A Level H2 Physics Mechanics Quiz

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A-Level Physics H2 Quiz - Mechanics

Name: ____________________
Class: ____________________
Date: ____________________
Score: ________ / 65

Duration: 90 Minutes
Total Marks: 65

Instructions:

• Answer all questions.
• Use $g = 9.81 \text{ m s}^{-2}$ unless otherwise stated.
• Show all working clearly.
• Give your answers to an appropriate number of significant figures.

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Section A: Fundamentals & Kinematics (Questions 1–5)

1. State the principle of conservation of linear momentum. [2]
   
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2. A projectile is launched at an angle $\theta$ to the horizontal. Explain why the horizontal component of its velocity remains constant throughout the flight, assuming air resistance is negligible. [2]
   
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3. A car accelerates uniformly from rest to a speed of $24 \text{ m s}^{-1}$ over a distance of $80 \text{ m}$. Calculate the acceleration of the car. [2]
   
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4. A ball is thrown vertically upwards. Sketch the velocity-time graph for the ball from the moment it is released until it returns to the thrower's hand. [2]
   
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5. Define the term displacement and explain how it differs from distance. [2]
   
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Section B: Dynamics & Energy (Questions 6–12)

6. A block of mass $2.0 \text{ kg}$ is pushed along a rough horizontal surface with a constant force of $15 \text{ N}$. If the coefficient of kinetic friction is $0.30$, calculate the acceleration of the block. [3]
   
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7. State Newton's Second Law of Motion in terms of the rate of change of momentum. [2]
   
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8. A $0.5 \text{ kg}$ object is dropped from a height of $10 \text{ m}$. Calculate its kinetic energy immediately before it hits the ground. [2]
   
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9. Two trolleys, $m_1 = 1.5 \text{ kg}$ and $m_2 = 2.5 \text{ kg}$, move towards each other with speeds $2.0 \text{ m s}^{-1}$ and $1.0 \text{ m s}^{-1}$ respectively. They collide and stick together. Calculate the final velocity of the combined mass. [3]
   
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10. Explain the difference between an elastic collision and an inelastic collision in terms of kinetic energy. [2]
    
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11. A force $F = (2.0\hat{i} - 3.0\hat{j}) \text{ N}$ acts on a particle of mass $0.1 \text{ kg}$. Calculate the magnitude of the acceleration of the particle. [3]
    
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12. A $0.2 \text{ kg}$ mass is attached to a spring with a spring constant $k = 20 \text{ N m}^{-1}$. If the mass is displaced $5 \text{ cm}$ from equilibrium and released, calculate the maximum acceleration of the mass. [3]
    
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Section C: Circular Motion & Gravitation (Questions 13–20)

13. A particle of mass $m$ moves in a horizontal circle of radius $r$ at a constant speed $v$. State the expression for the centripetal acceleration and identify the direction of the force causing it. [2]
    
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14. A $1.2 \text{ kg}$ mass is swung in a vertical circle of radius $0.8 \text{ m}$. At the top of the circle, the tension in the string is $2.0 \text{ N}$. Calculate the speed of the mass at this point. [3]
    
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15. A car travels over a convex bridge of radius $20 \text{ m}$. If the car's mass is $1200 \text{ kg}$ and it travels at $10 \text{ m s}^{-1}$, calculate the normal reaction force between the tires and the road at the peak of the bridge. [3]
    
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16. State Kepler's Third Law regarding the relationship between the orbital period $T$ and the orbital radius $r$ of a planet. [2]
    
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17. A satellite of mass $500 \text{ kg}$ orbits Earth at a height of $300 \text{ km}$ above the surface. Given Earth's mass $M = 5.97 \times 10^{24} \text{ kg}$ and radius $R = 6.37 \times 10^6 \text{ m}$, calculate the orbital speed of the satellite. [4]
    
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18. Define gravitational potential at a point in a gravitational field. [2]
    
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19. Calculate the escape velocity from the surface of a planet with mass $M$ and radius $R$. (Show the derivation steps). [5]
    
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20. A small sphere of mass $0.1 \text{ kg}$ is suspended by a string of length $1.0 \text{ m}$ and rotated in a horizontal circle (conical pendulum). If the string makes an angle of $15^\circ$ with the vertical, calculate the period of rotation. [4]
    
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A-Level Physics H2 Quiz - Mechanics (Answer Key)

1. Answer: In a closed system (or isolated system), the total momentum before an event equals the total momentum after the event, provided no external forces act. [2]

   • 1 mark for "closed/isolated system".
   • 1 mark for "total momentum before = total momentum after" and "no external forces".

