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Secondary 4 Pure Physics Energy Power Quiz

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Questions

Secondary 4 Pure Physics Quiz - Energy Power

Name: ________________________
Class: ________________________
Date: ________________________
Score: _____ / 40

Duration: 45 minutes
Total Marks: 40

Instructions:

Answer all questions.
Write your answers in the spaces provided.
Show all working for calculation questions.
Use $g = 10 \text{ N/kg}$ unless otherwise stated.
The number of marks is given in brackets [ ] at the end of each question or part question.

Section A: Multiple Choice Questions (10 marks)

Answer all questions. Choose the correct option and write the letter (A, B, C, or D) in the box provided.

1. A ball of mass 0.5 kg is dropped from a height of 20 m. Ignoring air resistance, what is the kinetic energy of the ball just before it hits the ground? [1]

☐ A. 50 J
☐ B. 100 J
☐ C. 150 J
☐ D. 200 J

2. A car of mass 1200 kg accelerates uniformly from rest to 25 m/s in 10 s. What is the average power developed by the engine during this acceleration? [1]

☐ A. 37.5 kW
☐ B. 75 kW
☐ C. 150 kW
☐ D. 300 kW

3. A force of 50 N is applied to move a box 8 m along a horizontal floor. The force is applied at an angle of 30° to the horizontal. What is the work done by the force? [1]

☐ A. 200 J
☐ B. 346 J
☐ C. 400 J
☐ D. 693 J

4. A hydroelectric power station has an efficiency of 80%. Water falls through a vertical height of 50 m at a rate of 200 kg/s. What is the electrical power output? (Take $g = 10 \text{ N/kg}$ ) [1]

☐ A. 80 kW
☐ B. 100 kW
☐ C. 800 kW
☐ D. 1000 kW

5. A spring with spring constant 200 N/m is compressed by 0.1 m. What is the elastic potential energy stored in the spring? [1]

☐ A. 0.5 J
☐ B. 1.0 J
☐ C. 2.0 J
☐ D. 4.0 J

6. A student runs up a flight of stairs of vertical height 3.0 m in 4.0 s. The student has a mass of 60 kg. What is the average power developed by the student against gravity? [1]

☐ A. 180 W
☐ B. 240 W
☐ C. 450 W
☐ D. 720 W

7. Which of the following statements about the principle of conservation of energy is correct? [1]

☐ A. Energy can be created but not destroyed.
☐ B. Energy can be destroyed but not created.
☐ C. The total energy of an isolated system remains constant.
☐ D. The total energy of any system remains constant.

8. A block of mass 2 kg slides down a frictionless inclined plane of length 5 m and vertical height 3 m. What is the speed of the block at the bottom of the incline? [1]

☐ A. 5.5 m/s
☐ B. 7.7 m/s
☐ C. 10 m/s
☐ D. 15 m/s

9. An electric motor lifts a load of 500 N through a height of 10 m in 20 s. The motor has an efficiency of 75%. What is the electrical energy input to the motor? [1]

☐ A. 50 kJ
☐ B. 66.7 kJ
☐ C. 75 kJ
☐ D. 100 kJ

10. A pendulum bob is released from rest at a height $h$ above its lowest point. At the lowest point, its speed is $v$ . If the bob is released from a height $4h$ , what will be its speed at the lowest point? [1]

☐ A. $v$
☐ B. $2v$
☐ C. $4v$
☐ D. $16v$

Section B: Structured Questions (30 marks)

Answer all questions in the spaces provided.

11. A roller coaster car of mass 500 kg starts from rest at point A, which is at a height of 40 m above the ground. The car travels along a frictionless track to point B at a height of 15 m, then to point C at a height of 25 m.

Image pending generation: diagram for Q11.

(a) Calculate the gravitational potential energy of the car at point A. [1]

Answer: ________________________ J

(b) Calculate the kinetic energy of the car at point B. [2]

Answer: ________________________ J

Answer: ________________________ m/s

(d) In reality, the track is not frictionless. The car reaches point C with a speed of 15 m/s. Calculate the average resistive force acting on the car between A and C if the track length from A to C is 120 m. [3]

Answer: ________________________ N

12. A crane lifts a concrete block of mass 800 kg vertically upwards at a constant speed of 0.5 m/s. The crane motor has an efficiency of 60%.

(a) Calculate the tension in the lifting cable. [1]

Answer: ________________________ N

(b) Calculate the useful power output of the motor (power used to lift the block). [2]

Answer: ________________________ W

(d) The block is lifted through a height of 12 m. Calculate the work done against gravity. [1]

Answer: ________________________ J

(e) Suggest one reason why the efficiency of the crane motor is less than 100%. [1]

Answer: _________________________________________________________________________

13. A toy gun uses a spring to launch a small ball of mass 0.02 kg vertically upwards. The spring has a spring constant of 150 N/m and is compressed by 0.08 m before release. Assume no energy losses.

(a) Calculate the elastic potential energy stored in the compressed spring. [1]

Answer: ________________________ J

(b) Calculate the maximum height reached by the ball above the launch point. [2]

Answer: ________________________ m

Answer: ________________________ m/s

(d) In practice, the ball reaches a lower height than calculated in (b). Explain why, referring to energy conversions. [2]

Answer: _________________________________________________________________________

14. A hydroelectric dam stores water in a reservoir at an average height of 80 m above the turbines. Water flows through the turbines at a rate of 500 kg/s. The overall efficiency of the hydroelectric system is 85%.

