Answers · Energy, work and power

Energy stores and transfers — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. EQ1 · Practice

Model answer. Rubbing moves charge between the cloth and the ruler, so the ruler becomes charged. A charged object has energy in its electrostatic store: it attracts or repels other charges, and here it pulls the light bits of paper up. The ruler is held still, so it has no kinetic energy, and it has cooled to the temperature of the room, so its internal store has not gained energy either.

A full answer includes

I chose electrostatic.
I did not choose kinetic: the ruler is held still, and only the bits of paper move.

Also accept

electrostatic

Watch for

“Kinetic, because the bits of paper move.” — Kinetic energy belongs to moving objects. The ruler is held still; the paper only starts to move because the ruler pulls on it.
“Chemical, because plastic is a chemical.” — The chemical store is energy released by chemical reactions, as in fuels, food and batteries. Rubbing does not change what the plastic is made of.
“Nuclear, because the energy is inside the atoms.” — The nuclear store is energy in the nuclei of atoms, released in nuclear reactions such as those in a power station. Rubbing a ruler does not change its nuclei.

2. EQ2 · Practice

Options as numbered on the pupil sheet: 1 — Gravitational potential; 2 — Elastic (strain); 3 — Chemical; 4 — Electrostatic; 5 — Kinetic; 6 — Nuclear; 7 — Internal (thermal).

Model answer. The candle wax can burn, so it has energy in its chemical store. A bicycle that is rolling has energy in its kinetic store. A hot iron has a lot of energy in its internal (thermal) store, in its fast-vibrating particles. A flowerpot on a high ledge has energy in its gravitational potential store, because it could fall. Clothes charged in a tumble dryer have energy in their electrostatic store: their charges attract each other, so they cling together. A stretched bungee cord has energy in its elastic (strain) store. Radioactive americium has energy in its nuclear store, in the nuclei of its atoms.

A full answer includes

I matched the candle to chemical.
I matched the rolling bicycle to kinetic.
I matched the hot iron to internal (thermal).
I matched the flowerpot to gravitational potential.
I matched the clinging clothes to electrostatic.
I matched the bungee cord to elastic (strain).
I matched the americium to nuclear.
I did not match the americium to chemical: its energy is in the nuclei of its atoms.

Also accept

candle chemical; bicycle kinetic; iron internal (thermal); flowerpot gravitational potential; clothes electrostatic; bungee cord elastic (strain); americium nuclear

Watch for

“A hot iron has heat energy stored in it.” — Heating is a way energy is transferred. The energy kept in a hot object is in its internal (thermal) store.
“Americium is a chemical element, so its energy is chemical.” — Every substance is made of elements. Chemical energy is released when substances react, as when candle wax burns. Americium is radioactive: its energy is in the nuclei of its atoms, in its nuclear store.

3. EQ3 · Practice

Model answer. (a) As she rolls down she gets lower, so energy leaves her gravitational potential store; she gets faster, so it goes to her kinetic store. (b) Rolling up the other side she slows down and gets higher: her kinetic store empties and her gravitational potential store fills. (c) Energy is not stored as “heat”. Friction has transferred some energy to the internal (thermal) store of the wheels, in their faster-vibrating particles. Heating is a way energy moves from a hotter object to a cooler one, not a place where it is kept.

A full answer includes

(a) I wrote gravitational potential.
(a) I did not name kinetic: that is the store that fills as she speeds up.
(b) I wrote that her kinetic store empties.
(b) I wrote that her gravitational potential store fills.
(c) I wrote that the energy in the warm wheels is in their internal (thermal) store.
(c) I wrote that heating is a way energy is transferred, not a store.

Also accept

(a) gravitational potential (b) kinetic empties; gravitational potential fills (c) the energy is in the wheels’ internal (thermal) store; heating is a transfer, not a store

Watch for

“As she rolls down, her kinetic store empties.” — She gets faster as she rolls down, so her kinetic store fills. It is her gravitational potential store that empties, because she gets lower.
“Heat is a store of energy.” — Heating is a way energy is transferred. The energy kept in a warm object is in its internal (thermal) store.

4. EQ4 · Practice

Options as numbered on the pupil sheet: 1 — Heating; 2 — Sound waves; 3 — Electromagnetic waves; 4 — A force doing work (mechanical work done); 5 — An electric current (electrical work done).

