A Level H1 Physics Mechanics Quiz

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A-Level Physics H1 Quiz - Mechanics

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

Duration: 75 Minutes
Total Marks: 55
Instructions: Answer all questions. Show all working for calculation questions. Use $g = 9.81 \text{ m s}^{-2}$ unless otherwise stated.

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Section A: Fundamental Concepts (Questions 1-5)

1. State the principle of conservation of linear momentum. [2]
   
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2. Write down the expressions for: (a) Momentum $p$ in terms of mass $m$ and velocity $v$. [1] (b) Kinetic energy $K$ in terms of mass $m$ and velocity $v$. [1]
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3. Define a "closed system" in the context of Newtonian mechanics. [2]
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4. A particle has a momentum of $12.0 \text{ kg m s}^{-1}$ and a kinetic energy of $36.0 \text{ J}$. Calculate the mass of the particle. [3]
   
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5. Distinguish between a scalar and a vector quantity, providing one example of each from the study of kinematics. [2]
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Section B: Kinematics and Dynamics (Questions 6-12)

6. A ball is dropped from a height. Sketch a graph of vertical speed $v$ against time $t$ considering the effect of air resistance. [2]
   
   
   
   
   
   
   
   
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7. Using your graph in Question 6, explain why the gradient of the curve decreases over time. [2]
   
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8. A projectile is launched at an angle $\theta$ to the horizontal. Explain why the horizontal component of its velocity remains constant throughout the flight (neglecting air resistance). [2]
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9. A block of mass $2.0 \text{ kg}$ 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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10. State Newton's Second Law of Motion in terms of momentum. [2]
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11. A $0.5 \text{ kg}$ ball moving at $4.0 \text{ m s}^{-1}$ strikes a stationary $0.5 \text{ kg}$ ball head-on. If the collision is perfectly elastic, determine the final velocity of the first ball. [3]
    
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12. Explain the difference between an elastic collision and an inelastic collision in terms of kinetic energy. [2]
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Section C: Forces, Energy, and Equilibrium (Questions 13-20)

13. A uniform plank AB of length $4.0 \text{ m}$ and weight $200 \text{ N}$ is supported by two pillars at its ends. A man of weight $800 \text{ N}$ stands $1.0 \text{ m}$ from end A. Draw a free-body diagram of the plank, labeling all forces. [3]
    
    
    
    
    
    
    
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14. For the plank in Question 13, calculate the reaction force at support B. [3]
    
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15. Define the "moment of a force" and state its SI unit. [2]
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16. A $1.5 \text{ kg}$ object is lifted vertically at a constant speed of $2.0 \text{ m s}^{-1}$. Calculate the power output required to lift the object. [3]
    
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17. A spring with force constant $k = 500 \text{ N m}^{-1}$ is compressed by $0.05 \text{ m}$. Calculate the elastic potential energy stored in the spring. [2]
    
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18. A car of mass $1200 \text{ kg}$ decelerates from $20 \text{ m s}^{-1}$ to $10 \text{ m s}^{-1}$ over a distance of $30 \text{ m}$. Calculate the average braking force. [3]
    
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19. Explain the principle of conservation of energy in the context of a falling object with air resistance. [3]
    
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20. A $0.2 \text{ kg}$ mass is attached to a string and swung in a vertical circle of radius $0.5 \text{ m}$. Calculate the tension in the string at the lowest point of the swing if the speed is $5.0 \text{ m s}^{-1}$. [4]
    
    
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A-Level Physics H1 Quiz - Mechanics (Answers)

1. Conservation of Linear Momentum

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

2. Expressions

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

3. Closed System

   • [B2] A system where no external forces act, or the net external force is zero, meaning momentum is only exchanged between objects within the system.