(a) Calculate the gravitational potential energy lost by the water per second. [2]

Answer: ________________________ J/s

(b) Calculate the electrical power output of the hydroelectric system. [2]

Answer: ________________________ W

(c) The dam generates electricity for a town that requires an average power of 2.5 MW. Calculate the minimum mass flow rate of water needed (in kg/s) if the efficiency remains 85%. [2]

Answer: ________________________ kg/s

(d) State one environmental advantage and one environmental disadvantage of hydroelectric power. [2]

Advantage: _____________________________________________________________________

Disadvantage: ___________________________________________________________________

15. A block of mass 3 kg is pulled up a rough inclined plane at a constant speed by a force of 40 N acting parallel to the plane. The plane is inclined at 30° to the horizontal. The block moves a distance of 5 m along the plane.

Image pending generation: diagram for Q15.

(a) Calculate the work done by the applied force. [1]

Answer: ________________________ J

(b) Calculate the gain in gravitational potential energy of the block. [2]

Answer: ________________________ J

(d) Calculate the frictional force acting on the block. [1]

Answer: ________________________ N

(e) Calculate the efficiency of this process in terms of useful energy gain (gravitational potential energy) compared to work input. [2]

Answer: ________________________ %

16. A wind turbine has blades of length 40 m. The density of air is 1.2 kg/m³. The wind speed is 12 m/s. The turbine has an efficiency of 40% (Betz limit considerations aside).

(a) Calculate the mass of air passing through the swept area of the blades per second. [2]

Answer: ________________________ kg/s

(b) Calculate the kinetic energy of this air per second (power in the wind). [2]

Answer: ________________________ W

(d) Explain why the efficiency of a wind turbine cannot reach 100%, even in ideal conditions. [2]

Answer: _________________________________________________________________________

17. A student investigates the relationship between the compression of a spring and the height reached by a toy car launched up a ramp. The spring constant is 250 N/m. The car has a mass of 0.1 kg. The ramp is frictionless and inclined at 20° to the horizontal.

(a) The spring is compressed by 0.05 m. Calculate the maximum vertical height gained by the car. [3]

Answer: ________________________ m

(b) The student repeats the experiment with different compressions and plots a graph of maximum vertical height $h$ against compression $x$ . Sketch the expected shape of this graph on the axes below. [2]

Image pending generation: graph for Q17.

Reason 1: _______________________________________________________________________

Reason 2: _______________________________________________________________________

18. A 60 kg athlete runs up a staircase of 80 steps, each of height 0.18 m, in 15 s.

(a) Calculate the total vertical height climbed. [1]

Answer: ________________________ m

(b) Calculate the work done against gravity. [1]

Answer: ________________________ J

Answer: ________________________ W

(d) The athlete's body has an efficiency of about 25% in converting chemical energy to mechanical work. Calculate the rate of chemical energy consumption (metabolic power) during this run. [2]

Answer: ________________________ W

(e) After reaching the top, the athlete walks down the stairs. Explain why the work done by gravity on the athlete during the descent is positive, but the athlete still expends chemical energy. [2]

Answer: _________________________________________________________________________

19. A pendulum consists of a bob of mass 0.2 kg attached to a light string of length 1.0 m. The bob is pulled aside until the string makes an angle of 30° with the vertical, then released from rest.

Image pending generation: diagram for Q19.

(a) Calculate the vertical height $h$ through which the bob is raised. [2]

Answer: ________________________ m

(b) Calculate the speed of the bob at the lowest point of its swing. [2]

Answer: ________________________ m/s

(c) The bob passes through the lowest point and rises to a maximum angle of 25° on the other side. Calculate the energy lost during this half-swing. [2]

Answer: ________________________ J

(d) Explain where this lost energy goes. [1]

Answer: _________________________________________________________________________

20. A solar panel of area 2.5 m² receives sunlight of intensity 800 W/m². The panel has an efficiency of 18%. The electrical energy generated is used to charge a battery. The charging process has an efficiency of 90%.

(a) Calculate the power incident on the solar panel. [1]

Answer: ________________________ W

(b) Calculate the electrical power output from the solar panel. [1]

Answer: ________________________ W

(d) The battery stores 1.5 MJ of energy. Calculate the minimum time needed to fully charge the battery from empty under these conditions. [2]

Answer: ________________________ s

(e) State two factors that affect the efficiency of a solar panel in real-world conditions. [2]

Factor 1: _______________________________________________________________________

Factor 2: _______________________________________________________________________

End of Quiz

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Answers

Secondary 4 Pure Physics Quiz - Energy Power (Answer Key)

Total Marks: 40

Section A: Multiple Choice Questions (10 marks)

1. Answer: B [1]

Working:

Gravitational potential energy at start = $mgh = 0.5 \times 10 \times 20 = 100 \text{ J}$
By conservation of energy (no air resistance), all GPE converts to KE at ground
KE = 100 J

Key concept: In free fall without air resistance, loss in GPE = gain in KE.

2. Answer: A [1]

Working:

Final KE = $\frac{1}{2}mv^2 = \frac{1}{2} \times 1200 \times 25^2 = 375,000 \text{ J}$
Average power = $\frac{\text{Work done}}{\text{time}} = \frac{375,000}{10} = 37,500 \text{ W} = 37.5 \text{ kW}$

Key concept: Work-energy theorem: net work done = change in KE. Power = work/time.