Model answer. The crane’s cable pulls the load upwards through a distance, so a force does mechanical work on it. The current in the toaster’s wires does electrical work, transferring energy from the mains; the hot wires then heat the bread. A hot radiator heats the cooler air in the room. Light from the lighthouse is an electromagnetic wave that carries energy across the sea to the ship. The sound of the drum is a wave in the air that carries energy to your ear.

A full answer includes

I matched the crane to a force doing work.
I matched the toaster’s current to electrical work.
I matched the radiator to heating.
I matched the lighthouse to electromagnetic waves.
I matched the drum to sound waves.
I did not match the toaster’s current to heating: the current does electrical work on the wires.

Also accept

crane force does work; toaster electrical work; radiator heating; lighthouse electromagnetic waves; drum sound waves

Watch for

“The lighthouse lamp is hot, so its light transfers energy by heating.” — Heating moves energy from a hotter object to the cooler things around it, as the radiator warms the air. The light crosses the sea as an electromagnetic wave.
“The current in a toaster transfers energy by heating.” — The current does electrical work on the toaster’s wires. The hot wires then heat the bread, but the current itself transfers energy by electrical work.

5. EQ5 · Practice

Model answer. Row C. The energy starts in the chemical store of the battery. The current does electrical work, transferring energy to the lamp. The lamp transfers energy away by light, which is an electromagnetic wave, and by heating the lamp and the air, so in the end the energy is in the internal store of the surroundings. Row A names an “electrical store”, which is not one of the seven stores; in row B the energy reaches the lamp by heating, but a current does electrical work; row D leaves out the heating, but a lit lamp gets warm.

A full answer includes

I chose row C.
I checked that the energy starts in the chemical store of the battery.
I checked that the current does electrical work on the lamp.
I checked that the lamp transfers energy by light and by heating.
I did not choose row A: “electrical” is a way of transferring energy, not a store.

Also accept

Watch for

“Row A.” — There is no electrical store. A battery keeps its energy in its chemical store; electrical work is how the current transfers it to the lamp.
“Row B.” — The battery does not heat the lamp. The current in the wires does electrical work, and that is how the energy reaches the lamp.
“Row D.” — A lamp that is switched on gets warm, so it also transfers energy by heating the lamp and the air, not by light only.

6. EQ6 · Practice

Model answer. (a) The current in the cable does electrical work: it transfers energy from the mains to the drill’s motor. (b) As the bit turns, friction acts between the bit and the wood, and the surfaces rub past each other through a distance, so the force of friction does mechanical work. This transfers energy to the internal (thermal) store of the bit and the wood, which get hotter. (c) The hot bit heats the cooler air around it. (d) The buzz is a sound wave: it carries energy through the air to the carpenter’s ears.

A full answer includes

(a) I wrote electrical work, done by the current.
(b) I wrote that friction acts between the turning bit and the wood.
(b) I wrote that this force does work, which transfers energy to their internal (thermal) store.
(b) I did not write that the current heats the bit.
(c) I wrote heating.
(d) I wrote sound waves.

Also accept

(a) electrical work (a current) (b) friction between the bit and the wood does work, transferring energy to their internal store (c) heating (d) sound waves

Watch for

“The current heats the drill bit.” — The current is in the cable and the motor, not in the bit. The bit gets hot because friction with the wood does work on it as it turns.
“The buzz reaches the carpenter by heating.” — Heating moves energy from a hotter object to a cooler one. The buzz is a sound wave that carries energy through the air.

7. EQ7 · Practice

Model answer. Energy cannot be created or destroyed, so the energy coming out of the lamp each second equals the energy going in: 60 J. Of that, 9 J leaves as light, so the rest heats the lamp and the air: 60 J − 9 J = 51 J.

Checked automatically

Energy heating the lamp and the air: 51 J (exact value)
- Common wrong answer 69 : You added. The energy out, 9 J plus the heating, must equal the 60 J in.
- Common wrong answer 9 : That is the light. Subtract it from the 60 J going in.

A full answer includes

Method: I took the light, 9 J, away from the 60 J going in.
Answer: I wrote 51 J.
I did not add the 9 J of light to the 60 J.

Also accept

51 J

Watch for

“The energy that is not light is used up.” — Energy is never used up. The 51 J that is not light heats the lamp and the air around it.

