model, calculation, or evidence comparison as requested.
  • State an assumption or limitation and suggest a useful next measurement.
Response guidance — after your attempt

Vertical:60 N over 0.5 m. Ramp:60×0.5/2=15 N over 2 m. Pulley:30 N over 1 m of input rope. Each ideal input is 30 J. Space, secure attachment, or friction may change the practical choice and real input. The smaller force does not reduce the ideal energy needed for the same height.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Use sketches and energy accounts before remembering machine formulas. Specify perpendicular lever arms and supporting pulley segments. The application is a design calculation, not a request to rig lifting equipment. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Simple machines trade force for distance or change force direction; they do not create energy.

Worked examples

Example 1

Two frictionless ramps reach the same 0.5 m platform. One is 1 m long and one is 2 m long. Which needs less force to raise the same load slowly?
  1. Both increase the load’s gravitational potential energy by the same amount.
  2. The 2 m ramp allows the force to act over twice the distance.
Answer: The 2 m ramp requires half the force; the ideal input work is the same.

Example 2 · Worked application

An ideal ramp raises a 100 N load by 1 m over a 5 m ramp. Compare the aligned pulling force with lifting directly.
  1. The needed gravitational-energy increase is 100×1=100 J.
  2. For a frictionless aligned pull over 5 m, F×5=100.
  3. F=20 N, but the pull acts over five times the distance.
Answer: 20 N on the ideal ramp versus 100 N for a direct slow lift.
Check the reasoning

Both ideal methods transfer 100 J; the ramp does not create energy.

Example 3

An ideal ramp raises a 60 N load by 0.5 m over a 3 m path. Find output work and ideal input force.
  1. Output work=60×0.5=30 J.
  2. Ideal input work is also 30 J; force=30/3=10 N.
Answer: 30 J of output work and 10 N ideal effort, ignoring friction.

Example 4 · Find and fix the mistake

Context: An ideal ramp raises a 100 N load by 1 m over a 5 m ramp. Compare the aligned pulling force with lifting directly. A student claims: “A machine reduces force, so it must also reduce ideal input work.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: Both ideal methods transfer 100 J; the ramp does not create energy.
  2. Ideal force reduction trades for increased distance. Real friction usually increases required input work.
Answer: Ideal force reduction trades for increased distance. Real friction usually increases required input work.
Check the reasoning

Both ideal methods transfer 100 J; the ramp does not create energy.

Example 5 · Interpret the visual model

A lever trades force against its distance from the pivotA lever trades force against its distance from the pivotEffort: 75 N downLoad on lever: 300 N downPivot support upArm: 4 m1 mTurning effects: 75×4 = 300×1. Forces shown act on the lever.
The ideal lever is balanced when the 75 N effort acts 4 m from the pivot and the 300 N load force acts 1 m from it. The turning effects match even though the forces differ. Both downward red arrows are forces on the lever; its upward force on the load is a different receiver’s force. Arrow lengths are qualitative here, while the arm distances and force labels supply the calculation.
Why can the smaller effort balance the larger load force? Would moving the effort closer to the pivot keep the same balance?
  1. Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
  2. The pivot is the turning point. A force’s perpendicular distance from it affects turning. The lever does not create energy; during a small movement the long effort end travels farther than the short load end.
  3. Its arm is four times as long: 75×4 = 300×1. Moving the effort closer reduces its turning effect, so a larger effort would be needed under the same ideal conditions.
Answer: Its arm is four times as long: 75×4 = 300×1. Moving the effort closer reduces its turning effect, so a larger effort would be needed under the same ideal conditions.
Check the reasoning

Keep the model’s stated limits explicit: The ideal lever is balanced when the 75 N effort acts 4 m from the pivot and the 300 N load force acts 1 m from it. The turning effects match even though the forces differ. Both downward red arrows are forces on the lever; its upward force on the load is a different receiver’s force. Arrow lengths are qualitative here, while the arm distances and force labels supply the calculation.

Avoid these mistakes

Check your understanding

An ideal ramp raises a 60 N load by 0.5 m over a 3 m path. Find output work and ideal input force.

Discuss the answer

30 J of output work and 10 N ideal effort, ignoring friction.

Why does a longer ramp reduce force without creating energy?

Discuss the answer

A machine can reduce the input force by increasing the input distance. An ideal ramp spreads the work of raising a load over a longer path. It does not reduce the required gain in gravitational potential energy. For a lever, turning effect depends on force and its perpendicular distance from the pivot. A long effort arm can balance a larger load on a short arm. For a pulley system, count the rope segments actually supporting the moving load; a fixed pulley may change direction without reducing effort.

Return to the phenomenon

Illustrative ideal ramps raise the same load by 0.5 m. Ramp A is 1 m long and B 2 m long; measured input forces are 20 and 10 N under the simplified no-loss model. Compare input work and explain the force–distance trade-off. State why actual friction would change the required input. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

Both have modeled input work 20 J: 20×1 and 10×2. The longer ramp reduces force while increasing travel distance for the same lift; it does not make energy. Actual friction can require greater input work and introduce thermal transfers. The simple along-ramp calculation uses the stated force direction and ideal model.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

Illustrative ideal ramps raise the same load by 0.5 m. Ramp A is 1 m long and B 2 m long; measured input forces are 20 and 10 N under the simplified no-loss model. Compare input work and explain the force–distance trade-off. State why actual friction would change the required input. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

  • Use two relevant stated records or conditions.
  • Explain the mechanism rather than only repeat a definition.
  • Label observation and inference.
  • Name a changed model feature or a remaining uncertainty.
Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

Both have modeled input work 20 J: 20×1 and 10×2. The longer ramp reduces force while increasing travel distance for the same lift; it does not make energy. Actual friction can require greater input work and introduce thermal transfers. The simple along-ramp calculation uses the stated force direction and ideal model.

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

Why are these ramps not a scale drawing? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

  • Answer the figure question with its stated labels.
  • Connect the visual representation to the scientific idea.
  • Identify a specific limitation from the caption.
  • Propose a useful change without misrepresenting supplied evidence.
Hint

The labeled lengths and forces, rather than the schematic slopes, define the ideal comparison. Both raise the same load by 0.5 m, with 20 J input work in this no-loss model. A longer path reduces required force but does not make energy; real friction changes the input.

Response guidance — discuss after your attempt

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning. The labeled lengths and forces, rather than the schematic slopes, define the ideal comparison. Both raise the same load by 0.5 m, with 20 J input work in this no-loss model. A longer path reduces required force but does not make energy; real friction changes the input.

Words to know

simple machine
A device that changes the size or direction of an applied force.
fulcrum
The pivot about which a lever turns.
ideal machine
A model with no dissipative energy losses.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Exit check

Why are these ramps not a scale drawing? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning. The labeled lengths and forces, rather than the schematic slopes, define the ideal comparison. Both raise the same load by 0.5 m, with 20 J input work in this no-loss model. A longer path reduces required force but does not make energy; real friction changes the input.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Mechanical Advantage

Learning goals

Readings for this unit

Before this unit

Divide output force by input force.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in mechanical advantage?