3. Answer: B [1]

Working:

Work done = $F \cdot s \cdot \cos\theta = 50 \times 8 \times \cos 30^\circ$
$\cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866$
Work done = $400 \times 0.866 = 346.4 \text{ J} \approx 346 \text{ J}$

Key concept: Work done by a force at an angle: $W = Fs\cos\theta$ . Only the component of force in the direction of displacement does work.

4. Answer: A [1]

Working:

Power input (gravitational) = $\frac{mgh}{t} = \dot{m}gh = 200 \times 10 \times 50 = 100,000 \text{ W} = 100 \text{ kW}$
Electrical power output = efficiency × power input = $0.80 \times 100 = 80 \text{ kW}$

Key concept: Power = rate of energy transfer. For fluid flow, $\dot{m}gh$ gives gravitational power. Efficiency = useful output / total input.

5. Answer: B [1]

Working:

Elastic potential energy = $\frac{1}{2}kx^2 = \frac{1}{2} \times 200 \times (0.1)^2 = 100 \times 0.01 = 1.0 \text{ J}$

Key concept: EPE stored in spring = $\frac{1}{2}kx^2$ where $k$ is spring constant and $x$ is extension/compression from natural length.

6. Answer: C [1]

Working:

Work done against gravity = $mgh = 60 \times 10 \times 3 = 1800 \text{ J}$
Power = $\frac{1800}{4} = 450 \text{ W}$

Key concept: Power against gravity = rate of gain of GPE = $\frac{mgh}{t}$ .

7. Answer: C [1]

Explanation: The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. The total energy of an isolated system remains constant. Option D is incorrect because non-isolated systems can exchange energy with surroundings.

8. Answer: B [1]

Working:

Loss in GPE = $mgh = 2 \times 10 \times 3 = 60 \text{ J}$
Gain in KE = $\frac{1}{2}mv^2 = 60$
$v^2 = \frac{120}{2} = 60$
$v = \sqrt{60} \approx 7.75 \text{ m/s} \approx 7.7 \text{ m/s}$

Key concept: On a frictionless incline, only vertical height matters for GPE change. Path length doesn't affect final speed.

9. Answer: B [1]

Working:

Useful work output = $Fh = 500 \times 10 = 5000 \text{ J}$
Efficiency = $\frac{\text{useful output}}{\text{input}} \Rightarrow 0.75 = \frac{5000}{E_{\text{in}}}$
$E_{\text{in}} = \frac{5000}{0.75} = 6666.7 \text{ J} \approx 66.7 \text{ kJ}$

Key concept: Efficiency = useful energy output / total energy input. Rearrange to find input.

10. Answer: B [1]

Working:

From conservation of energy: $mgh = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh}$
$v \propto \sqrt{h}$
If $h$ becomes $4h$ , then $v_{\text{new}} = \sqrt{2g(4h)} = 2\sqrt{2gh} = 2v$

Key concept: Speed at bottom of pendulum/slide $\propto \sqrt{\text{height}}$ . Quadrupling height doubles speed.

Section B: Structured Questions (30 marks)

11. Roller Coaster Energy Conservation

(a) GPE at A = $mgh_A = 500 \times 10 \times 40 = 200,000 \text{ J}$ [1]

Answer: 200,000 J (or $2.0 \times 10^5 \text{ J}$ )

(b) At point B:

GPE at B = $mgh_B = 500 \times 10 \times 15 = 75,000 \text{ J}$
By conservation of energy (frictionless): Total energy at A = Total energy at B
KE at B = GPE at A - GPE at B = $200,000 - 75,000 = 125,000 \text{ J}$ [2]

Answer: 125,000 J (or $1.25 \times 10^5 \text{ J}$ )

Mark breakdown: 1 mark for GPE at B, 1 mark for KE calculation using conservation.

(c) At point C:

GPE at C = $mgh_C = 500 \times 10 \times 25 = 125,000 \text{ J}$
KE at C = Total energy - GPE at C = $200,000 - 125,000 = 75,000 \text{ J}$
$\frac{1}{2}mv^2 = 75,000 \Rightarrow v^2 = \frac{150,000}{500} = 300$
$v = \sqrt{300} \approx 17.3 \text{ m/s}$ [2]

Answer: 17.3 m/s (accept 17.3 or $\sqrt{300}$ )

Mark breakdown: 1 mark for KE at C, 1 mark for speed calculation.

(d) With friction:

Actual KE at C = $\frac{1}{2} \times 500 \times 15^2 = 56,250 \text{ J}$
Energy lost to friction = Ideal KE - Actual KE = $75,000 - 56,250 = 18,750 \text{ J}$
Work done against friction = $F_{\text{friction}} \times \text{distance}$
$F_{\text{friction}} = \frac{18,750}{120} = 156.25 \text{ N}$ [3]

Answer: 156 N (or 156.25 N)

Mark breakdown: 1 mark for actual KE, 1 mark for energy lost, 1 mark for friction force.

Common mistake: Forgetting that work done against friction = energy lost, not just using $F = ma$ .

12. Crane Lifting at Constant Speed

(a) Constant speed $\Rightarrow$ net force = 0 $\Rightarrow$ Tension = Weight = $mg = 800 \times 10 = 8000 \text{ N}$ [1]

Answer: 8000 N

(b) Useful power output = Force × velocity = $T \times v = 8000 \times 0.5 = 4000 \text{ W}$ [2]

Answer: 4000 W (or 4.0 kW)

Mark breakdown: 1 mark for correct formula $P = Fv$ , 1 mark for correct substitution and answer.