8. EQ8 · Practice

Model answer. At each swing, air resistance and the friction at the hooks act against the motion. They transfer energy to the internal (thermal) store of the air, the chains and the hooks. Less energy is left in the swing’s kinetic and gravitational potential stores, so it rises a little less high each time. No energy is destroyed: the total stays the same, but more of it is spread out in the surroundings.

A full answer includes

I chose: air resistance and friction transfer energy to the internal store of the surroundings.
I did not choose “destroy”: energy cannot be destroyed.

Also accept

air resistance and friction transfer energy to the internal store of the surroundings

Watch for

“Air resistance and friction destroy a little of the energy at every single swing.” — Energy can never be destroyed. Air resistance and friction transfer it to the internal store of the air, the chains and the hooks, where it is spread out.
“Air resistance and friction keep some of the energy as heat stored in the air.” — Heat is not a store. The energy goes to the internal (thermal) store of the air and the swing’s hooks and chains; heating is how it moves there.
“Air resistance and friction use up the force that the push gave to the swing.” — A push is a force; it is not kept inside the swing. The push transferred energy to the swing, and air resistance and friction transfer that energy to the surroundings.

9. EQ9 · Practice

Model answer. (a) At the top her energy is in her gravitational potential store. As she slides down, energy is transferred to her kinetic store. Along the sand, friction does work on her and transfers her energy to the internal (thermal) store of the child, the sand and the air, until she stops. (b) Energy cannot be created. She started with 900 J, so at the bottom of the slide the energy in her kinetic store can be 900 J at most; 1100 J would mean that 200 J had been created. (c) Only if no energy is transferred to the internal store of the child, the slide and the air on the way down: there must be no friction and no air resistance. Then all 900 J is in her kinetic store at the bottom.

A full answer includes

(a) I wrote gravitational potential store to kinetic store as she slides down.
(a) I wrote that friction on the sand transfers the energy to the internal (thermal) store of the child, the sand and the air.
(a) I did not write that her energy is used up when she stops.
(b) I wrote that energy cannot be created.
(b) I wrote that she cannot have more than the 900 J she started with.
(c) I wrote that there must be no friction and no air resistance on the way down.

Also accept

(a) gravitational potential → kinetic → internal (thermal) store of the child, the sand and the air (b) energy cannot be created: she can have at most 900 J (c) no friction and no air resistance on the way down

Watch for

“When she stops, her energy has been used up.” — Energy is never used up. Friction transfers it to the internal store of the child, the sand and the air, where it is spread out.
“She speeds up on the slide, so she can gain more energy than she started with.” — Speeding up moves energy from her gravitational potential store to her kinetic store. The total cannot grow: no energy is created.

10. EQ10 · Practice

Model answer. Diagram C. In a Sankey diagram drawn to scale, the width of each arrow stands for the energy it carries. Energy is conserved, so the arrows coming out must together be exactly as wide as the arrow going in. In C they are, and the wasted arrow is only about three tenths as wide as the arrow going in, so the motor wastes about 30 J of the 100 J: less than half. In A the wasted arrow is wider than the useful one, so that motor wastes more than half. In B the two arrows coming out are the same width, so that motor wastes exactly half, not less. In D the arrows coming out are together wider than the arrow going in: that motor would give out more energy than it is supplied with, which is impossible.

A full answer includes

I chose diagram C.
I checked that the useful and the wasted arrows together are as wide as the arrow going in.
I checked that the wasted arrow is less than half as wide as the arrow going in.
I did not choose diagram D: its two arrows coming out are together wider than the arrow going in.

Also accept

Watch for

“Diagram A.” — In A the wasted arrow is wider than the useful arrow: about two thirds as wide as the arrow going in. That motor wastes more than half of its energy.
“Diagram B.” — In B the useful and the wasted arrows are the same width, so that motor wastes exactly half of its energy, not less than half.
“Diagram D.” — In D the useful and the wasted arrows are together wider than the arrow going in. That motor would give out more energy than it is supplied with, but energy cannot be created.

11. EQ11 · Practice

Model answer. (a) Energy is conserved, so the energy going out adds up to the 100 J going in: 100 J − 25 J − 5 J = 70 J heats the engine and the air. (b) The arrow widths are drawn to scale: 100 J is 50 mm, so each joule is 0.5 mm wide. The heating arrow is 70 J × 0.5 mm per joule = 35 mm wide, the widest of the arrows coming out.

