A Level H2 Physics Energy Power Quiz

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A-Level Physics H2 Quiz - Energy Power

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

Duration: 60 Minutes
Total Marks: 55 Marks

Instructions:

• Answer all questions.
• Show all working clearly for calculation questions.
• Use $g = 9.81 \text{ m s}^{-2}$ and $c = 3.00 \times 10^8 \text{ m s}^{-1}$ unless otherwise stated.
• Give non-exact numerical answers to three significant figures.

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Section A: Fundamental Concepts (Questions 1–5)

1. Define the term power in the context of energy transfer. [1]
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2. A block of mass $2.5 \text{ kg}$ is pushed across a rough horizontal surface at a constant speed of $3.0 \text{ m s}^{-1}$. If the coefficient of kinetic friction is $0.40$, calculate the power delivered by the pushing force. [2]
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3. State the principle of conservation of energy. [1]
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4. A light bulb is rated at $60 \text{ W}, 240 \text{ V}$. Calculate the resistance of the filament when it is operating at its rated power. [2]
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5. Explain why the power output of an engine is not always equal to the rate of energy released by the fuel. [2]
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Section B: Mechanics and Energy (Questions 6–12)

6. A $0.20 \text{ kg}$ ball is dropped from a height of $5.0 \text{ m}$. Calculate its kinetic energy immediately before it hits the ground, assuming air resistance is negligible. [2]
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7. A car of mass $1200 \text{ kg}$ accelerates from rest to $20 \text{ m s}^{-1}$ in $8.0 \text{ s}$. Calculate the average power delivered by the engine. [3]
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8. A mass $m$ is attached to a spring with spring constant $k$. If the spring is compressed by a distance $x$, express the elastic potential energy stored in terms of $k$ and $x$. [1]
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9. A $0.50 \text{ kg}$ block slides down a frictionless incline of angle $30^\circ$ from rest. After sliding a distance of $2.0 \text{ m}$ along the slope, calculate its speed. [3]
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10. A pump lifts $100 \text{ kg}$ of water per minute from a well $15 \text{ m}$ deep. Calculate the minimum power required for the pump. [3]
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11. A projectile is launched at an angle $\theta$ to the horizontal with velocity $u$. Show that the kinetic energy at the highest point of its trajectory is $KE = \frac{1}{2}mu^2\cos^2\theta$. [2]
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12. A $0.10 \text{ kg}$ ball bounces off a hard floor. It hits the floor at $4.0 \text{ m s}^{-1}$ and rebounds at $3.0 \text{ m s}^{-1}$. Calculate the energy lost during the collision. [2]
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Section C: Nuclear Energy and Power Laws (Questions 13–20)

13. Explain what is meant by the binding energy of a nucleus. [2]
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14. The mass of a ${}^{12}\text{C}$ nucleus is $11.001 \text{ u}$. The mass of a proton is $1.00727 \text{ u}$ and a neutron is $1.00866 \text{ u}$. Calculate the mass defect of the ${}^{12}\text{C}$ nucleus. [2]
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15. Using your answer to Question 14, calculate the binding energy of the ${}^{12}\text{C}$ nucleus in MeV. ($1 \text{ u} = 931.5 \text{ MeV}/c^2$) [2]
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16. In a nuclear fusion reaction, two light nuclei combine to form a heavier nucleus. Explain why energy is released during this process. [3]
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17. A variable $x$ and a current $I$ are related by a power law $x = kI^n$. If $x$ increases by a factor of 8 when $I$ is doubled, determine the value of the constant $n$. [3]
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18. For the power law $x = kI^n$ mentioned in Question 17, describe how a graph of $\log x$ against $\log I$ can be used to find $k$. [3]
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19. A radioactive sample has an activity of $200 \text{ Bq}$. If each decay releases $5.0 \text{ MeV}$ of energy, calculate the total power output of the sample in Watts. [3]
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20. A particle of mass $m$ is accelerated from rest through a potential difference $V$. Derive an expression for its final velocity $v$. [3]
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Answer Key - A-Level Physics H2 Quiz: Energy Power