Illustrative evidence case. An illustrative ideal machine takes a 15 N input through 0.8 m and applies a 60 N output through 0.2 m.

A force gain accompanies a distance trade-offA force gain accompanies a distance trade-offInput15 N × 0.8 mWork: 12 JIdeal machineForce ratio: 4No energy lossesOutput60 N × 0.2 mWork: 12 JIllustrative model • use the labels and stated assumptions
The input and output labels show equal ideal work despite a fourfold output force. The output displacement is one quarter of the input displacement. Mechanical advantage compares forces; energy efficiency needs a complete energy or work account and real losses if present.

Notice and wonder

Does force ratio 4 mean energy efficiency 400%? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Compute mechanical advantage and both works. Explain how all results fit one energy account. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

input force
The force applied to a machine.
output force
The force the machine applies to a load.
mechanical advantage
Output force divided by input force.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

Mechanical advantage tells how a machine changes force: actual mechanical advantage = output force ÷ input force. A machine that supplies 60 N to a load when you apply 20 N has mechanical advantage 3. The ratio has no unit because both forces are measured in newtons.

Force advantage against distance costMechanical advantage is a ratio, not a savingForce advantageload ÷ efforthow much less force you pull withDistance costeffort distance ÷ load distancehow much further you pullIn an ideal machine these two numbers are equalHalving the force means pulling twice as far, so the energy transferred is unchanged
A machine that multiplies force by four requires moving the effort four times as far. Seeing the two ratios side by side is what prevents the idea that a machine supplies energy from somewhere.

For an ideal ramp, mechanical advantage equals ramp length divided by vertical rise. A ramp 2 m long reaching 0.5 m high has ideal mechanical advantage 4. In a real test, friction commonly increases the required input force, so actual mechanical advantage is less than the ideal value.

A force advantage is not an energy advantage. Record both force and travel distance when evaluating a machine. For a fair comparison, use the same load, lift to the same height, and move slowly at approximately constant speed. Repeat trials and state which losses the ideal model ignores.

Force advantage can coexist with energy lossesForce advantage can coexist with energy lossesMeasured effort: 30 N through 0.5 m → input work 15 JMeasured load force: 100 N through 0.1 m → useful work 10 JInput: 15 JUseful output: 10 JOther: 5 JMA ≈ 3.33, but efficiency ≈ 66.7%. Neither ratio is the other.
The supplied input is 30 N×0.5 m = 15 J; useful output is 100 N×0.1 m = 10 J. Actual mechanical advantage is 100/30 ≈ 3.33, while efficiency is 10/15 ≈ 66.7%. The remaining 5 J needs other energy changes or transfers in a complete account. The bars share an energy scale rather than a force scale.

Actual mechanical advantage compares measured load force with measured effort force. Ideal mechanical advantage comes from geometry, such as ramp length divided by height. The actual value can be smaller because friction uses some input work.

For an ideal machine, force advantage trades for distance. If output force is three times input force, the effort typically moves three times as far as the load. Check the appropriate geometry rather than assuming every machine has the same formula.

Report the mechanical advantage without units because both numerator and denominator are forces. Compare machines at a similar load and speed, and repeat measurements. A high advantage may be useful for heavy loads but require more space or a longer effort movement.

Build your understanding

Where this fits

This unit helps answer the chapter question: How can a machine make a task easier without creating energy? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Identify the two forces in a ratio

Actual mechanical advantage compares output force with input force: MA=output/input. The ratio has no unit when both forces use the same unit. A larger output force gives MA above one, but a useful machine can also have MA equal to or below one if it serves another purpose.

Force advantage against distance costMechanical advantage is a ratio, not a savingForce advantageload ÷ efforthow much less force you pull withDistance costeffort distance ÷ load distancehow much further you pullIn an ideal machine these two numbers are equalHalving the force means pulling twice as far, so the energy transferred is unchanged
A machine that multiplies force by four requires moving the effort four times as far. Seeing the two ratios side by side is what prevents the idea that a machine supplies energy from somewhere.

Read the visual model

Why does mechanical advantage have no unit?

Visual reasoning — after your attempt

It divides one force by another in the same units, so the force units cancel. It expresses a ratio, not a new force.

A measured output of 80 N from 20 N input gives MA=4. Reversing the division would give 0.25 and answer a different question. Label forces on a drawing before placing them in the ratio.

Pause and explain

Why does mechanical advantage have no unit?

Check your reasoning after answering

It divides one force by another in the same units, so the force units cancel. It expresses a ratio, not a new force.

Part 2 · Use distance to predict an ideal advantage

In an ideal machine with no energy loss, input work equals useful output work. For aligned constant forces, the ideal force ratio equals input distance divided by output distance. This distance ratio describes geometry; the actual measured force ratio can differ because of friction or other effects.

A force gain accompanies a distance trade-offA force gain accompanies a distance trade-offInput15 N × 0.8 mWork: 12 JIdeal machineForce ratio: 4No energy lossesOutput60 N × 0.2 mWork: 12 JIllustrative model • use the labels and stated assumptions
The input and output labels show equal ideal work despite a fourfold output force. The output displacement is one quarter of the input displacement. Mechanical advantage compares forces; energy efficiency needs a complete energy or work account and real losses if present.

Read the visual model

Why distinguish ideal and actual mechanical advantage?

Visual reasoning — after your attempt

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

If an input moves 1.2 m while the load rises 0.3 m, ideal MA=1.2/0.3=4. Measure force separately for actual MA. Do not label a geometric prediction as measured performance.

Pause and explain

Why distinguish ideal and actual mechanical advantage?

Check your reasoning after answering

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

Part 3 · Compare ratios under matching conditions

A fair machine comparison uses a stated load, motion condition, and geometry. Force during starting or acceleration may differ from force during steady lifting. Measurements should use comparable positions and repeated trials. A single peak force does not necessarily describe the entire movement.

A ratio and an absolute force answer different questionsA ratio and an absolute force answer different questionsMachine AEffort 25 N; output 100 NMA = 100/25 = 4Machine BEffort 40 N; output 120 NMA = 120/40 = 3A has greater force advantage; B supplies a greater absolute output force.Keep the test loads and task comparable before ranking performance.
In the supplied records, A multiplies effort force by four while B multiplies it by three. B’s output force is nonetheless larger because the input force also differs. The records distinguish ratio from total output and do not establish one machine as universally better. A fair test of the same task needs matched requirements and measurements of travel and energy.

Read the visual model

Actual mechanical advantage is measured output force divided by measured effort force. A high ratio cannot by itself establish high efficiency, faster work or suitability for a particular job.

