A Level H1 Physics Energy Power Quiz

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A-Level Physics H1 Quiz - Energy Power

Name: ____________________
Class: ____________________
Date: ____________________
Score: ________ / 55

Duration: 60 Minutes
Total Marks: 55 Marks

Instructions:

• Answer all questions.
• Show all necessary working for calculation questions.
• Use $g = 9.81 \text{ m s}^{-2}$ where applicable.
• Give your answers to an appropriate number of significant figures.

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Section A: Fundamental Concepts (Questions 1-5)

Short answer and conceptual questions.

1. Define the term power in the context of energy transfer. [2]
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2. State the principle of conservation of energy. [2]
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3. A force $F$ acts on a body and moves it through a distance $d$ at an angle $\theta$ to the direction of motion. Write the expression for the work done by the force. [1]
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4. Distinguish between useful power output and total power input for a mechanical system. [2]
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5. A system is said to be "conservative" if the total mechanical energy remains constant. Name two forces that are considered conservative. [2]
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Section B: Mechanical Energy & Work (Questions 6-12)

Calculations and structured responses.

6. A block of mass $2.0 \text{ kg}$ is pushed $5.0 \text{ m}$ across a horizontal floor by a constant force of $20 \text{ N}$ acting at $30^\circ$ to the horizontal. Calculate the work done by the force. [3]
   
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7. A $0.5 \text{ kg}$ ball is thrown vertically upwards with an initial speed of $15 \text{ m s}^{-1}$. Calculate its maximum height, ignoring air resistance. [3]
   
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8. A car of mass $1200 \text{ kg}$ accelerates from rest to $25 \text{ m s}^{-1}$ in a straight line. Calculate the increase in its kinetic energy. [3]
   
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9. A spring with force constant $k = 500 \text{ N m}^{-1}$ is compressed by $0.10 \text{ m}$. (a) Calculate the elastic potential energy stored in the spring. [2] (b) If this energy is used to launch a $0.05 \text{ kg}$ pellet, calculate the launch speed. [2]
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10. A $10 \text{ kg}$ object slides down a frictionless inclined plane of height $4.0 \text{ m}$ and angle $30^\circ$. Calculate the speed of the object at the bottom of the plane. [3]
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11. A constant force of $15 \text{ N}$ acts on a $3.0 \text{ kg}$ mass initially at rest. Calculate the work done by the force after the mass has moved $4.0 \text{ m}$. [2]
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12. Explain why the actual height reached by a projectile is always less than the theoretical height calculated using conservation of mechanical energy when air resistance is present. [3]
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Section C: Power, Efficiency & Applications (Questions 13-20)

Advanced calculations and system analysis.

13. An electric motor lifts a $50 \text{ kg}$ crate at a constant speed of $0.8 \text{ m s}^{-1}$. Calculate the useful power output of the motor. [3]
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14. The motor in Question 13 has a total power input of $500 \text{ W}$. Calculate the efficiency of the motor. [3]
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15. A pump moves water from a depth of $10 \text{ m}$ to a tank at a rate of $0.2 \text{ kg s}^{-1}$. Calculate the minimum power required by the pump. [3]
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16. A car of mass $1500 \text{ kg}$ travels at a constant speed of $20 \text{ m s}^{-1}$. The total resistive force (air resistance and friction) is $600 \text{ N}$. Calculate the power developed by the engine to maintain this speed. [3]
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17. A $2.0 \text{ kW}$ electric heater is used to heat $1.0 \text{ kg}$ of water. If the heater is $80\%$ efficient, calculate the energy transferred to the water in $2.0$ minutes. [4]
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18. A roller coaster car of mass $400 \text{ kg}$ starts from rest at the top of a hill of height $30 \text{ m}$. (a) Calculate the theoretical speed at the bottom of the hill. [2] (b) If the actual speed is $20 \text{ m s}^{-1}$, calculate the energy lost to friction and heat. [3]
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19. A crane lifts a load of $200 \text{ kg}$ through a vertical height of $15 \text{ m}$ in $10 \text{ s}$. Calculate the average power output of the crane. [3]
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20. A light bulb is rated at $60 \text{ W}$ and $240 \text{ V}$. If the bulb is used for $5$ hours, calculate the total electrical energy consumed in Joules. [3]
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Answer Key - A-Level Physics H1 Quiz: Energy Power

1. Definition of Power

• The rate of doing work or the rate of energy transfer. [2]
• (1 mark for "rate", 1 mark for "work/energy transfer").

