Work, Energy & Momentum — Chapter quiz · Physics & Environmental Science, Grade 12

Account for work, power, stored energy, collisions, and force-time evidence.

Problem 1

A 40 N force pushes a crate 3.0 m in the direction of the force. How much work is done?
Answer and explanation

120 J

W = Fd = 40 × 3.0 = 120 J.

Problem 2

A motor does 6,000 J of work in 4.0 s. Find its power output.
Answer and explanation

1500 W

P = W/t = 6,000 ÷ 4.0 = 1,500 W.

Problem 3

Find the kinetic energy of a 2.0 kg object moving at 6.0 m/s.
Answer and explanation

36 J

KE = ½mv² = ½ × 2.0 × 6.0² = ½ × 2.0 × 36 = 36 J.

Problem 4

Find the gravitational potential energy of a 3.0 kg object 4.0 m above the ground. (g = 9.8 m/s²)
Answer and explanation

117.6 J

PE = mgh = 3.0 × 9.8 × 4.0 = 117.6 J.

Problem 5

If an object's speed doubles while its mass stays the same, its kinetic energy…
  1. doubles
  2. halves
  3. quadruples
  4. stays the same
Answer and explanation

quadruples

Because KE = ½mv² depends on speed squared, doubling the speed multiplies KE by 2² = 4.

Problem 6

The work-energy theorem states that the net work done on an object equals its change in…
  1. momentum
  2. kinetic energy
  3. potential energy
  4. temperature
Answer and explanation

kinetic energy

The work-energy theorem is W_net = ΔKE: net work changes an object's kinetic energy.

Problem 7

A ball has 90 J of gravitational potential energy at the top of a frictionless track and 0 J of kinetic energy. What is its kinetic energy at the bottom?
Answer and explanation

90 J

With no friction, mechanical energy is conserved, so all 90 J of PE becomes kinetic energy at the bottom.

Problem 8

A machine takes in 400 J of energy and delivers 300 J of useful work. Find its efficiency.
Answer and explanation

75 %

Efficiency = (useful output ÷ input) × 100% = (300 ÷ 400) × 100% = 75%.

Problem 9

When a real machine's mechanical energy seems to disappear, that energy has most often become…
  1. extra kinetic energy
  2. extra potential energy
  3. brand-new matter
  4. thermal energy from friction
Answer and explanation

thermal energy from friction

Friction and drag dissipate mechanical energy mainly as thermal energy (and some sound); the total energy is still conserved.

Problem 10

Find the momentum of a 4.0 kg object moving at 5.0 m/s.
Answer and explanation

20 kg·m/s

p = mv = 4.0 × 5.0 = 20 kg·m/s.

Problem 11

A 2.0 kg cart moving at 6.0 m/s collides with and sticks to a 4.0 kg cart at rest. Find their common velocity afterward.
Answer and explanation

2 m/s

Conservation of momentum: 2.0 × 6.0 + 4.0 × 0 = (2.0 + 4.0)v′, so 12 = 6.0v′ and v′ = 2.0 m/s.

Problem 12

Explain the difference between an elastic and an inelastic collision in terms of what is conserved.
Answer and explanation

In both kinds of collision, momentum is conserved. The difference is kinetic energy: in an elastic collision kinetic energy is also conserved (the objects bounce apart with no energy lost), while in an inelastic collision some kinetic energy is converted into heat, sound, and deformation. In a perfectly inelastic collision the objects stick together and the greatest possible amount of kinetic energy is lost — but momentum is still conserved.

Problem 13

Explain the following claim and supply a valid example or counterexample: A force perpendicular to displacement does no mechanical work in the point-particle model.
Answer and explanation

W=30 J; P=W/t=15W, if that force is constant. A force perpendicular to displacement does no mechanical work in the point-particle model.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 14

Independent chapter check: A motor raises a 20 kg load by 3 m in 6 s at 70% efficiency. Find useful work, output power and input energy.
Answer and explanation

Useful work=mgh=588 J. Output power=98 W. Input energy=588/0.70=840 J; other transfers/storage total252 J under the stated boundary.

Useful work=mgh=588 J.

Output power=98 W.

Input energy=588/0.70=840 J; other transfers/storage total252 J under the stated boundary.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 15

Explain the following claim and supply a valid example or counterexample: Gravitational potential energy needs a chosen reference; negative values can be valid.
Answer and explanation

U=mgh=58.8 J; changing the reference shifts absolute U but not energy differences. Gravitational potential energy needs a chosen reference; negative values can be valid.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 16

Independent chapter check: A1.5 kg cart has speed4 m/s. It compresses a loss-free spring with k=600 N/m on a level track. Find initial K and maximum compression.
Answer and explanation

K=½×1.5×16=12 J. Set12=½×600x², giving x=0.20 m within the spring’s assumed elastic range.

K=½×1.5×16=12 J.

Set12=½×600x², giving x=0.20 m within the spring’s assumed elastic range.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 17

Explain the following claim and supply a valid example or counterexample: Mechanical energy can decrease while total energy remains conserved.
Answer and explanation

Energy transfers into thermal energy, deformation, or sound of the chosen larger system; account for boundaries. Mechanical energy can decrease while total energy remains conserved.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 18

Independent chapter check: A system begins with200 J mechanical energy. It ends with120 J mechanical,50 J thermal increase and20 J transferred outward as sound/heat. Find the unaccounted energy and a useful next check.
Answer and explanation

The accounted final/output total is190 J, leaving10 J. Check boundary heat transfer, deformation/storage and instrument uncertainty rather than claiming energy was destroyed.

The accounted final/output total is190 J, leaving10 J.

Check boundary heat transfer, deformation/storage and instrument uncertainty rather than claiming energy was destroyed.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 19

Explain the following claim and supply a valid example or counterexample: Momentum conservation does not automatically imply kinetic-energy conservation.
Answer and explanation

Initialp=6 kg·m/s, totalm=3 kg, so vf=2 m/s with negligible external impulse. Momentum conservation does not automatically imply kinetic-energy conservation.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 20

Independent chapter check: A3 kg cart at4 m/s sticks to a1 kg cart initially at rest. Neglect external impulse. Find final velocity and kinetic-energy decrease.
Answer and explanation

Initial momentum=12 kg·m/s, so vf=3 m/s. Ki=24 J and Kf=18 J;6 J leaves the kinetic category through other energy forms.

Initial momentum=12 kg·m/s, so vf=3 m/s.

Ki=24 J and Kf=18 J;6 J leaves the kinetic category through other energy forms.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 21

Impulse 4N·s over.20 s gives what average force?
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

20 N

4/.20=20.

Problem 22

Can momentum be conserved while kinetic energy decreases?
Answer and explanation

Yes, in an inelastic collision with negligible external impulse.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 23

Independent chapter check: A0.50 kg object slows from6 m/s to0 over0.15 s. Find impulse and average net force. If it rebounds at−2 m/s instead, find the new impulse.
Answer and explanation

Stopping impulse=0.50(0−6)=−3 N·s and Favg=−20 N. With rebound, impulse=0.50(−2−6)=−4 N·s, so the fixed-impulse comparison no longer applies.

Stopping impulse=0.50(0−6)=−3 N·s and Favg=−20 N.

With rebound, impulse=0.50(−2−6)=−4 N·s, so the fixed-impulse comparison no longer applies.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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