Checked automatically

(a) Energy heating the engine and the air: 70 J (exact value)
- Common wrong answer 75 : You took away only the 25 J. The 5 J of sound is wasted too, but it is not heating.
- Common wrong answer 130 : Subtract the useful and the sound energy from the 100 J, do not add them.
(b) Width of that arrow: 35 mm (within ±0.5 mm)
- Common wrong answer 70 : Each joule is 0.5 mm wide, not 1 mm: 50 mm stands for 100 J.

A full answer includes

(a) Method: I took the 25 J and the 5 J away from the 100 J.
(a) Answer: I wrote 70 J.
(b) Method: I found that 50 mm stands for 100 J, so each joule is 0.5 mm wide.
(b) Answer: I wrote 35 mm.
(b) I did not use 1 mm for each joule.

Also accept

(a) 70 J (b) 35 mm

Watch for

“The arrows in a Sankey diagram can be any width.” — The widths are drawn to scale, so the arrows coming out add up to the width of the arrow going in.

12. ET1 · Apply

Model answer. (a) As she speeds up, energy fills her kinetic store; it comes from the chemical store of her muscles. (b) The bent pole is like a bent spring: it has energy in its elastic (strain) store. (c) As the pole straightens, it pushes her upwards while she rises, so a force does mechanical work on her and energy is transferred to her gravitational potential store. (d) Energy cannot be created or destroyed. When the mat stops her, its squashing and the friction in it transfer her energy to the internal (thermal) store of the mat, her body and the air, and a little leaves as sound. The total amount of energy is the same as before; it is just spread out where it is no longer useful.

A full answer includes

(a) I wrote kinetic.
(b) I wrote elastic (strain).
(c) I wrote that the straightening pole pushes her upwards through a distance.
(c) I wrote that this force does work, transferring energy to her gravitational potential store.
(d) I wrote that energy cannot be destroyed, so the total stays the same.
(d) I wrote that the mat transfers her energy to the internal (thermal) store of the mat, her body and the air.
(d) I wrote that some energy leaves as sound.
(d) I did not write that her energy is used up or destroyed.

Also accept

(a) kinetic (b) elastic (strain) (c) a force does work: to gravitational potential (d) internal store of the mat, her body and the air, and sound; total the same

Watch for

“The mat absorbs her energy and destroys it.” — The mat transfers her energy to the internal store of the mat and the air. Energy is never destroyed.
“The bent pole has kinetic energy.” — The bent pole is held bent, ready to spring back, so its energy is in its elastic (strain) store.

13. ET2 · Apply

Model answer. (a) Energy is conserved at the power station: 100 J goes in and 60 J heats the surroundings, so 100 J − 60 J = 40 J leaves by electrical work in the cables. (b) Along the cables, 4 J heats the cables and 36 J reaches the kettle (40 J − 4 J = 36 J). In the kettle, 3 J heats the kettle and the air, so 36 J − 3 J = 33 J reaches the internal store of the water. (c) The wasted energy is 60 J + 4 J + 3 J = 67 J. Useful and wasted together: 33 J + 67 J = 100 J, the energy that went in, as the conservation of energy says.

Checked automatically

(a) Energy in the cables: 40 J (exact value)
- Common wrong answer 160 : Subtract the 60 J wasted at the power station from the 100 J going in.
(b) Supplement: Energy reaching the water: 33 J (exact value)
- Common wrong answer 39 : The 3 J heating the kettle is taken away, not added.
- Common wrong answer 36 : That is the energy reaching the kettle; 3 J of it heats the kettle and the air.
(c) Supplement: Total energy wasted: 67 J (exact value)
- Common wrong answer 60 : Add the waste at every stage: the cables and the kettle waste some too.

A full answer includes

(a) Method: I took the 60 J wasted at the power station from the 100 J.
(a) Answer: I wrote 40 J.
(b) Method: I took the 3 J heating the kettle from the 36 J that reaches it.
(b) Answer: I wrote 33 J.
(c) Method: I added the energy wasted at every stage: 60 J + 4 J + 3 J.
(c) Answer: I wrote 67 J.
(c) I checked that 33 J + 67 J = 100 J.
I did not start each stage again from 100 J.

Also accept

(a) 40 J (b) 33 J (c) 67 J

Watch for

“Each stage starts again with 100 J.” — Each stage starts with what the stage before it passed on: the cables get 40 J, not 100 J.