4. Calculation (Mass)

   • $p = 12.0$, $K = 36.0$
   • $K = \frac{p^2}{2m} \implies m = \frac{p^2}{2K}$ [M1]
   • $m = \frac{12^2}{2 \times 36} = \frac{144}{72}$ [M1]
   • $m = 2.0 \text{ kg}$ [A1]

5. Scalar vs Vector

   • [B1] Scalar has magnitude only (e.g., speed, distance); Vector has magnitude and direction (e.g., velocity, displacement). [B1]

6. Graph

   • [B2] Curve starting at origin, increasing gradient, then flattening out to a horizontal asymptote (terminal velocity).

7. Graph Explanation

   • [B1] As speed increases, the drag force (air resistance) increases.
   • [B1] The net downward force ($W - D$) decreases, leading to a decrease in acceleration.

8. Projectile Motion

   • [B2] There are no horizontal forces acting on the projectile (neglecting air resistance), so according to Newton's First Law, the horizontal velocity remains constant.

9. Acceleration Calculation

   • $F_{net} = F_{applied} - f_k = 10 - (0.3 \times 2.0 \times 9.81)$ [M1]
   • $F_{net} = 10 - 5.886 = 4.114 \text{ N}$ [M1]
   • $a = F/m = 4.114 / 2.0 = 2.06 \text{ m s}^{-2}$ [A1]

10. Newton's Second Law

    • [B2] The rate of change of momentum of an object is directly proportional to the net force acting on it and takes place in the direction of the force ($\text{Force} = \Delta p / \Delta t$).

11. Elastic Collision

    • Since masses are equal and collision is elastic, velocities are exchanged.
    • [M1] Initial: $v_1 = 4, v_2 = 0$.
    • [M1] Final: $v_1 = 0, v_2 = 4$.
    • [A1] Final velocity of first ball = $0 \text{ m s}^{-1}$.

12. Collision Types

    • [B1] In an elastic collision, total kinetic energy is conserved.
    • [B1] In an inelastic collision, some kinetic energy is converted to other forms (heat, sound, deformation).

13. Free-Body Diagram

    • [B1] Weight of plank ($200 \text{ N}$) at center ($2.0 \text{ m}$ from A).
    • [B1] Weight of man ($800 \text{ N}$) at $1.0 \text{ m}$ from A.
    • [B1] Upward reaction forces $R_A$ and $R_B$ at ends.

14. Reaction Force $R_B$

    • Take moments about A: $\sum M_A = 0$ [M1]
    • $(800 \times 1.0) + (200 \times 2.0) - (R_B \times 4.0) = 0$ [M1]
    • $800 + 400 = 4 R_B \implies R_B = 1200 / 4 = 300 \text{ N}$ [A1]

15. Moment

    • [B1] The product of the force and the perpendicular distance from the pivot to the line of action of the force.
    • [B1] Unit: Newton-metre ($\text{N m}$).

16. Power Calculation

    • $F = mg = 1.5 \times 9.81 = 14.715 \text{ N}$ [M1]
    • $P = Fv = 14.715 \times 2.0$ [M1]
    • $P = 29.4 \text{ W}$ [A1]

17. Elastic PE

    • $E = \frac{1}{2}kx^2 = 0.5 \times 500 \times (0.05)^2$ [M1]
    • $E = 0.625 \text{ J}$ [A1]

18. Braking Force

    • $v^2 = u^2 + 2as \implies 10^2 = 20^2 + 2(a)(30)$ [M1]
    • $100 = 400 + 60a \implies a = -300/60 = -5 \text{ m s}^{-2}$ [M1]
    • $F = ma = 1200 \times 5 = 6000 \text{ N}$ [A1]

19. Energy Conservation

    • [B1] Total energy is conserved, but mechanical energy is not.
    • [B1] Gravitational potential energy is converted into kinetic energy and thermal energy.
    • [B1] Thermal energy is generated due to work done against air resistance.

20. Tension Calculation

    • At bottom: $T - mg = mv^2/r$ [M1]
    • $T = (0.2 \times 9.81) + (0.2 \times 5^2 / 0.5)$ [M1]
    • $T = 1.962 + (0.2 \times 25 / 0.5) = 1.962 + 10$ [M1]
    • $T = 11.96 \text{ N}$ [A1]