Efficiency & Improving a Design — Print · Grade 8 Science
Chapter: Work & MachinesEfficiency & Improving a Design
Learning goals
- I can calculate efficiency using useful output energy and input energy.
- I can evaluate a design improvement using measurements and a stated criterion.
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.
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.
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.
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.
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.
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.
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.
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
- OpenSciEd 8.1 Contact Forces — public unit overview
- OpenSciEd instructional model — storyline routines
- Creative Commons Attribution 4.0 — middle-school material license
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
- Efficiency = 150 ÷ 200 × 100 = 75%.
- Energy transferred elsewhere = 200 − 150 = 50 J.
Example 2 · Worked application
- Efficiency=useful output/input×100%.
- 175/250×100%=70%.
- Remaining energy=250−175=75 J, transferred to nonuseful outputs such as thermal energy and sound.
Useful plus other outputs must total 250 J.
Example 3
- Efficiency=(150/200)×100=75%.
- Remaining energy=200−150=50 J in other transfers such as thermal energy and sound.
Example 4 · Find and fix the mistake
- Test the claim against the stated conditions: Useful plus other outputs must total 250 J.
- It remains conserved but transfers to forms or surroundings that do not serve the task.
Useful plus other outputs must total 250 J.
Example 5 · Interpret the visual model
- Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
- 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.
- 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.
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
- A 70% efficient machine loses usefulness, not total energy.
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
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
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.
Problem 1
Answer and explanation
75 %
60 ÷ 80 × 100 = 75.
Problem 2
Answer and explanation
30 J
120 − 90 = 30.
Problem 3
Answer and explanation
All input energy is accounted for, including thermal energy and other outputs that are not useful for the task.
Problem 4
Answer and explanation
75% efficient; 50 J went to other parts of the system and surroundings.
Efficiency=(150/200)×100=75%.
Remaining energy=200−150=50 J in other transfers such as thermal energy and sound.
Response criteria
- Use the stated conditions.
- Show the evidence or calculation.
- Explain the conclusion and any stated limitation.
Problem 5
Hints
Divide the useful 300 J by the supplied 400 J, then multiply by 100%. Account for the remaining 100 J separately.
Answer and explanation
300/400×100%=75%.
Problem 6
Hints
State what the supplied observations or conditions establish, and separate that from any assumption.
Answer and explanation
The 120% result indicates an omitted energy source, incorrect boundary or measurement/calculation error; a complete account cannot produce energy from nothing.
Problem 7
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 8
Answer and explanation
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.
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.
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
Answer and explanation
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.
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.
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.
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
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.