Energy, work and power — final check key

1. EK1 · Final check

Model answer. (a) The raised hammer has energy in its gravitational potential store, the plutonium in its nuclear store and the hot bath water in its internal (thermal) store. (b) Energy is transferred by a force doing work (mechanical work done), by an electric current (electrical work done), by heating, and by waves: electromagnetic waves such as light, sound waves and other waves. (c) Energy cannot be created or destroyed. It can only be transferred from one store to another, so the total amount of energy stays the same. (d) The current from the mains does electrical work and transfers energy to the fan’s motor, which turns the blades: the force of the motor does work on them and fills their kinetic store. Some of the energy heats the motor and the air, and some leaves as sound.

A full answer includes

• (a) I wrote gravitational potential for the raised hammer.
• (a) I wrote nuclear for the plutonium.
• (a) I wrote internal (thermal) for the hot water.
• (b) I wrote a force doing work (mechanical work).
• (b) I wrote an electric current (electrical work).
• (b) I wrote heating.
• (b) I wrote waves: electromagnetic, sound or other waves.
• (c) I wrote that energy cannot be created or destroyed.
• (c) I wrote that the total amount of energy stays the same.
• (c) I did not write that energy is used up.
• (d) I wrote that the current does electrical work on the fan’s motor.
• (d) I wrote that the motor does work on the blades, filling their kinetic store.
• (d) I wrote that some energy heats the motor and the air.
• (d) I wrote that some energy leaves as sound.

Also accept

• (a) gravitational potential; nuclear; internal (thermal) (b) force doing work; electric current; heating; waves (c) energy not created or destroyed; total stays the same (d) electrical work → motor → kinetic store of the blades, plus heating and sound

Watch for

• “Energy is used up when a fan runs.” — It is transferred to the kinetic store of the blades and the air, and to the internal store of the surroundings. None is used up.
• “Plutonium is a fuel, so its energy is chemical.” — Plutonium is not burned. Its energy is in the nuclei of its atoms, in its nuclear store.

2. EK2 · Final check

Model answer. (a) At the panel, energy in = energy out: 500 J − 400 J = 100 J leaves by electrical work. (b) Along the wires 10 J is wasted, so 100 J − 10 J = 90 J reaches the lamp. The lamp gives out 18 J of light, so 90 J − 18 J = 72 J heats the lamp and the air.

Checked automatically

• (a) Energy leaving the panel by electrical work: 100 J (exact value)
  • Common wrong answer 900 : Subtract the 400 J heating the panel from the 500 J of light.
• (b) Energy heating the lamp and the air: 72 J (exact value)
  • Common wrong answer 82 : The 10 J heating the wires never reaches the lamp: start from 90 J.
  • Common wrong answer 482 : Start from the energy that reaches the lamp, 90 J, not the 500 J of light.

A full answer includes

• (a) Method: I took the 400 J heating the panel away from the 500 J of light.
• (a) Answer: I wrote 100 J.
• (b) Method: I took the 10 J heating the wires from 100 J, so 90 J reaches the lamp.
• (b) Method: I took the 18 J of light from the 90 J.
• (b) Answer: I wrote 72 J.
• (b) I did not start the lamp’s energy from 100 J or from 500 J.

Also accept

• (a) 100 J (b) 72 J

Watch for

• “The lamp starts with the 500 J from the Sun.” — Each stage only passes on what is left after the stage before it: the lamp gets 90 J.

3. EK3 · Final check

Model answer. (a) W = F d = 6000 N × 2.0 m = 12 000 J. (b) The power supplied is the energy transferred per unit time: P = ΔE / t = 20 000 J ÷ 4.0 s = 5000 W (5.0 kW). The work on the crate is done at only 12 000 J ÷ 4.0 s = 3000 W; the rest of the battery’s energy heats the motor and its surroundings. (c) Power is the work done per unit time, or the energy transferred per unit time.

Checked automatically

• (a) Work done: 12000 J (within ±1%)
  • Common wrong answer 3000 : Multiply the weight by the height.
• (b) Power supplied by the battery: 5000 W (within ±1%)
  • Common wrong answer 3000 : That is the rate of work on the crate. Use the 20 000 J the battery transferred.
  • Common wrong answer 80000 : Divide the energy by the time, do not multiply.

A full answer includes

• (a) Method: I multiplied 6000 N by 2.0 m.
• (a) Answer: I wrote 12 000 J.
• (b) Method: I divided the energy transferred, 20 000 J, by 4.0 s.
• (b) Answer: I wrote 5000 W.
• (b) I did not use the 12 000 J of work on the crate.
• (c) I wrote that power is the work done per unit time, or the energy transferred per unit time.
• (c) I did not leave out “per unit time”.

Also accept

• (a) 12 000 J (b) 5000 W (c) power is the work done, or the energy transferred, per unit time

Watch for

• “Work done = force ÷ distance.” — Work done is force multiplied by the distance moved in the direction of the force.
• “The power supplied is the work on the crate divided by the time.” — The question asks for the power supplied by the battery, so use the energy the battery transferred, 20 000 J. Some of it does not reach the crate.

4. EK4 · Final check

Model answer. (a) Ek = ½ m v² = ½ × 0.20 kg × (8.0 m/s)² = 6.4 J. (b) At the top all of this is in the gravitational potential store: m g Δh = 6.4 J, so Δh = 6.4 J ÷ (0.20 kg × 9.8 N/kg) = 3.27 m, which is 3.3 m to 2 significant figures.

Checked automatically

• (a) Kinetic energy: 6.4 J (within ±0.05 J)
  • Common wrong answer 0.8 : Square the speed: 8.0² = 64.
  • Common wrong answer 12.8 : Remember the ½.
• (b) Greatest height, to 2 significant figures: 3.3 m (2 significant figures)
  • Common wrong answer 32 : Divide by m × g = 0.20 × 9.8 = 1.96 N, not by 0.20 alone.
  • Common wrong answer 0.33 : Divide 6.4 J by 1.96 N.

A full answer includes

• (a) Method: I calculated ½ × 0.20 kg × (8.0 m/s)².
• (a) Answer: I wrote 6.4 J.
• (b) Method: I set m g Δh equal to 6.4 J.
• (b) Method: I divided 6.4 J by 0.20 kg × 9.8 N/kg = 1.96 N.
• (b) Answer: I wrote 3.3 m, to 2 significant figures.
• (b) I did not divide 6.4 J by 0.20 kg alone.

Also accept

• (a) 6.4 J (b) 3.3 m

Watch for

• “The ball keeps some kinetic energy at the top.” — At its highest point the ball stops for an instant, so all its kinetic energy has gone to its gravitational potential store.