1.1 Energy stores and transfers — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

A pupil of mass 45 kg climbs to the top of a 6.0 m climbing wall. Take $g = 9.8\,\text{N/kg}$ . Calculate the energy gained by the gravitational potential store.
A ball of mass 0.25 kg is thrown at 12 m/s. Calculate the energy in its kinetic store.
A spring with spring constant 150 N/m is stretched by 0.12 m. Calculate the energy stored in the elastic potential store.
A 2.0 kg block of aluminium is heated from 15 °C to 65 °C. The specific heat capacity of aluminium is 900 J/kg°C. Calculate the energy transferred to the block.
A pump transfers 36000 J of energy in 20 s. Calculate its power.
A microwave oven has a power of 1200 W and runs for 90 s. Calculate the energy transferred.
A force of 180 N moves a trolley 4.5 m along the line of the force. Calculate the work done.
A car of mass 900 kg slows from 15 m/s to rest. Calculate the energy transferred to the thermal store of the brakes.
A kettle transfers $5.0 \times 10^5\,\text{J}$ of energy in 200 s. Calculate its power.
In the chapter problem, 30 kg of water falls 12 m to the wheel each second. Take $g = 9.8\,\text{N/kg}$ . Calculate the energy the water gives up from its gravitational potential store each second.
A cyclist freewheels down a hill and speeds up. Name the store that decreases and the store that increases.
A box is pushed across a rough floor and slows down until it stops. Describe the energy transfer, naming both stores.

Answers and concise solutions

1. Energy gained by the gravitational potential store

Answer: $E_p = mgh = 45 \times 9.8 \times 6.0 = 2646\,\text{J}$ , so $2600\,\text{J}$ to 2 significant figures.

2. Energy in the kinetic store

Answer: $E_k = \tfrac{1}{2}mv^2 = 0.5 \times 0.25 \times 12^2 = 18\,\text{J}$ .

3. Energy in the elastic potential store

Answer: $E_e = \tfrac{1}{2}ke^2 = 0.5 \times 150 \times 0.12^2 = 1.08\,\text{J}$ , so $1.1\,\text{J}$ to 2 significant figures.

4. Energy transferred to the block

Answer: $\Delta E = mc\Delta\theta = 2.0 \times 900 \times 50 = 90000\,\text{J}$ , so $9.0 \times 10^4\,\text{J}$ to 2 significant figures.

5. Power of the pump

Answer: $P = \dfrac{E}{t} = \dfrac{36000}{20} = 1800\,\text{W}$ . The trailing zeros in 1800 are not significant here: the answer is quoted to 2 significant figures.

6. Energy transferred by the microwave

Answer: $E = Pt = 1200 \times 90 = 108000\,\text{J}$ , so $1.1 \times 10^5\,\text{J}$ to 2 significant figures.

7. Work done on the trolley

Answer: $W = Fs = 180 \times 4.5 = 810\,\text{J}$ .

8. Energy transferred to the brakes

Answer: $E_k = \tfrac{1}{2}mv^2 = 0.5 \times 900 \times 15^2 = 101250\,\text{J}$ , so $1.0 \times 10^5\,\text{J}$ to 2 significant figures.

9. Power of the kettle

Answer: $P = \dfrac{E}{t} = \dfrac{500000}{200} = 2500\,\text{W}$ , quoted to 2 significant figures.

10. Energy given up each second

Answer: $E_p = mgh = 30 \times 9.8 \times 12 = 3528\,\text{J}$ each second, so $3500\,\text{J}$ to 2 significant figures.

11. The two stores that change

The gravitational potential store decreases, because the cyclist is lower down.
The kinetic store increases, because the cyclist speeds up.

12. The energy transfer

The kinetic store of the box decreases as the box slows.
Friction transfers energy to the thermal store of the floor and the box, which increases.