Section A: Fundamental Concepts

1. Power: The rate of energy transfer or the rate at which work is done. [1]
2. $F = \mu R = 0.40 \times (2.5 \times 9.81) = 9.81 \text{ N}$. $P = Fv = 9.81 \times 3.0 = 29.4 \text{ W}$. [2]
3. Conservation of Energy: Energy cannot be created or destroyed; it can only be converted from one form to another. The total energy of a closed system remains constant. [1]
4. $P = V^2/R \implies R = V^2/P = 240^2 / 60 = 960 \ \Omega$. [2]
5. Energy is lost to the surroundings as heat (due to friction/resistance) or sound, meaning not all chemical energy from fuel is converted into useful mechanical work. [2]

Section B: Mechanics and Energy

6. $KE = mgh = 0.20 \times 9.81 \times 5.0 = 9.81 \text{ J}$. [2]
7. $\Delta KE = \frac{1}{2}mv^2 = 0.5 \times 1200 \times 20^2 = 240,000 \text{ J}$. $P_{\text{avg}} = \Delta E / t = 240,000 / 8.0 = 30,000 \text{ W}$ (or $30 \text{ kW}$). [3]
8. $E_p = \frac{1}{2}kx^2$. [1]
9. $h = 2.0 \sin(30^\circ) = 1.0 \text{ m}$. $mgh = \frac{1}{2}mv^2 \implies v = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 1.0} = 4.43 \text{ m s}^{-1}$. [3]
10. $m = 100 \text{ kg}$, $h = 15 \text{ m}$, $t = 60 \text{ s}$. $P = mgh/t = (100 \times 9.81 \times 15) / 60 = 245 \text{ W}$. [3]
11. At highest point, $v_y = 0$, $v_x = u\cos\theta$. $KE = \frac{1}{2}m(u\cos\theta)^2 = \frac{1}{2}mu^2\cos^2\theta$. [2]
12. $\Delta KE = \frac{1}{2}m(v_1^2 - v_2^2) = 0.5 \times 0.10 \times (4.0^2 - 3.0^2) = 0.05 \times (16 - 9) = 0.35 \text{ J}$. [2]

Section C: Nuclear Energy and Power Laws

13. Binding Energy: The minimum energy required to completely separate a nucleus into its constituent protons and neutrons. [2]
14. Mass of constituents $= 6(1.00727) + 6(1.00866) = 6.04362 + 6.05196 = 12.09558 \text{ u}$. $\Delta m = 12.09558 - 11.001 = 1.09458 \text{ u}$ (Note: Example values used for template; actual C-12 mass is closer to 12.000, but calculation follows provided numbers). [2]
15. $BE = 1.09458 \times 931.5 = 1019 \text{ MeV}$. [2]
16. The mass of the resulting nucleus is less than the sum of the masses of the original nuclei (mass defect). This mass difference is converted into energy according to $E = \Delta mc^2$. [3]
17. $x = kI^n \implies 8x_0 = k(2I_0)^n \implies 8x_0 = 2^n (kI_0^n) \implies 8 = 2^n \implies n = 3$. [3]
18. $\log x = n \log I + \log k$. The graph is a straight line where the y-intercept is $\log k$. To find $k$, take the antilog of the y-intercept ($k = 10^{\text{intercept}}$). [3]
19. Power $= \text{Activity} \times \text{Energy per decay}$. $P = 200 \text{ s}^{-1} \times (5.0 \times 10^6 \times 1.6 \times 10^{-19} \text{ J}) = 200 \times 8.0 \times 10^{-13} = 1.6 \times 10^{-10} \text{ W}$. [3]
20. $W = qV = \frac{1}{2}mv^2 \implies v = \sqrt{2qV/m}$. [3]