A Level H1 Physics Practice Paper 4

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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 necessary working for calculation questions. Use $g = 9.81\text{ m s}^{-2}$ unless otherwise stated.

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Section A: Short Answer & Definitions (Questions 1–5)

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]
   $p =$ ____________________
   $K =$ ____________________

3. Define the term terminal velocity in the context of an object falling through a viscous fluid. [2]
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4. A particle is said to be in equilibrium if the net force acting on it is zero. State the condition for the equilibrium of a rigid body in terms of moments. [2]
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5. Distinguish between a scalar quantity and a vector quantity, providing one example of each from the study of mechanics. [2]
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Section B: Calculations & Applications (Questions 6–15)

6. A projectile is launched from ground level with an initial velocity of $25\text{ m s}^{-1}$ at an angle of $35^\circ$ to the horizontal. Calculate the maximum height reached. [3]
   
   
   
   Answer: ____________________

7. A block of mass $2.0\text{ kg}$ is pushed across a rough horizontal surface with a constant horizontal force of $15\text{ N}$. If the coefficient of kinetic friction is $0.30$, calculate the acceleration of the block. [3]
   
   
   
   Answer: ____________________

8. A small sphere has a horizontal momentum of $4.5\text{ N s}$ and a kinetic energy of $11.25\text{ J}$. Calculate the mass and velocity of the sphere. [3]
   
   
   
   Answer: $m =$ ____________________, $v =$ ____________________

9. A $0.5\text{ kg}$ ball moving at $8\text{ m s}^{-1}$ collides head-on with a stationary $0.8\text{ kg}$ ball. After the collision, the first ball rebounds at $2\text{ m s}^{-1}$. Calculate the final velocity of the second ball. [3]
   
   
   
   Answer: ____________________

10. A uniform beam of length $4.0\text{ m}$ and mass $20\text{ kg}$ is supported by two vertical pillars at its ends. A $60\text{ kg}$ person stands $1.0\text{ m}$ from the left pillar. Calculate the reaction force at the right pillar. [4]
    
    
    
    Answer: ____________________

11. An object of mass $m$ is dropped from rest in air. Sketch a graph of acceleration $a$ against time $t$ until terminal velocity is reached. [3]
    
    
    
    (Sketch below)
    
    
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12. A car of mass $1200\text{ kg}$ accelerates from $10\text{ m s}^{-1}$ to $25\text{ m s}^{-1}$ in $6.0\text{ s}$. Calculate the average net force acting on the car. [3]
    
    
    
    Answer: ____________________

13. A $0.2\text{ kg}$ mass is attached to a spring with a spring constant $k = 200\text{ N m}^{-1}$. If the mass is displaced $0.1\text{ m}$ from equilibrium, calculate the elastic potential energy stored. [3]
    
    
    
    Answer: ____________________

14. A $50\text{ kg}$ crate is pulled up a frictionless incline of $30^\circ$ at a constant speed of $2\text{ m s}^{-1}$ by a force $F$ acting parallel to the incline. Calculate the power delivered by the force $F$. [3]
    
    
    
    Answer: ____________________

15. Two particles of masses $m_1 = 2\text{ kg}$ and $m_2 = 3\text{ kg}$ move towards each other with speeds $4\text{ m s}^{-1}$ and $2\text{ m s}^{-1}$ respectively. If they stick together after a perfectly inelastic collision, calculate the final velocity of the combined mass. [3]
    
    
    
    Answer: ____________________

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Section C: Structured Reasoning & Analysis (Questions 16–20)

16. A ball is dropped from a height $h$. (a) Explain why the speed of the ball does not increase linearly with time. [2] (b) Describe the relationship between the drag force and the velocity of the ball. [2]
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17. A uniform plank AB of length $L$ and weight $W$ is placed across two supports. (a) Draw a free-body diagram of the plank when a weight $P$ is placed at a distance $x$ from end A. [3] (b) Explain how the reaction forces at the supports change as the weight $P$ moves from A towards B. [2]
    
    
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18. Compare and contrast an elastic collision with an inelastic collision in terms of momentum and kinetic energy. [4]
    
    
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19. A mass $M$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal. (a) State the conditions for the mass to be in static equilibrium. [2] (b) Explain how the tension in the strings would change if the angle $\theta_1$ were decreased while $\theta_2$ remained constant. [3]
    
    
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20. A projectile is launched at an angle $\theta$. (a) Explain why the horizontal component of velocity remains constant throughout the flight (neglecting air resistance). [2] (b) Show that the time of flight is given by $t = \frac{2u \sin\theta}{g}$. [3]
    
    
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A-Level Physics H1 Quiz - Mechanics (Answer Key)

Section A

1. Conservation of Linear Momentum: In a closed/isolated system, the total linear momentum remains constant provided no external forces act on the system. [B1 for constant momentum, B1 for closed system/no external forces]
2. Expressions: $p = mv$ [B1], $K = \frac{1}{2}mv^2$ [B1].
3. Terminal Velocity: The constant maximum velocity attained by a falling object when the drag force (air resistance) equals the weight of the object, resulting in zero net force and zero acceleration. [B2]
4. Equilibrium of Rigid Body: The sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about that same point (Net moment = 0). [B2]
5. Scalar vs Vector: A scalar has magnitude only (e.g., mass, energy, speed) [B1]; a vector has both magnitude and direction (e.g., force, velocity, acceleration) [B1].