Which has greater mechanical advantage, and which has larger output force in the supplied records?

Visual reasoning — after your attempt

A has MA 4, greater than B’s MA 3. B has output 120 N, larger than A’s 100 N. These are different comparisons.

A ramp requires different pulls when roughness or slope changes. Record whether values are average steady pulls or starting peaks. Comparing one peak with another machine’s steady value can hide the actual difference.

Pause and explain

What motion condition should be recorded with an input-force measurement?

Check your reasoning after answering

State whether the load is starting, accelerating, or moving steadily. These conditions affect the force and make comparisons meaningful.

Part 4 · Separate force advantage from energy efficiency

Mechanical advantage compares forces, while efficiency compares useful output energy with input energy. A machine can have high MA and still lose a substantial fraction of input energy because the input travels a long distance. You need distances or energy measurements to judge efficiency.

Force advantage can coexist with energy lossesForce advantage can coexist with energy lossesMeasured effort: 30 N through 0.5 m → input work 15 JMeasured load force: 100 N through 0.1 m → useful work 10 JInput: 15 JUseful output: 10 JOther: 5 JMA ≈ 3.33, but efficiency ≈ 66.7%. Neither ratio is the other.
The supplied input is 30 N×0.5 m = 15 J; useful output is 100 N×0.1 m = 10 J. Actual mechanical advantage is 100/30 ≈ 3.33, while efficiency is 10/15 ≈ 66.7%. The remaining 5 J needs other energy changes or transfers in a complete account. The bars share an energy scale rather than a force scale.

Read the visual model

Read numerator and denominator as quantities with units before forming a ratio. A machine’s force multiplication is paid for through travel and, in real operation, additional energy transfers; it is not an energy multiplier.

Why is multiplying 3.33 by 100% not a valid efficiency calculation?

Visual reasoning — after your attempt

3.33 compares forces, while efficiency compares useful output energy with input energy. The travel distances matter, giving 66.7%, not 333%.

An output of 80 N with input 20 N gives MA=4 regardless of distances. If the input moves 2 m and output 0.3 m, input work is 40 J and useful work 24 J. The force advantage alone does not reveal that energy difference.

Pause and explain

Does MA=4 mean efficiency is 400%?

Check your reasoning after answering

No. MA is a force ratio; efficiency is an energy ratio. Input and output distances also matter when calculating work.

Apply the whole unit · Distinguish geometric and measured advantage

Illustrative machine: input moves 1.5 m; load rises 0.3 m. Measured steady input force is 24 N and output load force is 96 N. Use aligned constant forces.

Your task

Calculate ideal MA, actual MA, input work, and useful output work. Explain why the two MA values differ and why a force ratio cannot by itself establish energy efficiency.

What your response should show

  • Use the supplied observations and measurements accurately; include units where needed.
  • Explain the science behind your answer, rather than giving only a number or label.
  • Show a labeled model, calculation, or evidence comparison as requested.
  • State an assumption or limitation and suggest a useful next measurement.
Response guidance — after your attempt

Ideal MA=1.5/0.3=5. Actual MA=96/24=4. Input work=36 J; useful output=28.8 J. The 7.2 J difference can be transferred to friction-related thermal stores or other effects. Force ratios and energy ratios answer different questions; efficiency here is 28.8/36=80% under the stated model.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Keep measured and model-derived columns distinct. Require output/input for force ratio and input/output for distance ratio. Check understanding using a direction-changing fixed pulley with ideal MA=1. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Mechanical advantage compares forces; energy accounting also requires distances.

Worked examples

Example 1

A machine exerts 80 N on a load while the input force is 20 N. Find its actual mechanical advantage.
  1. MA = output force ÷ input force.
  2. MA = 80 ÷ 20.
Answer: 4, with no unit

Example 2 · Worked application

A machine raises a 180 N load using 45 N input force. Find actual mechanical advantage.
  1. Mechanical advantage compares output force to input force.
  2. MA=180/45.
  3. The ratio has no units.
Answer: MA=4.
Check the reasoning

It describes force multiplication, not energy creation.

Example 3

A machine lifts a 120 N load with 40 N effort. Find actual mechanical advantage.
  1. Mechanical advantage=output force/input force.
  2. 120/40=3; the force units cancel.
Answer: Mechanical advantage is 3; this does not specify efficiency without distances.

Example 4 · Find and fix the mistake

Context: A machine raises a 180 N load using 45 N input force. Find actual mechanical advantage. A student claims: “A mechanical advantage of 4 means four times as much output energy as input energy.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: It describes force multiplication, not energy creation.
  2. The force ratio is 4. Output displacement is smaller in an ideal machine, and real energy losses lower efficiency.
Answer: The force ratio is 4. Output displacement is smaller in an ideal machine, and real energy losses lower efficiency.
Check the reasoning

It describes force multiplication, not energy creation.

Example 5 · Interpret the visual model

A ratio and an absolute force answer different questionsA ratio and an absolute force answer different questionsMachine AEffort 25 N; output 100 NMA = 100/25 = 4Machine BEffort 40 N; output 120 NMA = 120/40 = 3A has greater force advantage; B supplies a greater absolute output force.Keep the test loads and task comparable before ranking performance.
In the supplied records, A multiplies effort force by four while B multiplies it by three. B’s output force is nonetheless larger because the input force also differs. The records distinguish ratio from total output and do not establish one machine as universally better. A fair test of the same task needs matched requirements and measurements of travel and energy.
Which has greater mechanical advantage, and which has larger output force in the supplied records?
  1. Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
  2. Actual mechanical advantage is measured output force divided by measured effort force. A high ratio cannot by itself establish high efficiency, faster work or suitability for a particular job.
  3. A has MA 4, greater than B’s MA 3. B has output 120 N, larger than A’s 100 N. These are different comparisons.
Answer: A has MA 4, greater than B’s MA 3. B has output 120 N, larger than A’s 100 N. These are different comparisons.
Check the reasoning

Keep the model’s stated limits explicit: In the supplied records, A multiplies effort force by four while B multiplies it by three. B’s output force is nonetheless larger because the input force also differs. The records distinguish ratio from total output and do not establish one machine as universally better. A fair test of the same task needs matched requirements and measurements of travel and energy.

Avoid these mistakes

Check your understanding

A machine lifts a 120 N load with 40 N effort. Find actual mechanical advantage.

Discuss the answer

Mechanical advantage is 3; this does not specify efficiency without distances.

Why do effort and load travel distances matter when judging energy use?

Discuss the answer

Actual mechanical advantage compares measured load force with measured effort force. Ideal mechanical advantage comes from geometry, such as ramp length divided by height. The actual value can be smaller because friction uses some input work. For an ideal machine, force advantage trades for distance. If output force is three times input force, the effort typically moves three times as far as the load. Check the appropriate geometry rather than assuming every machine has the same formula.