(c) Efficiency = $\frac{\text{useful power output}}{\text{electrical power input}}$

$0.60 = \frac{4000}{P_{\text{in}}} \Rightarrow P_{\text{in}} = \frac{4000}{0.60} = 6666.7 \text{ W}$ [2]

Answer: 6670 W (or 6.67 kW)

Mark breakdown: 1 mark for efficiency formula rearrangement, 1 mark for calculation.

(d) Work done against gravity = $mgh = 800 \times 10 \times 12 = 96,000 \text{ J}$ [1]

Answer: 96,000 J (or $9.6 \times 10^4 \text{ J}$ )

(e) Any one valid reason, e.g.:

Energy lost as heat in motor windings due to electrical resistance
Energy lost as sound from moving parts
Friction in bearings and gears
Air resistance on moving parts
Eddy currents in motor core [1]

Answer: Energy is lost as heat due to electrical resistance in the motor windings / friction in moving parts / sound energy.

13. Spring-Launched Ball

(a) EPE = $\frac{1}{2}kx^2 = \frac{1}{2} \times 150 \times (0.08)^2 = 75 \times 0.0064 = 0.48 \text{ J}$ [1]

Answer: 0.48 J

(b) At max height, all EPE $\rightarrow$ GPE (no losses)

$mgh = 0.48 \Rightarrow h = \frac{0.48}{0.02 \times 10} = \frac{0.48}{0.2} = 2.4 \text{ m}$ [2]

Answer: 2.4 m

Mark breakdown: 1 mark for equating EPE to GPE, 1 mark for correct calculation.

(c) At half max height ( $h = 1.2 \text{ m}$ ):

GPE at half height = $mgh = 0.02 \times 10 \times 1.2 = 0.24 \text{ J}$
KE at half height = Total energy - GPE = $0.48 - 0.24 = 0.24 \text{ J}$
$\frac{1}{2}mv^2 = 0.24 \Rightarrow v^2 = \frac{0.48}{0.02} = 24$
$v = \sqrt{24} \approx 4.9 \text{ m/s}$ [2]

Answer: 4.9 m/s (or $\sqrt{24} \text{ m/s}$ )

Mark breakdown: 1 mark for energy at half height, 1 mark for speed calculation.

(d) In practice, energy is lost due to:

Air resistance acting on the ball during flight (kinetic energy $\rightarrow$ heat/sound)
Internal friction in the spring (elastic potential energy $\rightarrow$ heat)
Friction between ball and launch tube (if any)
Sound energy produced during launch [2]

Answer: Air resistance converts some kinetic energy to heat and sound during flight. Internal friction in the spring converts some elastic potential energy to heat during expansion.

Mark breakdown: 1 mark for identifying air resistance, 1 mark for identifying spring/internal friction or sound.

14. Hydroelectric Dam

(a) GPE lost per second = $\dot{m}gh = 500 \times 10 \times 80 = 400,000 \text{ J/s} = 400 \text{ kW}$ [2]

Answer: 400,000 J/s (or 400 kW)

Mark breakdown: 1 mark for formula $\dot{m}gh$ , 1 mark for correct calculation with units.

(b) Electrical power output = efficiency × power input = $0.85 \times 400,000 = 340,000 \text{ W} = 340 \text{ kW}$ [2]

Answer: 340,000 W (or 340 kW)

Mark breakdown: 1 mark for efficiency formula, 1 mark for calculation.

(c) Required electrical power = 2.5 MW = 2,500,000 W

Power input needed = $\frac{2,500,000}{0.85} = 2,941,176 \text{ W}$
$\dot{m}gh = 2,941,176 \Rightarrow \dot{m} = \frac{2,941,176}{10 \times 80} = 3676.5 \text{ kg/s}$ [2]

Answer: 3680 kg/s (or 3676 kg/s)

Mark breakdown: 1 mark for working backwards from output to input power, 1 mark for mass flow rate calculation.

(d) Advantage: Renewable, no greenhouse gas emissions during operation, reliable/base-load capable, long lifespan. [1] Disadvantage: Habitat destruction/flooding, methane from reservoirs, disrupts fish migration, high initial cost, limited suitable sites, sediment buildup. [1]

Answer: Advantage: No carbon emissions during electricity generation / renewable energy source. Disadvantage: Flooding of large areas destroys habitats / disrupts river ecosystems and fish migration.

15. Block on Rough Inclined Plane

(a) Work done by applied force = $F \times s = 40 \times 5 = 200 \text{ J}$ [1]

Answer: 200 J

(b) Vertical height gained = $s \sin\theta = 5 \times \sin 30^\circ = 5 \times 0.5 = 2.5 \text{ m}$

Gain in GPE = $mgh = 3 \times 10 \times 2.5 = 75 \text{ J}$ [2]

Answer: 75 J

Mark breakdown: 1 mark for vertical height, 1 mark for GPE calculation.

(c) Work-energy: Work input = Gain in GPE + Work against friction

$200 = 75 + W_{\text{friction}}$
$W_{\text{friction}} = 125 \text{ J}$ [2]

Answer: 125 J

Mark breakdown: 1 mark for work-energy equation, 1 mark for calculation.

