Work, Power & Energy Calculations

IGCSE Edexcel Physics
4.11–4.17 Work done, power, GPE and KE
Key Concepts: Work done: $W = Fd$ (joules). Power: $P = W/t$ (watts). Gravitational PE: $E_{gpe} = mgh$. Kinetic energy: $E_k = \tfrac{1}{2}mv^2$. When an object falls freely: $\Delta E_{gpe} = \Delta E_k$ (no friction).

Section A — Work Done

1. Define work done and write its equation. State the conditions required for work to be done. [3]
2. A force of 40 N moves a box 5 m. Calculate the work done. [2]
3. A car exerts a driving force of 800 N over a distance of 1.5 km. Calculate the work done. [2]
4. A student pushes a trolley with 60 N of force and does 1800 J of work. How far does the trolley move? [2]

Section B — Power

5. Define power and write its equation, including units. [2]
6. A motor does 500 J of work in 25 s. Calculate the power. [2]
7. A crane lifts a load of 5000 N through 8 m in 10 s. Calculate the power. [3]

Section C — Gravitational Potential Energy

8. Write the equation for gravitational potential energy, defining all symbols. [2]
9. A 2 kg book is placed on a shelf 1.5 m above the floor. Calculate its gravitational PE. ($g = 9.8\,\text{N/kg}$) [2]
10. A 60 kg person climbs 12 m up a ladder. Calculate the increase in GPE. [2]

Section D — Kinetic Energy

11. Write the equation for kinetic energy, defining all symbols. [2]
12. A 3 kg object moves at $4\,\text{m/s}$. Calculate its kinetic energy. [2]
13. A 1200 kg car travels at $20\,\text{m/s}$. Calculate its kinetic energy. [2]
14. A ball of mass 0.5 kg is dropped from a height of 5 m. Assuming no air resistance, calculate its speed just before it hits the ground. ($g = 9.8\,\text{N/kg}$) [4]

Total marks: 32

Mark Scheme

1. Work done is the energy transferred when a force moves an object [1]; $W = Fd$ [1]; work is done only when there is a force AND movement in the direction of the force [1] [3]
2. $W = Fd = 40 \times 5 = 200\,\text{J}$ [2]
3. $d = 1.5\,\text{km} = 1500\,\text{m}$ [1]; $W = 800 \times 1500 = 1\,200\,000\,\text{J}$ (1.2 MJ) [1] [2]
4. $d = W/F = 1800/60 = 30\,\text{m}$ [2]
5. Power is the rate of doing work / rate of energy transfer [1]; $P = W/t$; unit: watt (W) [1] [2]
6. $P = W/t = 500/25 = 20\,\text{W}$ [2]
7. $W = Fd = 5000 \times 8 = 40\,000\,\text{J}$ [1]; $P = W/t = 40\,000/10 = 4000\,\text{W}$ (4 kW) [2] [3]
8. $E_{gpe} = mgh$ [1]; $m$ = mass (kg), $g$ = gravitational field strength (N/kg), $h$ = height (m) [1] [2]
9. $E_{gpe} = mgh = 2 \times 9.8 \times 1.5 = 29.4\,\text{J}$ [2]
10. $E_{gpe} = 60 \times 9.8 \times 12 = 7056\,\text{J}$ [2]
11. $E_k = \tfrac{1}{2}mv^2$ [1]; $m$ = mass (kg), $v$ = speed (m/s) [1] [2]
12. $E_k = 0.5 \times 3 \times 16 = 24\,\text{J}$ [2]
13. $E_k = 0.5 \times 1200 \times 400 = 240\,000\,\text{J}$ (240 kJ) [2]
14. $E_{gpe} = mgh = 0.5 \times 9.8 \times 5 = 24.5\,\text{J}$ [1]; set equal to $E_k$: $\tfrac{1}{2}mv^2 = 24.5$ [1]; $v^2 = 24.5 \times 2/0.5 = 98$ [1]; $v = \sqrt{98} \approx 9.9\,\text{m/s}$ [1] [4]