Return to the phenomenon

An illustrative ideal machine takes a 15 N input through 0.8 m and applies a 60 N output through 0.2 m. Compute mechanical advantage and both works. Explain how all results fit one energy account. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

Mechanical advantage is 60/15=4. Input and output works are each 12 J. The fourfold force is paired with one-quarter the distance, so this ideal model conserves work. Real machines can have losses; a force ratio alone does not establish energy efficiency without displacement or other energy information.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

An illustrative ideal machine takes a 15 N input through 0.8 m and applies a 60 N output through 0.2 m. Compute mechanical advantage and both works. Explain how all results fit one energy account. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

  • Use two relevant stated records or conditions.
  • Explain the mechanism rather than only repeat a definition.
  • Label observation and inference.
  • Name a changed model feature or a remaining uncertainty.
Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

Mechanical advantage is 60/15=4. Input and output works are each 12 J. The fourfold force is paired with one-quarter the distance, so this ideal model conserves work. Real machines can have losses; a force ratio alone does not establish energy efficiency without displacement or other energy information.

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

Does force ratio 4 mean energy efficiency 400%? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

  • Answer the figure question with its stated labels.
  • Connect the visual representation to the scientific idea.
  • Identify a specific limitation from the caption.
  • Propose a useful change without misrepresenting supplied evidence.
Hint

The input and output labels show equal ideal work despite a fourfold output force. The output displacement is one quarter of the input displacement. Mechanical advantage compares forces; energy efficiency needs a complete energy or work account and real losses if present.

Response guidance — discuss after your attempt

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work. The input and output labels show equal ideal work despite a fourfold output force. The output displacement is one quarter of the input displacement. Mechanical advantage compares forces; energy efficiency needs a complete energy or work account and real losses if present.

Words to know

input force
The force applied to a machine.
output force
The force the machine applies to a load.
mechanical advantage
Output force divided by input force.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Exit check

Does force ratio 4 mean energy efficiency 400%? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work. The input and output labels show equal ideal work despite a fourfold output force. The output displacement is one quarter of the input displacement. Mechanical advantage compares forces; energy efficiency needs a complete energy or work account and real losses if present.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Efficiency & Improving a Design

Learning goals

Readings for this unit

Before this unit

Calculate a fraction as a percentage and distinguish useful output from input.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in efficiency & improving a design?

Illustrative evidence case. Illustrative machine A receives 250 J and delivers 150 J useful output; B receives 200 J and delivers 150 J. Their task and measurement boundary match.

Account for useful and other outputsAccount for useful and other outputsQuantity (J)Input energy250Useful output150Other pathways100Illustrative model • use the labels and stated assumptions
The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

Notice and wonder

What should change if the purpose is heating rather than lifting? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Compare efficiencies and account for each remaining energy amount. Explain why purpose matters to the useful fraction. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

efficiency
Useful output energy divided by input energy, often expressed as a percentage.
criterion
A feature used to judge how well a design meets its goal.
energy dissipation
Energy spreading into less useful forms, often thermal energy in the surroundings.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

Efficiency describes the fraction of input energy transferred to a useful output: efficiency = useful output energy ÷ input energy × 100%. Define what counts as useful before calculating. For a hoist, useful output may be the increase in the load’s gravitational potential energy.

Account for useful and other outputsAccount for useful and other outputsQuantity (J)Input energy250Useful output150Other pathways100Illustrative model • use the labels and stated assumptions
The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

If a machine receives 100 J and transfers 70 J to the intended output, its efficiency is 70%. The other 30 J has not disappeared. It has transferred to other parts of the system or surroundings, often as thermal energy and sound. Energy is conserved even when it becomes less useful for the task.

Engineers compare designs using criteria and constraints. Reducing rubbing friction can increase efficiency, but a low-friction design might cost more or be less durable. Test the same task with the same load and conditions. Compare repeated measurements and report uncertainty instead of treating one unusually good trial as proof.

Locate the other energy pathways before improving a deviceLocate the other energy pathways before improving a deviceInput: 100 JUseful job: 70 JThermal / sound: 30 JImprovement may redirect more of the input to the defined useful job.
A supplied 100 J input gives 70 J to the stated useful output and 30 J to other changes such as thermal motion and sound. The branch arrows show pathways qualitatively, not a calibrated Sankey width. Energy in the other branch is not destroyed; whether a pathway is useful depends on the actual job.

Efficiency is useful output energy divided by input energy, multiplied by 100%. First define the intended useful output. In a lamp it may be light; in a heater thermal energy is useful. The same energy form can count differently for different jobs.

An inefficient machine does not destroy energy. Friction can transfer energy to thermal motion and sound instead of the intended mechanical output. Include the surrounding air, supports and machine in the energy accounting.

Test a design change while keeping load, height and measurement method comparable. Lubrication, alignment or a smoother bearing may reduce unwanted transfer, but every change has costs and limits. Repeat the test and compare variation before deciding a small improvement is real.

Build your understanding

Where this fits

This unit helps answer the chapter question: How can a machine make a task easier without creating energy? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Define useful output for a specific job

Efficiency is useful output energy divided by total input energy, multiplied by 100%. Useful depends on the job: raising a load, lighting a space, or heating a room. Energy not counted as useful has not vanished; it may enter surroundings as thermal energy, sound, or another form.

Account for useful and other outputsAccount for useful and other outputsQuantity (J)Input energy250Useful output150Other pathways100Illustrative model • use the labels and stated assumptions
The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

Read the visual model

Why must the job be named before calculating efficiency?

Visual reasoning — after your attempt

The job determines which energy transfer or store counts as useful output. The same physical output can be useful for one task and unwanted for another.

For a lift supplied with 100 J that raises a load by 70 J of gravitational potential energy, efficiency is 70%. The remaining 30 J needs an energy destination. A different job, such as producing heat, would classify useful output differently.

Pause and explain

Why must the job be named before calculating efficiency?

Check your reasoning after answering

The job determines which energy transfer or store counts as useful output. The same physical output can be useful for one task and unwanted for another.

Part 2 · Check that numerator and denominator match

Input and output must cover the same time interval, system, and energy units. Dividing a force by an energy or comparing one minute of input with five minutes of output is not efficiency. For a simple lift with no release of stored energy, useful output cannot exceed total supplied input.

Where the input energy goesEfficiency is useful output over total inputenergy in — 100 Juseful output 65 Jwasted as heat and sound 35 J65 ÷ 100 = 65% efficient. The other 35 J went somewhere; it was not destroyed.
Efficiency is a ratio and both parts have to describe the same system over the same interval. The wasted fraction has not disappeared — naming where it went is what turns a percentage into something you can act on.

Read the visual model

What should you investigate after calculating efficiency above 100%?