(d) Work against friction = $f \times s \Rightarrow 125 = f \times 5 \Rightarrow f = 25 \text{ N}$ [1]

Answer: 25 N

(e) Efficiency = $\frac{\text{Useful energy output}}{\text{Energy input}} \times 100\% = \frac{\text{GPE gain}}{\text{Work by applied force}} \times 100\% = \frac{75}{200} \times 100\% = 37.5\%$ [2]

Answer: 37.5%

Mark breakdown: 1 mark for correct efficiency definition, 1 mark for calculation.

16. Wind Turbine

(a) Swept area = $\pi r^2 = \pi \times 40^2 = 1600\pi \approx 5026.5 \text{ m}^2$

Volume flow rate = Area × wind speed = $5026.5 \times 12 = 60,318 \text{ m}^3/\text{s}$
Mass flow rate = density × volume flow rate = $1.2 \times 60,318 = 72,382 \text{ kg/s}$ [2]

Answer: 72,400 kg/s (or $7.24 \times 10^4 \text{ kg/s}$ )

Mark breakdown: 1 mark for swept area, 1 mark for mass flow rate calculation.

(b) Power in wind = KE per second = $\frac{1}{2} \dot{m} v^2 = \frac{1}{2} \times 72,382 \times 12^2 = 36,191 \times 144 = 5,211,504 \text{ W} \approx 5.21 \text{ MW}$ [2]

Answer: 5.21 MW (or 5,210,000 W)

Mark breakdown: 1 mark for formula $\frac{1}{2}\dot{m}v^2$ , 1 mark for calculation.

(c) Electrical power output = efficiency × power in wind = $0.40 \times 5,211,504 = 2,084,602 \text{ W} \approx 2.08 \text{ MW}$ [1]

Answer: 2.08 MW (or 2,080,000 W)

(d) Reasons why efficiency < 100% (Betz limit = 59.3% max for ideal turbine):

Air must retain some kinetic energy to move away from turbine (cannot bring air to rest)
Turbulence and wake losses behind blades
Friction in gearbox and generator
Electrical resistance losses in generator
Blade drag and tip losses [2]

Answer: Air cannot be brought to rest behind the turbine (must keep moving), so some kinetic energy remains in the wind. Additional losses include turbulence, friction in moving parts, and electrical resistance in the generator.

Mark breakdown: 1 mark for Betz limit concept (air must keep moving), 1 mark for additional practical losses.

17. Spring-Launched Car on Ramp

(a) EPE = $\frac{1}{2}kx^2 = \frac{1}{2} \times 250 \times (0.05)^2 = 125 \times 0.0.0025 = 0.3125 \text{ J}$

At max height, EPE $\rightarrow$ GPE: $mgh = 0.3125$
$h = \frac{0.3125}{0.1 \times 10} = \frac{0.3125}{1} = 0.3125 \text{ m}$ [3]

Answer: 0.313 m (or 0.3125 m)

Mark breakdown: 1 mark for EPE calculation, 1 mark for equating to GPE, 1 mark for height calculation.

(b) Graph sketch: $h \propto x^2$ (since $h = \frac{k}{2mg}x^2$ )

Curve passes through origin
Quadratic shape (parabola opening upward)
Increasing gradient [2]

Answer: Parabolic curve starting at origin, curving upward with increasing slope. Axes labeled $h/\text{m}$ and $x/\text{m}$ .

Mark breakdown: 1 mark for correct quadratic shape through origin, 1 mark for labeled axes with units.

(c) Reasons for lower actual heights:

Friction between car and ramp (KE $\rightarrow$ heat)
Air resistance on car (KE $\rightarrow$ heat/sound)
Spring internal friction / not ideal (EPE $\rightarrow$ heat)
Car may not launch perfectly along ramp (some energy into rotation/wobble) [2]

Answer: Reason 1: Friction between the car wheels/body and the ramp converts mechanical energy to heat. Reason 2: Air resistance on the moving car dissipates kinetic energy.

18. Athlete Running Up Stairs

(a) Total height = $80 \times 0.18 = 14.4 \text{ m}$ [1]

Answer: 14.4 m

(b) Work against gravity = $mgh = 60 \times 10 \times 14.4 = 8640 \text{ J}$ [1]

Answer: 8640 J

(c) Average power = $\frac{8640}{15} = 576 \text{ W}$ [1]

Answer: 576 W

(d) Efficiency = 25% = 0.25 = $\frac{\text{mechanical power}}{\text{metabolic power}}$

Metabolic power = $\frac{576}{0.25} = 2304 \text{ W}$ [2]

Answer: 2304 W (or 2.3 kW)

Mark breakdown: 1 mark for efficiency formula, 1 mark for calculation.

(e) During descent:

Gravity does positive work on athlete (force and displacement both downward) $\rightarrow$ athlete gains KE
But athlete must exert muscular force to control descent (eccentric contraction) and maintain balance
Muscles consume chemical energy even when doing negative work (absorbing energy)
Energy is dissipated as heat in muscles [2]

Answer: Gravity does positive work as the athlete's weight and displacement are both downward. However, the athlete's muscles must contract eccentrically to control the descent and maintain stability, which consumes chemical energy (converted to heat) even though the net work done by the athlete on the surroundings is negative.

