A Level H1 Physics Practice Paper 2

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A-Level Physics H1 Quiz - Mechanics

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

Duration: 60 Minutes
Total Marks: 55 Marks

Instructions:

• Answer all questions.
• Use $g = 9.81\text{ m s}^{-2}$ unless otherwise stated.
• Show all working clearly for calculation questions.
• Use a scientific calculator where necessary.

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

1. State the principle of conservation of linear momentum. [2]
   
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2. Write down the expressions for the momentum $p$ and kinetic energy $K$ of a particle of mass $m$ moving with velocity $v$. [2] (a) $p =$ ____________________ (b) $K =$ ____________________

3. A small metal sphere has a horizontal momentum of $0.45\text{ N s}$ and a kinetic energy of $0.12\text{ J}$. Calculate the mass and velocity of the sphere. [3]
   
   
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4. A ball is dropped from a height of $20\text{ m}$. Sketch the graph of vertical speed $v$ against time $t$ for the ball's motion, taking into account the effect of air resistance. [2]
   
   
   (Space for graph)
   
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5. Explain the shape of the graph you sketched in Question 4, specifically referring to the concept of terminal velocity. [2]
   
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6. A projectile is launched with an initial velocity $u$ at an angle $\theta$ to the horizontal. State the acceleration of the projectile in the horizontal direction, assuming no air resistance. [1]
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7. A car accelerates uniformly from $10\text{ m s}^{-1}$ to $25\text{ m s}^{-1}$ over a distance of $100\text{ m}$. Calculate the acceleration of the car. [3]
   
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Section B: Dynamics and Forces (Questions 8–14)

8. Define the term impulse and state its SI unit. [2]
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9. 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 kinetic friction is $0.3$, calculate the acceleration of the block. [3]
   
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10. A uniform plank AB of length $4.0\text{ m}$ and weight $120\text{ N}$ is placed across two supports. A person of weight $600\text{ N}$ stands at a distance $x$ from end A. Draw a free-body diagram of the plank, labeling all forces acting on it. [3]
    
    (Space for diagram)
    
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11. Using the scenario in Question 10, if the plank is in equilibrium and the supports are at the ends A and B, calculate the reaction force at support B when the person is $1.0\text{ m}$ from end A. [4]
    
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12. Two trolleys, A ($1.0\text{ kg}$) and B ($2.0\text{ kg}$), move toward each other with speeds $3.0\text{ m s}^{-1}$ and $2.0\text{ m s}^{-1}$ respectively. They collide and stick together. Calculate the final velocity of the combined mass. [3]
    
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13. Distinguish between an elastic collision and an inelastic collision in terms of kinetic energy. [2]
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14. A $2.0\text{ kg}$ object is acted upon by two perpendicular forces: $F_1 = 6.0\text{ N}$ and $F_2 = 8.0\text{ N}$. Calculate the magnitude of the resultant acceleration. [3]
    
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Section C: Work, Energy, and Power (Questions 15–20)

15. Define work done by a force and state the condition under which no work is done even if a force is applied. [2]
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16. A $0.2\text{ kg}$ ball is thrown vertically upwards with an initial speed of $15\text{ m s}^{-1}$. Calculate the maximum height reached by the ball, ignoring air resistance. [3]
    
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17. A motor lifts a $50\text{ kg}$ load through a height of $10\text{ m}$ in $5.0\text{ s}$. Calculate the average power output of the motor. [3]
    
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18. A car of mass $1200\text{ kg}$ travels at a constant speed of $30\text{ m s}^{-1}$. If the total resistive force is $600\text{ N}$, calculate the power required to maintain this speed. [3]
    
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19. An object of mass $m$ is compressed against a spring of spring constant $k$ by a distance $x$. If the object is released, derive an expression for the maximum speed $v$ of the object. [3]
    
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20. A $0.1\text{ kg}$ block slides down a rough inclined plane at $30^\circ$ to the horizontal. If the block starts from rest and slides $2.0\text{ m}$ before stopping, calculate the work done against friction. [4]
    
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Answer Key - A-Level Physics H1 Quiz (Mechanics)

1. In a closed/isolated system, the total linear momentum remains constant provided no external forces act. [B1 for constant momentum, B1 for no external forces]

2. (a) $p = mv$ [B1] (b) $K = \frac{1}{2}mv^2$ [B1]

3.