Visual reasoning — after your attempt

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

An apparent 120% result calls for checking omitted inputs, released stored energy, units, and measurement methods. It does not justify a claim that the device creates energy. A charged spring or battery can contribute energy that a narrow input measurement missed.

Pause and explain

What should you investigate after calculating efficiency above 100%?

Check your reasoning after answering

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

Part 3 · Locate losses to improve a design

Identify where energy transfers away from the intended output. Friction, deformation, heating of components, and noise can matter in a mechanical device. A redesign should target a measured mechanism while respecting constraints such as stability and cost. Reducing one loss can introduce a new problem.

Locate the other energy pathways before improving a deviceLocate the other energy pathways before improving a deviceInput: 100 JUseful job: 70 JThermal / sound: 30 JImprovement may redirect more of the input to the defined useful job.
A supplied 100 J input gives 70 J to the stated useful output and 30 J to other changes such as thermal motion and sound. The branch arrows show pathways qualitatively, not a calibrated Sankey width. Energy in the other branch is not destroyed; whether a pathway is useful depends on the actual job.

Read the visual model

Useful is a design judgment about the intended result, not a different kind of physical energy. An improvement should name the unwanted mechanism it reduces and measure whether more energy reaches the intended output.

If the intended job is heating, must thermal output be counted as a loss? Explain why the job definition matters.

Visual reasoning — after your attempt

No. Thermal output can be the useful output for a heater. Define the job first, then classify each pathway for that job rather than always calling heat wasted.

A smoother ramp may reduce sliding resistance but also make an unattended load slip more easily. Compare useful lifting energy and total pull work under the same load and rise, then evaluate secure control as well as energy performance.

Pause and explain

Why is highest efficiency not the only design criterion?

Check your reasoning after answering

A design must also meet safety, reliability, cost, and other requirements. An efficiency improvement can create an unacceptable trade-off.

Part 4 · Use repeat trials rather than one favorable result

Measure the same task several times with a consistent procedure. Compare ranges and average values, and avoid excessive precision. If differences are small relative to variation, evidence may not support a clear winner. Explain uncertainty and a useful next test rather than reporting only the best trial.

Repeat a revised design before claiming an efficiency gainRepeat a revised design before claiming an efficiency gainEfficiency (%)55657585123456Trial numberOriginal: trials 1–3Revised: trials 4–6Same task and measurement method; example variation retained.
These illustrative efficiency results compare original trials 65, 68 and 67% with revised trials 73, 75 and 74% under matched task definitions. Each dot is a separate trial, not an assumed continuous time trend. Means are about 66.7% and 74.0%. The records support a gain in this test range while preserving measurement variation.

Read the visual model

A percentage-point difference compares two percentages by subtraction. A relative percent increase is a different ratio. Define which measure is requested and check that the same useful-output definition was used in every trial.

What is the mean gain in percentage points, and why should all dots remain visible?

Visual reasoning — after your attempt

The gain is about 74.0−66.7 = 7.3 percentage points. Keeping all trials shows variation and prevents a claim based on only the best revised result.

Design A has efficiencies 72%, 75%, and 73%; B has 73%, 74%, and 72%. The overlapping results are much less decisive than two carefully measured sets separated by a large difference. Repeat testing can resolve whether a consistent improvement exists.

Pause and explain

Why is comparing only each design’s best trial misleading?

Check your reasoning after answering

Best trials can reflect random variation or favorable conditions. Comparable repeated results provide a more representative performance comparison.

Apply the whole unit · Evaluate a lifting redesign

Illustrative repeated input energies: design A uses 40, 42, and 38 J; design B uses 34, 35, and 33 J. Every trial raises the same load by 30 J of gravitational potential energy. Both designs satisfy the stated stability test.

Your task

Calculate mean input energy and efficiency based on that mean for each design. Account for non-useful energy, recommend a design for the stated job, and propose a test for durability or another missing criterion.

What your response should show

  • Use the supplied observations and measurements accurately; include units where needed.
  • Explain the science behind your answer, rather than giving only a number or label.
  • Show a labeled model, calculation, or evidence comparison as requested.
  • State an assumption or limitation and suggest a useful next measurement.
Response guidance — after your attempt

Mean inputs are 40 J for A and 34 J for B. Mean-task efficiencies are 30/40=75% and 30/34≈88.2%. Non-useful differences are 10 J and 4 J per mean task, transferred to other stores or surroundings. B uses less input for this tested job. Repeated durability or load-range testing is needed before claiming it best in every circumstance.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Check that all energies describe the same lift. Permit sensible rounding and require an energy destination. Separate improved tested performance from a broad claim about all possible uses. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Efficiency is the useful share of input energy. Improving it means reducing unwanted transfers, not creating energy.

Worked examples

Example 1

A lift receives 200 J and raises a load’s potential energy by 150 J. Find efficiency and account for the remainder.
  1. Efficiency = 150 ÷ 200 × 100 = 75%.
  2. Energy transferred elsewhere = 200 − 150 = 50 J.
Answer: 75% efficient; 50 J is transferred to other forms or surroundings.

Example 2 · Worked application

A machine receives 250 J and delivers 175 J of useful lifting energy. Find efficiency and account for the rest.
  1. Efficiency=useful output/input×100%.
  2. 175/250×100%=70%.
  3. Remaining energy=250−175=75 J, transferred to nonuseful outputs such as thermal energy and sound.
Answer: 70% efficient; 75 J goes to other outputs.
Check the reasoning

Useful plus other outputs must total 250 J.

Example 3

A lift takes in 200 J and gives the load 150 J. Find efficiency and account for the remaining energy.
  1. Efficiency=(150/200)×100=75%.
  2. Remaining energy=200−150=50 J in other transfers such as thermal energy and sound.
Answer: 75% efficient; 50 J went to other parts of the system and surroundings.

Example 4 · Find and fix the mistake

Context: A machine receives 250 J and delivers 175 J of useful lifting energy. Find efficiency and account for the rest. A student claims: “Wasted energy vanishes from the universe.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: Useful plus other outputs must total 250 J.
  2. It remains conserved but transfers to forms or surroundings that do not serve the task.
Answer: It remains conserved but transfers to forms or surroundings that do not serve the task.
Check the reasoning

Useful plus other outputs must total 250 J.

Example 5 · Interpret the visual model

Locate the other energy pathways before improving a deviceLocate the other energy pathways before improving a deviceInput: 100 JUseful job: 70 JThermal / sound: 30 JImprovement may redirect more of the input to the defined useful job.
A supplied 100 J input gives 70 J to the stated useful output and 30 J to other changes such as thermal motion and sound. The branch arrows show pathways qualitatively, not a calibrated Sankey width. Energy in the other branch is not destroyed; whether a pathway is useful depends on the actual job.
If the intended job is heating, must thermal output be counted as a loss? Explain why the job definition matters.
  1. Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
  2. Useful is a design judgment about the intended result, not a different kind of physical energy. An improvement should name the unwanted mechanism it reduces and measure whether more energy reaches the intended output.
  3. No. Thermal output can be the useful output for a heater. Define the job first, then classify each pathway for that job rather than always calling heat wasted.
Answer: No. Thermal output can be the useful output for a heater. Define the job first, then classify each pathway for that job rather than always calling heat wasted.
Check the reasoning

Keep the model’s stated limits explicit: A supplied 100 J input gives 70 J to the stated useful output and 30 J to other changes such as thermal motion and sound. The branch arrows show pathways qualitatively, not a calibrated Sankey width. Energy in the other branch is not destroyed; whether a pathway is useful depends on the actual job.