Section B

6. $v_{iy} = 25 \sin(35^\circ) \approx 14.34\text{ m s}^{-1}$. At max height, $v_y = 0$. $0 = (14.34)^2 - 2(9.81)h \implies h = \frac{205.6}{19.62} \approx 10.5\text{ m}$. [M1 for $v_{iy}$, M1 for formula, A1 for answer]
7. $F_{net} = F_{app} - f_k = 15 - (0.30 \times 2.0 \times 9.81) = 15 - 5.886 = 9.114\text{ N}$. $a = F_{net}/m = 9.114 / 2.0 = 4.56\text{ m s}^{-2}$. [M1 for friction, M1 for net force, A1 for answer]
8. $K = \frac{p^2}{2m} \implies 11.25 = \frac{4.5^2}{2m} \implies m = \frac{20.25}{22.5} = 0.9\text{ kg}$. $v = p/m = 4.5 / 0.9 = 5.0\text{ m s}^{-1}$. [M1 for $m$ formula, M1 for $v$ formula, A1 for answers]
9. $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$ $(0.5 \times 8) + (0.8 \times 0) = (0.5 \times -2) + (0.8 \times v_2)$ $4 = -1 + 0.8v_2 \implies 5 = 0.8v_2 \implies v_2 = 6.25\text{ m s}^{-1}$. [M1 for momentum eq, M1 for substitution, A1 for answer]
10. Take moments about left pillar: $\sum \tau = 0 \implies (20 \times 9.81 \times 2.0) + (60 \times 9.81 \times 1.0) = R_{right} \times 4.0$ $392.4 + 588.6 = 4R_{right} \implies 981 = 4R_{right} \implies R_{right} = 245.25\text{ N}$. [M1 for weight of beam, M1 for weight of person, M1 for moment eq, A1 for answer]
11. Graph: Y-axis (a), X-axis (t). Starts at $g$ ($9.81$), curves downwards (concave) asymptotically approaching $a = 0$. [B1 for start point, B1 for curve shape, B1 for $a=0$ asymptote]
12. $a = (25 - 10) / 6.0 = 2.5\text{ m s}^{-2}$. $F = ma = 1200 \times 2.5 = 3000\text{ N}$. [M1 for acceleration, M1 for $F=ma$, A1 for answer]
13. $U = \frac{1}{2}kx^2 = 0.5 \times 200 \times (0.1)^2 = 100 \times 0.01 = 1.0\text{ J}$. [M1 for formula, M1 for substitution, A1 for answer]
14. $F = mg \sin(30^\circ) = 50 \times 9.81 \times 0.5 = 245.25\text{ N}$. $P = Fv = 245.25 \times 2 = 490.5\text{ W}$. [M1 for force, M1 for power formula, A1 for answer]
15. $(2 \times 4) + (3 \times -2) = (2 + 3)v_f$ $8 - 6 = 5v_f \implies 2 = 5v_f \implies v_f = 0.4\text{ m s}^{-1}$. [M1 for momentum eq, M1 for substitution, A1 for answer]

Section C

16. (a) Air resistance (drag) increases as speed increases. This reduces the net downward force ($W - D$), thus reducing acceleration over time. [B2] (b) Drag force is typically proportional to velocity (at low speeds) or velocity squared (at high speeds). As $v$ increases, $D$ increases. [B2]
17. (a) Diagram must show: Weight of plank at center (down), Weight $P$ at $x$ (down), Reaction $R_A$ (up), Reaction $R_B$ (up). [B3] (b) As $P$ moves towards B, the moment about A increases and the moment about B decreases. Consequently, $R_B$ increases and $R_A$ decreases. [B2]
18. Elastic: Both momentum and kinetic energy are conserved. [B2] Inelastic: Momentum is conserved, but kinetic energy is not (some is converted to heat/sound/deformation). [B2]
19. (a) $\sum F_x = 0$ and $\sum F_y = 0$ (or $\sum \text{Forces} = 0$ and $\sum \text{Moments} = 0$). [B2] (b) Decreasing $\theta_1$ makes the string more horizontal. To balance the same vertical weight component, the tension in the strings must increase. [B3]
20. (a) There are no horizontal forces acting on the projectile (neglecting air resistance), so by Newton's First Law, the horizontal acceleration is zero and velocity remains constant. [B2] (b) Vertical motion: $v_y = u_y - gt$. At peak, $v_y = 0 \implies 0 = u \sin\theta - gt_{up} \implies t_{up} = \frac{u \sin\theta}{g}$. Total time $t = 2 \times t_{up} = \frac{2u \sin\theta}{g}$. [B3]