*Mark breakdown: 1 mark for explaining positive work by gravity, 1 mark

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Secondary 4 Pure Physics Quiz - Energy Power (Answer Key)

Total Marks: 40

Section A: Multiple Choice Questions (10 marks)

1. Answer: B [1]

Working:

Gravitational potential energy at start = $mgh = 0.5 \times 10 \times 20 = 100 \text{ J}$
By conservation of energy (no air resistance), all GPE converts to KE at ground
KE = 100 J

Key concept: In free fall without air resistance, loss in GPE = gain in KE.

2. Answer: A [1]

Working:

Final KE = $\frac{1}{2}mv^2 = \frac{1}{2} \times 1200 \times 25^2 = 375,000 \text{ J}$
Average power = $\frac{\text{Work done}}{\text{time}} = \frac{375,000}{10} = 37,500 \text{ W} = 37.5 \text{ kW}$

Key concept: Work-energy theorem: net work done = change in KE. Power = work/time.

3. Answer: B [1]

Working:

Work done = $F \cdot s \cdot \cos\theta = 50 \times 8 \times \cos 30^\circ$
$\cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866$
Work done = $400 \times 0.866 = 346.4 \text{ J} \approx 346 \text{ J}$

Key concept: Work done by a force at an angle: $W = Fs\cos\theta$ . Only the component of force in the direction of displacement does work.

4. Answer: A [1]

Working:

Power input (gravitational) = $\frac{mgh}{t} = \dot{m}gh = 200 \times 10 \times 50 = 100,000 \text{ W} = 100 \text{ kW}$
Electrical power output = efficiency × power input = $0.80 \times 100 = 80 \text{ kW}$

Key concept: Power = rate of energy transfer. For fluid flow, $\dot{m}gh$ gives gravitational power. Efficiency = useful output / total input.

5. Answer: B [1]

Working:

Elastic potential energy = $\frac{1}{2}kx^2 = \frac{1}{2} \times 200 \times (0.1)^2 = 100 \times 0.01 = 1.0 \text{ J}$

Key concept: EPE stored in spring = $\frac{1}{2}kx^2$ where $k$ is spring constant and $x$ is extension/compression from natural length.

6. Answer: C [1]

Working:

Work done against gravity = $mgh = 60 \times 10 \times 3 = 1800 \text{ J}$
Power = $\frac{1800}{4} = 450 \text{ W}$

Key concept: Power against gravity = rate of gain of GPE = $\frac{mgh}{t}$ .

7. Answer: C [1]

Explanation: The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. The total energy of an isolated system remains constant.

8. Answer: B [1]

Working:

Loss in GPE = $mgh = 2 \times 10 \times 3 = 60 \text{ J}$
Gain in KE = $\frac{1}{2}mv^2 = 60$
$v^2 = \frac{120}{2} = 60$
$v = \sqrt{60} \approx 7.75 \text{ m/s} \approx 7.7 \text{ m/s}$

Key concept: On a frictionless incline, loss in GPE = gain in KE. The path length does not matter, only the vertical height change.

9. Answer: B [1]

Working:

Useful work output = $Fh = 500 \times 10 = 5000 \text{ J}$
Efficiency = $\frac{\text{useful output}}{\text{input}} \Rightarrow 0.75 = \frac{5000}{\text{input}}$
Electrical energy input = $\frac{5000}{0.75} = 6666.7 \text{ J} \approx 66.7 \text{ kJ}$

Key concept: Efficiency = useful energy output / total energy input. Rearrange to find input.

10. Answer: B [1]

Working:

From conservation of energy: $mgh = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh}$
If height becomes $4h$ , new speed $v' = \sqrt{2g(4h)} = \sqrt{4} \cdot \sqrt{2gh} = 2v$

Key concept: Speed at bottom is proportional to square root of height: $v \propto \sqrt{h}$ .

Section B: Structured Questions (30 marks)

11. (a) Answer: 200,000 J [1]

Working:

GPE = $mgh = 500 \times 10 \times 40 = 200,000 \text{ J}$

(b) Answer: 125,000 J [2]

Working:

GPE at B = $500 \times 10 \times 15 = 75,000 \text{ J}$
Total energy conserved = 200,000 J
KE at B = Total energy - GPE at B = $200,000 - 75,000 = 125,000 \text{ J}$

Working:

GPE at C = $500 \times 10 \times 25 = 125,000 \text{ J}$
KE at C = $200,000 - 125,000 = 75,000 \text{ J}$
$\frac{1}{2} \times 500 \times v^2 = 75,000$
$v^2 = 300$
$v = \sqrt{300} \approx 17.3 \text{ m/s}$

(d) Answer: 417 N (or 416.7 N) [3]

Working:

Actual KE at C = $\frac{1}{2} \times 500 \times 15^2 = 56,250 \text{ J}$
Energy lost to friction = Ideal KE - Actual KE = $75,000 - 56,250 = 18,750 \text{ J}$
Work done against friction = $F_{\text{friction}} \times \text{distance}$
$F_{\text{friction}} = \frac{18,750}{120} = 156.25 \text{ N}$

Wait, let me recalculate:

Total energy at A = 200,000 J
Energy at C (actual) = GPE + KE = $125,000 + 56,250 = 181,250 \text{ J}$
Energy lost = $200,000 - 181,250 = 18,750 \text{ J}$
Average resistive force = $\frac{18,750}{120} = 156.25 \text{ N}$

Answer: 156.25 N [3]