2. Answer: In the absence of air resistance, there is no force acting in the horizontal direction. According to Newton's First Law, if the net force is zero, the acceleration is zero, thus the velocity remains constant. [2]

3. Answer: $v^2 = u^2 + 2as \implies 24^2 = 0 + 2(a)(80) \implies 576 = 160a \implies a = 3.6 \text{ m s}^{-2}$. [2]

4. Answer: A straight line starting at $+v$, sloping downwards with a constant negative gradient (representing $-g$), crossing the x-axis (peak height), and ending at $-v$. [2]

5. Answer: Displacement is the straight-line distance from the start point to the end point in a specific direction (vector). Distance is the total path length traveled (scalar). [2]

6. Answer: $F_{net} = F_{push} - f_k = 15 - (0.30 \times 2.0 \times 9.81) = 15 - 5.886 = 9.114 \text{ N}$. $a = F_{net}/m = 9.114 / 2.0 = 4.56 \text{ m s}^{-2}$. [3]

7. Answer: The resultant force acting on an object is equal to the rate of change of its momentum: $F = \frac{dp}{dt}$. [2]

8. Answer: $KE = mgh = 0.5 \times 9.81 \times 10 = 49.05 \text{ J} \approx 49 \text{ J}$. [2]

9. Answer: $m_1u_1 + m_2u_2 = (m_1+m_2)v \implies (1.5 \times 2.0) + (2.5 \times -1.0) = (1.5+2.5)v$ $3.0 - 2.5 = 4.0v \implies 0.5 = 4.0v \implies v = 0.125 \text{ m s}^{-1}$ (in direction of $m_1$). [3]

10. Answer: In an elastic collision, total kinetic energy is conserved. In an inelastic collision, total kinetic energy is not conserved (some is converted to heat/sound/deformation). [2]

11. Answer: $F_{net} = \sqrt{2^2 + (-3)^2} = \sqrt{4+9} = \sqrt{13} = 3.61 \text{ N}$. $a = F/m = 3.61 / 0.1 = 36.1 \text{ m s}^{-2}$. [3]

12. Answer: $\omega^2 = k/m = 20/0.2 = 100 \implies \omega = 10 \text{ rad s}^{-1}$. $a_{max} = \omega^2 X_0 = 100 \times 0.05 = 5.0 \text{ m s}^{-2}$. [3]

13. Answer: $a = v^2/r$. The force is the centripetal force, directed towards the center of the circle. [2]

14. Answer: $T + mg = mv^2/r \implies 2.0 + (1.2 \times 9.81) = 1.2(v^2/0.8)$ $2.0 + 11.77 = 1.5v^2 \implies 13.77 = 1.5v^2 \implies v = \sqrt{9.18} = 3.03 \text{ m s}^{-1}$. [3]

15. Answer: $mg - N = mv^2/r \implies N = m(g - v^2/r) = 1200(9.81 - 10^2/20) = 1200(9.81 - 5) = 5772 \text{ N}$. [3]

16. Answer: The square of the orbital period $T$ is proportional to the cube of the semi-major axis (or radius) $r$: $T^2 \propto r^3$. [2]

17. Answer: $r = 6.37 \times 10^6 + 300,000 = 6.67 \times 10^6 \text{ m}$. $v = \sqrt{GM/r} = \sqrt{(6.67 \times 10^{-11} \times 5.97 \times 10^{24}) / 6.67 \times 10^6} = \sqrt{5.97 \times 10^7} = 7726 \text{ m s}^{-1}$. [4]

18. Answer: The work done per unit mass in bringing a mass from infinity to that point in the gravitational field. [2]

19. Answer: $KE + PE = 0 \implies \frac{1}{2}mv^2 - GMm/R = 0 \implies \frac{1}{2}v^2 = GM/R \implies v = \sqrt{2GM/R}$. [5]

    • 1 mark for energy balance.
    • 2 marks for substitution of PE and KE.
    • 2 marks for final expression.

20. Answer: $T \cos(15^\circ) = mg$ and $T \sin(15^\circ) = mv^2/r$. $\tan(15^\circ) = v^2/(rg)$. $r = L \sin(15^\circ) = 1.0 \times 0.2588 = 0.2588 \text{ m}$. $v^2 = 0.2588 \times 9.81 \times \tan(15^\circ) = 2.539 \times 0.2679 = 0.68 \implies v = 0.825 \text{ m s}^{-1}$. $Period = 2\pi r / v = (2\pi \times 0.2588) / 0.825 = 1.97 \text{ s}$. [4]