• $p = mv \implies v = p/m$
• $K = \frac{1}{2}mv^2 \implies K = \frac{1}{2}m(p/m)^2 = p^2 / 2m$ [M1]
• $m = p^2 / 2K = (0.45)^2 / (2 \times 0.12) = 0.2025 / 0.24 = 0.844\text{ kg}$ [A1]
• $v = 0.45 / 0.844 = 0.533\text{ m s}^{-1}$ [A1]

4. Graph should show a curve starting from origin, increasing gradient initially, then flattening off to a horizontal asymptote (terminal velocity). [B2]

5. As speed increases, the air resistance (drag) increases. [B1] The net downward force ($W - \text{Drag}$) decreases, causing acceleration to decrease until it becomes zero when air resistance equals weight, resulting in a constant terminal velocity. [B1]

6. $0\text{ m s}^{-2}$ (Acceleration is zero in the horizontal direction). [B1]

7. $v^2 = u^2 + 2as \implies (25)^2 = (10)^2 + 2a(100)$ [M1]

• $625 = 100 + 200a$
• $525 = 200a$
• $a = 2.625\text{ m s}^{-2}$ [A2]

8. Impulse is the product of the force acting on an object and the time interval over which it acts (or the change in momentum). [B1] Unit: $\text{N s}$ or $\text{kg m s}^{-1}$. [B1]

9. $F_{\text{net}} = F_{\text{push}} - f_k = 10 - (0.3 \times 0.5 \times 9.81)$ [M1]

• $F_{\text{net}} = 10 - 1.47 = 8.53\text{ N}$ [M1]
• $a = F_{\text{net}} / m = 8.53 / 0.5 = 17.06\text{ m s}^{-2}$ [A1]

10. Diagram must show:

• Weight of plank ($120\text{ N}$) acting at the center ($2.0\text{ m}$ from A). [B1]
• Weight of person ($600\text{ N}$) acting at distance $x$. [B1]
• Upward reaction forces $R_A$ and $R_B$ at ends A and B. [B1]

11. Take moments about A:

• $\sum \text{Clockwise Moments} = \sum \text{Anti-clockwise Moments}$
• $(600 \times 1.0) + (120 \times 2.0) = R_B \times 4.0$ [M1]
• $600 + 240 = 4.0 R_B$ [M1]
• $840 = 4.0 R_B$
• $R_B = 210\text{ N}$ [A2]

12. $m_A u_A + m_B u_B = (m_A + m_B)v$ (taking direction of A as positive) [M1]

• $(1.0 \times 3.0) + (2.0 \times -2.0) = (1.0 + 2.0)v$
• $3.0 - 4.0 = 3.0v$ [M1]
• $-1.0 = 3.0v \implies v = -0.333\text{ m s}^{-1}$ (opposite to A's initial direction) [A1]

13. In an elastic collision, total kinetic energy is conserved. [B1] In an inelastic collision, total kinetic energy is not conserved (some is converted to heat/sound). [B1]

14. $F_{\text{res}} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = 10\text{ N}$ [M1]

• $a = F_{\text{res}} / m = 10 / 2.0 = 5.0\text{ m s}^{-2}$ [A2]

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

16. $mgh = \frac{1}{2}mv^2 \implies h = v^2 / 2g$ [M1]

• $h = (15)^2 / (2 \times 9.81) = 225 / 19.62$ [M1]
• $h = 11.47\text{ m}$ [A1]

17. $W = mgh = 50 \times 9.81 \times 10 = 4905\text{ J}$ [M1]

• $P = W / t = 4905 / 5.0 = 981\text{ W}$ [A2]

18. $P = Fv$ (for constant speed) [M1]

• $P = 600 \times 30 = 18,000\text{ W}$ or $18\text{ kW}$ [A2]

19. Energy conservation: $\frac{1}{2}kx^2 = \frac{1}{2}mv^2$ [M1]

• $v^2 = kx^2 / m$ [M1]
• $v = x \sqrt{k/m}$ [A1]

20. Change in Energy = Work done by friction

• $\Delta E = mgh - 0 = m(s \sin 30^\circ)g$ [M1]
• $W_{\text{fric}} = 0.1 \times (2.0 \times 0.5) \times 9.81$ [M1]
• $W_{\text{fric}} = 0.1 \times 1.0 \times 9.81 = 0.981\text{ J}$ [A2]