A Level H1 Physics Practice Paper 3

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A-Level Physics H1 Quiz - Mechanics

Name: ____________________
Class: ____________________
Date: ____________________
Score: ________ / 60

Duration: 60 Minutes
Total Marks: 60
Instructions: Answer all questions. Show all working clearly. Use $g = 9.81\text{ m s}^{-1}$.

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Section A: Kinematics and Dynamics (Questions 1–7)

1. State the principle of conservation of linear momentum. [2]
   
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2. A particle has a horizontal momentum of $12.0\text{ kg m s}^{-1}$ and a kinetic energy of $36.0\text{ J}$. Calculate the mass and velocity of the particle. [3]
   
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3. A ball is thrown from the edge of a cliff of height $20.0\text{ m}$ with a horizontal velocity of $15.0\text{ m s}^{-1}$. Calculate the time taken to reach the ground and the horizontal distance traveled. [3]
   
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4. Sketch a graph of vertical speed versus time for an object falling from rest in a medium with air resistance. Label the terminal velocity $v_T$. [2]
   
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5. Explain the shape of the graph sketched in Question 4, referring to the net force acting on the object. [2]
   
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6. A projectile is launched at $25.0\text{ m s}^{-1}$ at an angle of $40^\circ$ to the horizontal. Determine the maximum height reached. [3]
   
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7. A $0.5\text{ kg}$ block is pushed across a rough horizontal surface with a constant force of $10\text{ N}$. If the coefficient of friction is $0.3$, calculate the acceleration of the block. [3]
   
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Section B: Momentum and Collisions (Questions 8–14)

8. Distinguish between an elastic collision and an inelastic collision. [2]
   
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9. A $0.2\text{ kg}$ trolley moving at $3.0\text{ m s}^{-1}$ collides with a stationary $0.3\text{ kg}$ trolley. They stick together after the collision. Calculate their common velocity. [3]
   
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10. In the collision described in Question 9, calculate the loss in kinetic energy. [3]
    
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11. A $0.1\text{ kg}$ mass moving at $4.0\text{ m s}^{-1}$ hits a stationary $0.1\text{ kg}$ mass. After the collision, the first mass moves at $2.0\text{ m s}^{-1}$ at $30^\circ$ to the original path. Determine the final velocity (magnitude and direction) of the second mass. [4]
    
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12. Define "Impulse" and state its relationship to the force-time graph. [2]
    
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13. A tennis ball of mass $0.06\text{ kg}$ hits a wall at $20\text{ m s}^{-1}$ and rebounds at $18\text{ m s}^{-1}$. If the contact time is $0.01\text{ s}$, calculate the average force exerted by the wall. [3]
    
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14. Two particles of equal mass $m$ move toward each other with speeds $u$ and $v$. If they collide elastically and head-on, show that they exchange their velocities. [3]
    
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Section C: Forces, Energy, and Power (Questions 15–20)

15. A uniform plank of length $4.0\text{ m}$ and weight $100\text{ N}$ is supported by two pivots at its ends. A $600\text{ N}$ person stands $1.0\text{ m}$ from the left end. Calculate the reaction force at each pivot. [4]
    
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16. Define "Work Done" and state the condition under which a force does no work on an object. [2]
    
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17. A $2.0\text{ kg}$ object is pulled up a smooth incline of $30^\circ$ at a constant speed of $1.5\text{ m s}^{-1}$. Calculate the power delivered by the pulling force. [3]
    
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18. A motor of input power $1.2\text{ kW}$ is used to lift a $50\text{ kg}$ mass vertically at a constant speed of $0.8\text{ m s}^{-1}$. Calculate the efficiency of the motor. [3]
    
    
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19. An object of mass $m$ is dropped from height $h$. Using the principle of conservation of energy, derive an expression for the speed of the object just before it hits the ground. [2]
    
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20. A car of mass $1200\text{ kg}$ accelerates from $0$ to $27\text{ m s}^{-1}$ in $10\text{ s}$. If the total resistive force is $400\text{ N}$, calculate the average power output of the engine. [4]
    
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A-Level Physics H1 Quiz - Mechanics (Answer Key)

Section A: Kinematics and Dynamics

1. [2 marks]

   • [B1] In a closed/isolated system, the total linear momentum remains constant.
   • [B1] Provided no external forces act on the system.

2. [3 marks]

   • $p = mv \rightarrow v = p/m$ and $K = \frac{1}{2}mv^2$
   • Substitute $v$: $K = \frac{1}{2}m(p/m)^2 = p^2 / 2m$
   • $m = p^2 / 2K = (12.0)^2 / (2 \times 36.0) = 144 / 72 = 2.0\text{ kg}$ [M1, A1]
   • $v = 12.0 / 2.0 = 6.0\text{ m s}^{-1}$ [A1]

3. [3 marks]

   • Vertical: $s = \frac{1}{2}gt^2 \rightarrow 20.0 = 0.5(9.81)t^2 \rightarrow t = \sqrt{4.077} = 2.02\text{ s}$ [M1, A1]
   • Horizontal: $x = vt = 15.0 \times 2.02 = 30.3\text{ m}$ [A1]

4. [2 marks]

   • [B1] Graph: Speed on y-axis, Time on x-axis. Curve starts at $(0,0)$, increases with decreasing gradient, and levels off at a horizontal asymptote $v_T$.
   • [B1] Correct labeling of $v_T$.