12. (a) Answer: 8000 N [1]

Working:

Constant speed $\Rightarrow$ net force = 0
Tension = Weight = $mg = 800 \times 10 = 8000 \text{ N}$

(b) Answer: 4000 W [2]

Working:

Useful power = Force × velocity = $8000 \times 0.5 = 4000 \text{ W}$
(Alternatively: rate of GPE gain = $\frac{mgh}{t} = mgv = 800 \times 10 \times 0.5 = 4000 \text{ W}$ )

Working:

Efficiency = $\frac{\text{useful output}}{\text{input}} = 0.60$
Input power = $\frac{4000}{0.60} = 6666.7 \text{ W} \approx 6667 \text{ W}$

(d) Answer: 96,000 J [1]

Working:

Work against gravity = $mgh = 800 \times 10 \times 12 = 96,000 \text{ J}$

(e) Answer: Energy is lost as heat due to friction in moving parts, electrical resistance in motor windings, sound energy, and air resistance. [1]

13. (a) Answer: 0.48 J [1]

Working:

EPE = $\frac{1}{2}kx^2 = \frac{1}{2} \times 150 \times (0.08)^2 = 75 \times 0.0064 = 0.48 \text{ J}$

(b) Answer: 2.4 m [2]

Working:

EPE converts to GPE at max height: $\frac{1}{2}kx^2 = mgh$
$0.48 = 0.02 \times 10 \times h$
$h = \frac{0.48}{0.2} = 2.4 \text{ m}$

Working:

At half max height (1.2 m), GPE = $0.02 \times 10 \times 1.2 = 0.24 \text{ J}$
Total energy = 0.48 J
KE = $0.48 - 0.24 = 0.24 \text{ J}$
$\frac{1}{2} \times 0.02 \times v^2 = 0.24$
$v^2 = 24$
$v = \sqrt{24} \approx 4.9 \text{ m/s}$

(d) Answer: In practice, air resistance acts on the ball, converting some kinetic energy to thermal energy (heat) and sound. Also, some energy is lost as heat due to internal friction in the spring and friction between the ball and the gun barrel. [2]

14. (a) Answer: 400,000 J/s (or 400 kW) [2]

Working:

GPE lost per second = $\dot{m}gh = 500 \times 10 \times 80 = 400,000 \text{ J/s}$

(b) Answer: 340,000 W (or 340 kW) [2]

Working:

Electrical power output = efficiency × power input = $0.85 \times 400,000 = 340,000 \text{ W}$

Working:

Required electrical power = 2.5 MW = 2,500,000 W
Required input power = $\frac{2,500,000}{0.85} = 2,941,176 \text{ W}$
$\dot{m}gh = 2,941,176$
$\dot{m} \times 10 \times 80 = 2,941,176$
$\dot{m} = \frac{2,941,176}{800} = 3676.5 \text{ kg/s}$

Wait, let me recalculate:

$P_{\text{out}} = \eta \dot{m} g h$
$\dot{m} = \frac{P_{\text{out}}}{\eta g h} = \frac{2,500,000}{0.85 \times 10 \times 80} = \frac{2,500,000}{680} = 3676.5 \text{ kg/s}$

Answer: 3676 kg/s (or 3676.5 kg/s) [2]

(d) Advantage: No greenhouse gas emissions during operation; renewable energy source. [1]

Disadvantage: Disrupts river ecosystems and fish migration; flooding of large areas of land displaces communities and wildlife. [1]

15. (a) Answer: 200 J [1]

Working:

Work done = Force × distance = $40 \times 5 = 200 \text{ J}$

(b) Answer: 75 J [2]

Working:

Vertical height gained = $5 \times \sin 30^\circ = 5 \times 0.5 = 2.5 \text{ m}$
Gain in GPE = $mgh = 3 \times 10 \times 2.5 = 75 \text{ J}$

Working:

Work input = 200 J
Useful energy gain (GPE) = 75 J
Work against friction = Work input - GPE gain = $200 - 75 = 125 \text{ J}$

(d) Answer: 25 N [1]

Working:

Work against friction = friction force × distance
$125 = f \times 5$
$f = 25 \text{ N}$

(e) Answer: 37.5% [2]

Working:

Efficiency = $\frac{\text{useful energy output}}{\text{energy input}} \times 100\% = \frac{75}{200} \times 100\% = 37.5\%$

16. (a) Answer: 7238 kg/s (or 7240 kg/s) [2]

Working:

Swept area = $\pi r^2 = \pi \times 40^2 = 1600\pi \text{ m}^2$
Volume flow rate = area × wind speed = $1600\pi \times 12 = 19,200\pi \text{ m}^3/\text{s}$
Mass flow rate = density × volume flow rate = $1.2 \times 19,200\pi = 23,040\pi \approx 72,382 \text{ kg/s}$

Wait, that seems too large. Let me check:

$r = 40 \text{ m}$ , $A = \pi \times 40^2 = 5026.5 \text{ m}^2$
Volume/s = $5026.5 \times 12 = 60,318 \text{ m}^3/\text{s}$
Mass/s = $1.2 \times 60,318 = 72,382 \text{ kg/s}$

Answer: 72,400 kg/s (or 72,382 kg/s) [2]

(b) Answer: 5.21 MW (or 5,210,000 W) [2]

Working:

KE per second = $\frac{1}{2} \dot{m} v^2 = \frac{1}{2} \times 72,382 \times 12^2$
$= 36,191 \times 144 = 5,211,504 \text{ W} \approx 5.21 \text{ MW}$

Working:

Electrical output = $0.40 \times 5.21 \text{ MW} = 2.084 \text{ MW} \approx 2.08 \text{ MW}$

(d) Answer: According to Betz's law, the maximum theoretical efficiency is 59.3% (16/27) because some kinetic energy must remain in the air downstream to allow it to move away; if all KE were extracted, air would stop behind the turbine, blocking further flow. Additional losses include friction in bearings, gearbox, generator inefficiencies, and blade drag. [2]

17. (a) Answer: 0.319 m (or 0.32 m) [3]

Working:

EPE = $\frac{1}{2} \times 250 \times (0.05)^2 = 125 \times 0.0025 = 0.3125 \text{ J}$
EPE converts to GPE: $mgh = 0.3125$
$0.1 \times 10 \times h = 0.3125$
$h = \frac{0.3125}{1} = 0.3125 \text{ m} \approx 0.313 \text{ m}$

Answer: 0.313 m [3]

(b) Answer: Sketch shows a quadratic curve ( $h \propto x^2$ ) passing through origin, with increasing gradient. Axes labeled: $h$ (m) vertical, $x$ (m) horizontal. [2]

Description: The graph is a parabola opening upward, starting at (0,0), curving upward with increasing slope. Since $h = \frac{kx^2}{2mg}$ , it's a quadratic relationship.

Reason 2: Air resistance acts on the car, dissipating kinetic energy. [1]

(Other valid reasons: spring not ideal/massless, rotational KE of wheels not accounted for, energy lost as sound.)

18. (a) Answer: 14.4 m [1]

Working:

Total height = $80 \times 0.18 = 14.4 \text{ m}$

(b) Answer: 86,400 J [1]

Working:

Work against gravity = $mgh = 60 \times 10 \times 14.4 = 86,400 \text{ J}$

Working:

Power = $\frac{86,400}{15} = 5760 \text{ W}$

(d) Answer: 23,040 W (or 23.0 kW) [2]

Working:

Efficiency = $\frac{\text{mechanical power}}{\text{metabolic power}} = 0.25$
Metabolic power = $\frac{5760}{0.25} = 23,040 \text{ W}$

(e) Answer: During descent, gravity does positive work on the athlete (force and displacement in same direction), increasing kinetic energy. However, the athlete must exert muscular force to control speed, maintain balance, and absorb impact, which requires chemical energy conversion. Muscles consume energy even when doing negative work (eccentric contraction) to control the descent. [2]

19. (a) Answer: 0.134 m (or 0.13 m) [2]

Working:

Vertical height $h = L - L\cos\theta = L(1 - \cos\theta)$
$h = 1.0 \times (1 - \cos 30^\circ) = 1 - \frac{\sqrt{3}}{2} = 1 - 0.866 = 0.134 \text{ m}$

(b) Answer: 1.63 m/s (or $\sqrt{2.68}$ m/s) [2]

Working:

GPE lost = $mgh = 0.2 \times 10 \times 0.134 = 0.268 \text{ J}$
KE at bottom = $\frac{1}{2}mv^2 = 0.268$
$v^2 = \frac{0.536}{0.2} = 2.68$
$v = \sqrt{2.68} \approx 1.637 \text{ m/s} \approx 1.64 \text{ m/s}$

Working:

Height at 25°: $h' = 1.0 \times (1 - \cos 25^\circ) = 1 - 0.9063 = 0.0937 \text{ m}$
GPE at 25° = $0.2 \times 10 \times 0.0937 = 0.1874 \text{ J}$
Initial GPE = 0.268 J
Energy lost = $0.268 - 0.1874 = 0.0806 \text{ J}$

Wait, let me recalculate more precisely:

$\cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866025$
$h_{30} = 1 - 0.866025 = 0.133975 \text{ m}$
GPE initial = $0.2 \times 10 \times 0.133975 = 0.26795 \text{ J}$
$\cos 25^\circ \approx 0.906308$
$h_{25} = 1 - 0.906308 = 0.093692 \text{ m}$
GPE final = $0.2 \times 10 \times 0.093692 = 0.187384 \text{ J}$
Energy lost = $0.26795 - 0.187384 = 0.080566 \text{ J} \approx 0.081 \text{ J}$

Answer: 0.081 J [2]

(d) Answer: The lost energy is dissipated as heat due to air resistance and friction at the pivot point, and as sound energy. [1]

20. (a) Answer: 2000 W [1]

Working:

Power incident = intensity × area = $800 \times 2.5 = 2000 \text{ W}$

(b) Answer: 360 W [1]

Working:

Electrical output = $0.18 \times 2000 = 360 \text{ W}$

Working:

Power stored = $0.90 \times 360 = 324 \text{ W}$

(d) Answer: 4630 s (or 1.29 hours) [2]

Working:

Energy to store = 1.5 MJ = 1,500,000 J
Time = $\frac{1,500,000}{324} = 4629.6 \text{ s} \approx 4630 \text{ s}$

(e) Factor 1: Angle of incidence of sunlight (panel orientation relative to sun). [1]

Factor 2: Temperature of the panel (efficiency decreases as temperature increases). [1]

(Other valid factors: shading, dust/dirt on panel, spectral distribution of sunlight, aging/degradation of cells.)

End of Answer Key