Avoid these mistakes

Check your understanding

A lift takes in 200 J and gives the load 150 J. Find efficiency and account for the remaining energy.

Discuss the answer

75% efficient; 50 J went to other parts of the system and surroundings.

Why must useful output be defined before calculating efficiency?

Discuss the answer

Efficiency is useful output energy divided by input energy, multiplied by 100%. First define the intended useful output. In a lamp it may be light; in a heater thermal energy is useful. The same energy form can count differently for different jobs. An inefficient machine does not destroy energy. Friction can transfer energy to thermal motion and sound instead of the intended mechanical output. Include the surrounding air, supports and machine in the energy accounting.

Return to the phenomenon

Illustrative machine A receives 250 J and delivers 150 J useful output; B receives 200 J and delivers 150 J. Their task and measurement boundary match. Compare efficiencies and account for each remaining energy amount. Explain why purpose matters to the useful fraction. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

A is 60% efficient and B 75% for the stated task. The remaining modeled outputs are 100 J and 50 J in other pathways, such as thermal changes or sound. These amounts are not destroyed. An output called waste for lifting might be useful for heating, so usefulness must be defined before comparing fractions.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

Illustrative machine A receives 250 J and delivers 150 J useful output; B receives 200 J and delivers 150 J. Their task and measurement boundary match. Compare efficiencies and account for each remaining energy amount. Explain why purpose matters to the useful fraction. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

  • Use two relevant stated records or conditions.
  • Explain the mechanism rather than only repeat a definition.
  • Label observation and inference.
  • Name a changed model feature or a remaining uncertainty.
Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

A is 60% efficient and B 75% for the stated task. The remaining modeled outputs are 100 J and 50 J in other pathways, such as thermal changes or sound. These amounts are not destroyed. An output called waste for lifting might be useful for heating, so usefulness must be defined before comparing fractions.

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

What should change if the purpose is heating rather than lifting? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

  • Answer the figure question with its stated labels.
  • Connect the visual representation to the scientific idea.
  • Identify a specific limitation from the caption.
  • Propose a useful change without misrepresenting supplied evidence.
Hint

The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

Response guidance — discuss after your attempt

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task. The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

Words to know

efficiency
Useful output energy divided by input energy, often expressed as a percentage.
criterion
A feature used to judge how well a design meets its goal.
energy dissipation
Energy spreading into less useful forms, often thermal energy in the surroundings.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Exit check

What should change if the purpose is heating rather than lifting? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task. The illustrative outputs add to the 250 J input: 150 J useful for the chosen task and 100 J in other pathways. The useful fraction is 60%. The bar chart is an accounting model rather than a measured device trace; “other” must be investigated and is not energy destruction.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Power: The Rate of Energy Transfer

Learning goals

Readings for this unit

Before this unit

Review the earlier work and efficiency units. The visible language notes explain this unit’s quantities; then connect them to its concrete records and figure.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in power: the rate of energy transfer?

Illustrative evidence case. Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J.

The same useful energy at different ratesThe same useful energy at different ratesQuantity (W)A useful power30B useful power20Each delivers 240 J; A takes 8 s, B takes 12 s.Power = energy / time; efficiency needs input energy.Illustrative model • use the labels and stated assumptions
Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

Notice and wonder

If A receives 400 J and B 300 J, which is more efficient? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

power
Rate of energy transfer or work.
watt
Unit of power: one joule per second.
average power
Transferred energy divided by the stated elapsed time.
kilowatt
One thousand watts.
kilowatt-hour
Energy transferred by an average power of one kilowatt over one hour.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

Two devices can transfer the same amount of energy but take different amounts of time. Power describes this rate.

The same useful energy at different ratesThe same useful energy at different ratesQuantity (W)A useful power30B useful power20Each delivers 240 J; A takes 8 s, B takes 12 s.Power = energy / time; efficiency needs input energy.Illustrative model • use the labels and stated assumptions
Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

A watt, written W, is one joule per second; a joule, written J, is a unit of energy. Energy answers how much is transferred, while power answers how rapidly.

Same lifting work, different average powerSame lifting work, different average power3 m height gain4 kg object; g = 10 N/kg; ideal steady liftingWork = 4×10×3 = 120 J. If time = 2 s, average power = 60 W.Another device taking 6 s does the same 120 J at only 20 W.
The stated 4 kg object gains 3 m in height, receiving 120 J of gravitational energy in the ideal steady-lift model. Completing that lift in 2 s gives average useful power 60 W; taking 6 s gives 20 W. More power describes a faster energy transfer, not more energy required for the same ideal height change.

Do not confuse W for watts with W sometimes used as a work symbol; label quantities in words when unsure. Household electricity bills usually report energy in kilowatt-hours, not power alone.

Use supplied lifting and device records; there is no need to test a wall-powered appliance or lift a heavy load.

An observation is what a person or instrument records. An inference is a proposed interpretation of those records. Keep the two separate: a graph can show a pattern while more than one mechanism might explain it. State the chosen system, or part of the world being studied, and its boundary before accounting for material or energy transfers.

Use each figure as a reasoning tool. Read its caption and labels, describe the pattern, then explain a cause. If the picture is schematic, use the stated numbers rather than measuring its printed size. Check whether its simplified conditions match the problem before applying a formula.

Build your understanding

Where this fits

This unit helps answer the chapter question: How can a machine make a task easier without creating energy? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Build the rate from energy and time

Average power equals transferred energy divided by elapsed time. The result must include J/s or W. Average describes the whole stated interval; power at particular instants may vary. A value without the time interval cannot determine the average rate.

The same useful energy at different ratesThe same useful energy at different ratesQuantity (W)A useful power30B useful power20Each delivers 240 J; A takes 8 s, B takes 12 s.Power = energy / time; efficiency needs input energy.Illustrative model • use the labels and stated assumptions
Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

Read the visual model

Does the slower motor necessarily transfer less energy?

Visual reasoning — after your attempt

No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

A model motor transfers 120 J in 6 s, giving 20 J/s or 20 W. Another takes 12 s for the same transfer and averages 10 W. Both transfer 120 J; their rates differ.

Pause and explain

Does the slower motor necessarily transfer less energy?