5. [2 marks]

   • [B1] As speed increases, air resistance (drag) increases.
   • [B1] Net force ($W - \text{Drag}$) decreases, causing acceleration to decrease until net force is zero at terminal velocity.

6. [3 marks]

   • $u_y = 25.0 \sin 40^\circ = 16.07\text{ m s}^{-1}$ [M1]
   • $v_y^2 = u_y^2 + 2as \rightarrow 0 = (16.07)^2 - 2(9.81)h$
   • $h = (16.07)^2 / 19.62 = 13.16\text{ m}$ [A1, A1]

7. [3 marks]

   • $F_{\text{net}} = F_{\text{push}} - f_k = 10 - \mu mg$
   • $F_{\text{net}} = 10 - (0.3 \times 0.5 \times 9.81) = 10 - 1.47 = 8.53\text{ N}$ [M1]
   • $a = F_{\text{net}} / m = 8.53 / 0.5 = 17.06\text{ m s}^{-2}$ [A1, A1]

Section B: Momentum and Collisions

8. [2 marks]

   • [B1] Elastic: Both momentum and kinetic energy are conserved.
   • [B1] Inelastic: Momentum is conserved, but kinetic energy is not (some converted to heat/sound).

9. [3 marks]

   • $m_1u_1 + m_2u_2 = (m_1 + m_2)v$
   • $(0.2 \times 3.0) + 0 = (0.2 + 0.3)v$ [M1]
   • $0.6 = 0.5v \rightarrow v = 1.2\text{ m s}^{-1}$ [A1, A1]

10. [3 marks]

    • $K_{\text{initial}} = \frac{1}{2}(0.2)(3.0)^2 = 0.9\text{ J}$ [M1]
    • $K_{\text{final}} = \frac{1}{2}(0.5)(1.2)^2 = 0.36\text{ J}$ [M1]
    • Loss $= 0.9 - 0.36 = 0.54\text{ J}$ [A1]

11. [4 marks]

    • $x$-axis: $0.1(4) = 0.1(2\cos 30^\circ) + 0.1v_{2x} \rightarrow v_{2x} = 4 - 1.732 = 2.268\text{ m s}^{-1}$ [M1]
    • $y$-axis: $0 = 0.1(2\sin 30^\circ) + 0.1v_{2y} \rightarrow v_{2y} = -1.0\text{ m s}^{-1}$ [M1]
    • $v_2 = \sqrt{2.268^2 + (-1.0)^2} = 2.48\text{ m s}^{-1}$ [A1]
    • $\theta = \tan^{-1}(-1.0 / 2.268) = -23.8^\circ$ (below original path) [A1]

12. [2 marks]

    • [B1] Impulse is the change in momentum ($\Delta p$).
    • [B1] It is equal to the area under a force-time graph.

13. [3 marks]

    • $\Delta p = m(v - u) = 0.06(18 - (-20)) = 0.06(38) = 2.28\text{ kg m s}^{-1}$ [M1]
    • $F_{\text{avg}} = \Delta p / t = 2.28 / 0.01 = 228\text{ N}$ [A1, A1]

14. [3 marks]

    • Momentum: $mu + mv = mv' + mu'$
    • Energy: $\frac{1}{2}mu^2 + \frac{1}{2}mv^2 = \frac{1}{2}m(u')^2 + \frac{1}{2}m(v')^2$
    • Solving these simultaneous equations for equal masses leads to $u' = v$ and $v' = u$. [M1, A1, A1]

Section C: Forces, Energy, and Power

15. [4 marks]

    • Let $R_L$ and $R_R$ be reactions.
    • Moments about $L$: $(100 \times 2.0) + (600 \times 1.0) - (R_R \times 4.0) = 0$
    • $200 + 600 = 4R_R \rightarrow R_R = 200\text{ N}$ [M1, A1]
    • Vertical equilibrium: $R_L + R_R = 100 + 600$
    • $R_L = 700 - 200 = 500\text{ N}$ [M1, A1]

16. [2 marks]

    • [B1] Work done is the product of the force and the displacement in the direction of the force ($W = Fs\cos\theta$).
    • [B1] No work is done if the force is perpendicular to the displacement ($\theta = 90^\circ$) or if displacement is zero.

17. [3 marks]

    • $F = mg\sin 30^\circ = (2.0 \times 9.81 \times 0.5) = 9.81\text{ N}$ [M1]
    • $P = Fv = 9.81 \times 1.5 = 14.72\text{ W}$ [A1, A1]

18. [3 marks]

    • $P_{\text{out}} = Fv = (50 \times 9.81) \times 0.8 = 392.4\text{ W}$ [M1]
    • $\text{Efficiency} = (392.4 / 1200) \times 100\% = 32.7\%$ [A1, A1]

19. [2 marks]

    • $mgh = \frac{1}{2}mv^2$ [B1]
    • $v = \sqrt{2gh}$ [B1]

20. [4 marks]

    • $a = (27 - 0) / 10 = 2.7\text{ m s}^{-2}$ [M1]
    • $F_{\text{engine}} = ma + F_{\text{resist}} = (1200 \times 2.7) + 400 = 3240 + 400 = 3640\text{ N}$ [M1, A1]
    • $P_{\text{avg}} = F_{\text{engine}} \times v_{\text{avg}} = 3640 \times (27/2) = 3640 \times 13.5 = 49,140\text{ W}$ (or $49.1\text{ kW}$) [A1]