2. Conservation of Energy

• Energy cannot be created or destroyed; it can only be transformed from one form to another. [2]
• (1 mark for "cannot be created/destroyed", 1 mark for "transformed").

3. Expression for Work

• $W = Fd \cos \theta$ [1]

4. Useful vs Total Power

• Total power input is the total energy supplied to the system per unit time. [1]
• Useful power output is the rate at which energy is converted into the intended/useful form of work. [1]

5. Conservative Forces

• Gravitational force, Electrostatic force, Spring/Elastic force. (Any two) [2]

6. Work Calculation

• $W = Fd \cos \theta = 20 \times 5.0 \times \cos 30^\circ$ [1]
• $W = 100 \times 0.866 = 86.6 \text{ J}$ [2]

7. Maximum Height

• $mgh = \frac{1}{2}mv^2 \rightarrow h = \frac{v^2}{2g}$ [1]
• $h = \frac{15^2}{2 \times 9.81} = \frac{225}{19.62}$ [1]
• $h = 11.47 \text{ m}$ [1]

8. Kinetic Energy Increase

• $\Delta KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 1200 \times 25^2$ [1]
• $\Delta KE = 600 \times 625$ [1]
• $\Delta KE = 375,000 \text{ J}$ or $3.75 \times 10^5 \text{ J}$ [1]

9. Spring Energy

• (a) $E = \frac{1}{2}kx^2 = \frac{1}{2} \times 500 \times (0.10)^2 = 2.5 \text{ J}$ [2]
• (b) $\frac{1}{2}mv^2 = 2.5 \rightarrow v = \sqrt{\frac{5.0}{0.05}} = \sqrt{100} = 10 \text{ m s}^{-1}$ [2]

10. Speed at Bottom

• $mgh = \frac{1}{2}mv^2 \rightarrow v = \sqrt{2gh}$ [1]
• $v = \sqrt{2 \times 9.81 \times 4.0} = \sqrt{78.48}$ [1]
• $v = 8.86 \text{ m s}^{-1}$ [1]

11. Work Done

• $W = Fd = 15 \times 4.0 = 60 \text{ J}$ [2]

12. Air Resistance Explanation

• Work is done against air resistance (friction). [1]
• This converts some of the initial kinetic/potential energy into thermal energy. [1]
• Consequently, the final kinetic energy (and thus the peak height) is reduced. [1]

13. Useful Power Output

• $P = Fv = (mg)v = (50 \times 9.81) \times 0.8$ [1]
• $P = 490.5 \times 0.8$ [1]
• $P = 392.4 \text{ W}$ [1]

14. Efficiency

• $\text{Efficiency} = \frac{\text{Useful Power Out}}{\text{Total Power In}} \times 100\%$ [1]
• $\text{Efficiency} = \frac{392.4}{500} \times 100\%$ [1]
• $\text{Efficiency} = 78.48\%$ [1]

15. Pump Power

• $P = \frac{mgh}{t} = \frac{\Delta m}{\Delta t} gh$ [1]
• $P = 0.2 \times 9.81 \times 10$ [1]
• $P = 19.62 \text{ W}$ [1]

16. Engine Power

• $P = Fv = 600 \times 20$ [1]
• $P = 12,000 \text{ W}$ or $12 \text{ kW}$ [2]

17. Heater Energy

• Total energy input $= P \times t = 2000 \times (2 \times 60) = 240,000 \text{ J}$ [1]
• Useful energy $= 0.80 \times 240,000$ [2]
• $E = 192,000 \text{ J}$ or $1.92 \times 10^5 \text{ J}$ [1]

18. Roller Coaster

• (a) $v = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 30} = \sqrt{588.6} = 24.26 \text{ m s}^{-1}$ [2]
• (b) $E_{\text{lost}} = mgh - \frac{1}{2}mv^2 = (400 \times 9.81 \times 30) - (0.5 \times 400 \times 20^2)$ [1]
• $E_{\text{lost}} = 117,720 - 80,000$ [1]
• $E_{\text{lost}} = 37,720 \text{ J}$ [1]

19. Crane Power

• $W = mgh = 200 \times 9.81 \times 15 = 29,430 \text{ J}$ [1]
• $P = \frac{W}{t} = \frac{29,430}{10}$ [1]
• $P = 2,943 \text{ W}$ [1]

20. Bulb Energy

• $E = P \times t = 60 \times (5 \times 3600)$ [1]
• $E = 60 \times 18,000$ [1]
• $E = 1,080,000 \text{ J}$ or $1.08 \times 10^6 \text{ J}$ [1]