Check your reasoning after answering

No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

Part 2 · Connect lifting work with power

For a constant upward force along the displacement, work equals force × distance. Calculate the work first, then divide by time. A longer lifting time reduces average useful power for the same load and height, without reducing the ideal work needed.

Same lifting work, different average powerSame lifting work, different average power3 m height gain4 kg object; g = 10 N/kg; ideal steady liftingWork = 4×10×3 = 120 J. If time = 2 s, average power = 60 W.Another device taking 6 s does the same 120 J at only 20 W.
The stated 4 kg object gains 3 m in height, receiving 120 J of gravitational energy in the ideal steady-lift model. Completing that lift in 2 s gives average useful power 60 W; taking 6 s gives 20 W. More power describes a faster energy transfer, not more energy required for the same ideal height change.

Read the visual model

A watt is one joule per second. Separate how much useful energy changes from how long the change takes. Do not infer efficiency from timing alone without measuring input energy as well.

If the lift takes 4 s instead, what are work and average useful power?

Visual reasoning — after your attempt

The ideal lifting work stays 120 J; average useful power is 120/4 = 30 W. Conditions and any additional acceleration or losses must be accounted for separately.

A supplied model lifts with 30 N through 2 m in 5 s. Useful work is 60 J and average useful power 12 W. This model does not include starting motion, frictional losses or a person’s metabolism.

Pause and explain

What information is missing to find input power?

Check your reasoning after answering

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

Part 3 · Distinguish power from efficiency

Efficiency is the fraction of input energy reaching the chosen useful output. Power and efficiency describe different things: a high-power device can have high or low efficiency. Compare input and output over the same interval and define usefulness.

Fast energy transfer and efficient transfer are differentFast energy transfer and efficient transfer are differentDevice A: input 100 JUseful 80 J in 4 s80% efficient; 20 W usefulDevice B: input 100 JUseful 60 J in 2 s60% efficient; 30 W usefulB has greater useful power; A has greater efficiency in these supplied tests.
The supplied A test gives useful average power 80/4 = 20 W and efficiency 80%. B gives 60/2 = 30 W and efficiency 60%. The larger power does not imply the larger fraction of input reaching the intended output. These different useful amounts also need consideration when comparing a fixed real task.

Read the visual model

Power divides an energy transfer by elapsed time. Efficiency divides useful output energy by input energy. Both require a clear job definition, but they answer different questions and cannot be ranked by one number alone.

Which device is more efficient, and which has greater useful average power? Explain both calculations.

Visual reasoning — after your attempt

A is more efficient: 80/100 = 80% versus 60%. B has greater useful power: 60/2 = 30 W versus 20 W.

A modeled device receives 100 J in 5 s and supplies 60 J of useful work. Input power is 20 W, useful power is 12 W and efficiency is 60%. The remaining 40 J is energy in other pathways, not destroyed energy.

Pause and explain

Does 60% efficiency mean the input power is 60 W?

Check your reasoning after answering

No. Efficiency is a ratio. The power also depends on the energy amount and time interval.

Part 4 · Interpret energy units in device comparisons

A kilowatt is 1,000 W. A kilowatt-hour is the energy transferred at 1 kW for one hour. It is not power per hour. Multiplying power by time gives energy when the average power is appropriate for the interval. Actual devices may cycle on and off.

A power rating becomes energy only after time is includedA power rating becomes energy only after time is includedEnergy transferred (kJ)0601201800123Operating time (min)Model constant 1 kW power: 60 kJ each minute; 1 kWh = 3600 kJ.
For the supplied constant 1 kW model, energy increases by 60 kJ each minute, reaching 180 kJ in 3 minutes. A kilowatt is 1000 W, while a kilowatt-hour is an energy unit: 1 kWh = 3.6 million J = 3600 kJ. A real device may cycle or change its power; a rated maximum should not be silently treated as a continuously measured draw.

Read the visual model

The slope of an energy–time graph gives power after units are converted consistently. Minutes on this axis require 60 s per minute. kW and kWh differ because one is a rate and the other includes duration.

How much energy would this ideal device transfer in 6 minutes, in kJ and kWh?

Visual reasoning — after your attempt

360 kJ, equivalent to 0.1 kWh. Six minutes is 0.1 hour, so 1 kW×0.1 h = 0.1 kWh.

A hypothetical 0.5 kW device operating at that average power for 2 h transfers 1 kWh, or 3.6 million J. This is an illustrative arithmetic case, not a current price or an actual appliance guarantee.

Pause and explain

Why can rated power alone fail to predict a daily energy bill?

Check your reasoning after answering

The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

Apply the whole unit · Equal energy at different rates

Illustrative case for analysis, not measurements collected by the learner. Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J.

Your task

Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient. Use the supplied conditions, show intermediate reasoning and distinguish the supported conclusion from a broader claim.

What your response should show

  • Use the specified quantities and units.
  • Explain an intermediate step or comparison.
  • Connect the pattern to the physical mechanism.
  • State an assumption or limitation.
Response guidance — after your attempt

  1. Use useful power = delivered energy / time: A is 240/8=30 W; B is 240/12=20 W.

  2. Use efficiency = useful output / input: A is 240/400=0.60 or 60%.

  3. For B, 240/300=0.80 or 80%; both comparisons use the same useful output definition.

  4. Conclude that A transfers useful energy faster while B directs a larger input fraction to it; power and efficiency differ.

Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Ask the learner to describe the phenomenon before naming a formula. Discuss each checkpoint after an attempt. Use the supplied records when equipment is unavailable and label them illustrative rather than actual measurements. The final explanation should identify a mechanism and a limit, with different defensible wording accepted. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy. Useful powers are 30 W for A and 20 W for B.

Worked examples

Example 1 · Build the first reasoning step

Does the slower motor necessarily transfer less energy?
  1. Identify what the question asks and what the stated observation establishes.
  2. No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.
Answer: No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

Example 2 · Equal energy at different rates

Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J. Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient.
  1. Use useful power = delivered energy / time: A is 240/8=30 W; B is 240/12=20 W.
  2. Use efficiency = useful output / input: A is 240/400=0.60 or 60%.
  3. For B, 240/300=0.80 or 80%; both comparisons use the same useful output definition.
  4. Conclude that A transfers useful energy faster while B directs a larger input fraction to it; power and efficiency differ.
Answer: Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.
Check the reasoning

Explain why each stated condition matters.

Example 3 · Transfer to a different condition

A 50 W model device operates steadily for 20 s. Find the transferred energy and identify an assumption.
  1. Identify the changed condition.
  2. Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.
Answer: Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.

Example 4 · Find and fix the mistake

A student claims: “Watts measure the total energy a device uses.” Evaluate the claim.
  1. Distinguish what is observed from what is inferred.
  2. Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy.
Answer: Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy.
Check the reasoning

Compare the claim with the stated observations and model assumptions.

