The problems are on the work and power worksheet. Try them on your own first, then compare with the answers below.
Quick answer: Work is the energy transferred when a force moves an object, found from W = F × d and measured in joules. These worked answers correct the 20 problems of the Physics 9-10 worksheet on work and power, from formulas and units to stair-climbing comparison: each solution shows the formula, the substitution and the final answer with its unit.
Each answer shows the equation, the substitution and the final result with its unit in bold. Use the working to find where a mistake started, not only to check the number. Where g is needed, the value 9.8 N/kg is used.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: HS-PS3-1
Problem 1 Formulas and units
1. W = F × d.2. P = E ÷ t.
3. 1 W = 1 J/s.
4. KE = ½ m v² and GPE = m g h.
Problem 2 Pushing a handcart
1. W = F × d.2. W = 220 × 35 = 7700 J.
Problem 3 Tractor and plough
1. d = W ÷ F.2. d = 4800 ÷ 600 = 8.0 m.
Problem 4 A motor at work
1. P = W ÷ t = 7500 ÷ 30 = 250 W.2. 250 J every second.
Problem 5 Unit conversions
1. 2.5 × 1000 = 2500 W.2. 450 × 1000 = 450 000 J.
3. 3 × 60 = 180 s.
4. E = P × t = 1500 × 240 = 360 000 J (360 kJ).
Problem 6 Is work being done?
1. No work. The upward force is at right angles to the horizontal movement.2. No work. The barbell does not move, so the distance is zero.
3. Yes. The lifting force acts in the direction of the movement, so the container gains potential energy.
Problem 7 Climbing the stairs
1. W = m g h = 52 × 9.8 × 3.6 = 1830 J (1834.6 J).2. P = W ÷ t = 1834.6 ÷ 8.0 = 229 W.
Problem 8 Cricket ball
1. KE = ½ × 0.16 × 30² = ½ × 0.16 × 900 = 72 J.Problem 9 Water on the roof
1. GPE = 800 × 9.8 × 12 = 94 080 J.2. 94.1 kJ.
Problem 10 Variable force
1. Rectangle: 40 × 2 = 80 J.2. Triangle: ½ × 4 × 40 = 80 J.
3. 80 + 80 = 160 J.
Problem 11 Doubling the speed
1. At 10 m/s: ½ × 1200 × 100 = 60 000 J. At 20 m/s: ½ × 1200 × 400 = 240 000 J.2. 240 000 ÷ 60 000 = 4.
Problem 12 Crane power
1. W = 500 × 9.8 × 18 = 88 200 J.2. P = 88 200 ÷ 25 = 3528 W = 3.5 kW.
Problem 13 Speed from energy
1. v² = 2 × KE ÷ m.2. v² = 2 × 20 ÷ 0.40 = 100, so v = 10 m/s.
Problem 14 Cement on a scaffold
1. h = GPE ÷ (m g).2. h = 147 ÷ (2.5 × 9.8) = 147 ÷ 24.5 = 6.0 m.
Problem 15 Cyclist braking
1. 18 ÷ 3.6 = 5.0 m/s.2. KE = ½ × 84 × 5.0² = 1050 J.
3. Work by brakes = KE, so F = 1050 ÷ 10 = 105 N.
Problem 16 Stopping a truck
1. KE = ½ × 8000 × 12² = 576 000 J.2. d = KE ÷ F = 576 000 ÷ 24 000 = 24 m.
3. KE = ½ × 8000 × 24² = 2 304 000 J; d = 2 304 000 ÷ 24 000 = 96 m.
4. Doubling the speed gives 4 × the kinetic energy. The same braking force must do 4 × the work, so the distance is 4 × larger.
Problem 17 Roller coaster
1. GPE = 400 × 9.8 × 25 = 98 000 J.2. GPE at B = 400 × 9.8 × 5.0 = 19 600 J, so KE = 98 000 − 19 600 = 78 400 J. v² = 2 × 78 400 ÷ 400 = 392, so v = 19.8 m/s.
3. At C all 98 000 J is kinetic: v² = 2 × 98 000 ÷ 400 = 490, so v = 22 m/s.
4. The energies double, but the speeds do not change, because the mass cancels in ½ m v² = m g h.
Problem 18 Farm pump
1. W = 1200 × 9.8 × 9.0 = 105 840 J.2. P = 105 840 ÷ 60 = 1764 W (about 1.8 kW).
3. 18 000 ÷ 1200 = 15 minutes.
Problem 19 Power and speed
1. P = W ÷ t = F d ÷ t, and d ÷ t = v, so P = F v.2. P = 25 × 8.0 = 200 W.
3. W = P t = 200 × 600 = 120 000 J.
4. P = 100 × 16 = 1600 W, which is 8 times more: twice the speed and four times the force.
Problem 20 Stair-climbing comparison
1. A: 45 × 9.8 × 4.0 = 1764 J; B: 60 × 9.8 × 4.0 = 2352 J; C: 50 × 9.8 × 4.0 = 1960 J.2. A: 1764 ÷ 6.0 = 294 W; B: 2352 ÷ 10 = 235 W; C: 1960 ÷ 5.5 = 356 W.
3. Most work: B. Greatest power: C.