Example 5 · Interpret the visual model

Same lifting work, different average powerSame lifting work, different average power3 m height gain4 kg object; g = 10 N/kg; ideal steady liftingWork = 4×10×3 = 120 J. If time = 2 s, average power = 60 W.Another device taking 6 s does the same 120 J at only 20 W.
The stated 4 kg object gains 3 m in height, receiving 120 J of gravitational energy in the ideal steady-lift model. Completing that lift in 2 s gives average useful power 60 W; taking 6 s gives 20 W. More power describes a faster energy transfer, not more energy required for the same ideal height change.
If the lift takes 4 s instead, what are work and average useful power?
  1. Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
  2. A watt is one joule per second. Separate how much useful energy changes from how long the change takes. Do not infer efficiency from timing alone without measuring input energy as well.
  3. The ideal lifting work stays 120 J; average useful power is 120/4 = 30 W. Conditions and any additional acceleration or losses must be accounted for separately.
Answer: The ideal lifting work stays 120 J; average useful power is 120/4 = 30 W. Conditions and any additional acceleration or losses must be accounted for separately.
Check the reasoning

Keep the model’s stated limits explicit: The stated 4 kg object gains 3 m in height, receiving 120 J of gravitational energy in the ideal steady-lift model. Completing that lift in 2 s gives average useful power 60 W; taking 6 s gives 20 W. More power describes a faster energy transfer, not more energy required for the same ideal height change.

Avoid these mistakes

Check your understanding

Does the slower motor necessarily transfer less energy?

Discuss the answer

No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

What information is missing to find input power?

Discuss the answer

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

Does 60% efficiency mean the input power is 60 W?

Discuss the answer

No. Efficiency is a ratio. The power also depends on the energy amount and time interval.

Why can rated power alone fail to predict a daily energy bill?

Discuss the answer

The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

Return to the phenomenon

Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J. Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J. Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

  • Use two relevant stated records or conditions.
  • Explain the mechanism rather than only repeat a definition.
  • Label observation and inference.
  • Name a changed model feature or a remaining uncertainty.
Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

If A receives 400 J and B 300 J, which is more efficient? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

  • Answer the figure question with its stated labels.
  • Connect the visual representation to the scientific idea.
  • Identify a specific limitation from the caption.
  • Propose a useful change without misrepresenting supplied evidence.
Hint

Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

Response guidance — discuss after your attempt

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison. Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

Words to know

power
Rate of energy transfer or work.
watt
Unit of power: one joule per second.
average power
Transferred energy divided by the stated elapsed time.
kilowatt
One thousand watts.
kilowatt-hour
Energy transferred by an average power of one kilowatt over one hour.
model
A representation that explains selected features and makes predictions; it leaves other details out.
evidence
Relevant observations or records used to support or challenge a claim.
system boundary
The chosen limit separating the objects being studied from their surroundings.
assumption
A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J.

Exit check

If A receives 400 J and B 300 J, which is more efficient? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison. Both devices deliver 240 J, but the different times produce 30 W and 20 W useful power. The bars show rates, not different total delivered energies. Input energy must also be supplied to compare efficiencies; faster transfer alone does not imply a larger useful fraction.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Problem 1

Which condition is needed for simply using W=Fd?
Answer and explanation

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 2

Would the same horizontal displacement give work by a vertical force?
Answer and explanation

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work.

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 3

Visual-model chapter review: A box moves 4 m right under a constant 12 N rightward push and 3 N leftward resistance. Find each work contribution and net work.
Answer and explanation

Push +48 J; resistance −12 J; net +36 J in the stated aligned-force comparison.

Multiply each force by the common displacement and include direction.

Add the work contributions rather than adding force and energy units.

Push +48 J; resistance −12 J; net +36 J in the stated aligned-force comparison.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 4

Why can pushing farther from the pivot reduce the needed force?
Answer and explanation

A larger perpendicular distance gives a larger turning effect for the same force. A smaller force can then balance the same load turning effect.

A larger perpendicular distance gives a larger turning effect for the same force. A smaller force can then balance the same load turning effect.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 5

Why are these ramps not a scale drawing?
Answer and explanation

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning.

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 6

Visual-model chapter review: For an ideal balanced lever, the load exerts 180 N at an arm 0.2 m long. The effort arm is 0.6 m. Find the effort force and explain its distance tradeoff.
Answer and explanation

Effort is 180×0.2/0.6 = 60 N. The effort end travels about three times the load-end distance for the small-motion ideal comparison; the lever does not create energy.

Match turning effects F×arm on opposite sides.

Connect the 3:1 arm ratio to effort travel as well as force.

Effort is 180×0.2/0.6 = 60 N. The effort end travels about three times the load-end distance for the small-motion ideal comparison; the lever does not create energy.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 7

Why distinguish ideal and actual mechanical advantage?
Answer and explanation

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 8

Does force ratio 4 mean energy efficiency 400%?
Answer and explanation

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work.

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 9

Visual-model chapter review: A measured machine uses effort 20 N through 0.9 m to lift a 60 N load by 0.2 m. Find actual mechanical advantage and useful efficiency.
Answer and explanation

MA = 60/20 = 3. Input work 18 J; useful output 12 J; efficiency = 12/18×100 ≈ 66.7%.

Keep force ratio separate from work ratio.

Include both travel distances in the energy account.

MA = 60/20 = 3. Input work 18 J; useful output 12 J; efficiency = 12/18×100 ≈ 66.7%.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 10

What should you investigate after calculating efficiency above 100%?
Answer and explanation

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 11

What should change if the purpose is heating rather than lifting?
Answer and explanation

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task.

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 12

Visual-model chapter review: A device receives 240 J, delivering 150 J to its defined useful output and 90 J to other changes. Find efficiency and explain what is wrong with calling the 90 J destroyed.
Answer and explanation

Efficiency = 150/240×100 = 62.5%. The other 90 J remains in other stores/transfers included in a complete account; usefulness is a job definition, not conservation.

Divide useful output by total input.

Account for every supplied contribution with the same energy units.

Efficiency = 150/240×100 = 62.5%. The other 90 J remains in other stores/transfers included in a complete account; usefulness is a job definition, not conservation.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 13

What information is missing to find input power?
Answer and explanation

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 14

If A receives 400 J and B 300 J, which is more efficient?
Answer and explanation

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison.

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 15

Visual-model chapter review: A device transfers a useful 180 J in 3 s while receiving 240 J in that interval. Find useful average power and efficiency, then explain which changes if the same energy transfers take 6 s.
Answer and explanation

Useful power is 60 W and efficiency 75%. Taking 6 s reduces useful power to 30 W while the same energy ratio stays 75%.

Use energy/time for power and useful/input for efficiency.

Change only the interval in the second comparison.

Useful power is 60 W and efficiency 75%. Taking 6 s reduces useful power to 30 W while the same energy ratio stays 75%.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

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