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A Level H2 Physics Practice Paper 2

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TuitionGoWhere Exam Practice (AI) — Physics H2 A-Level

Practice Paper: Mechanics (Version 2 of 5)

School: TuitionGoWhere Exam Practice (AI)
Subject: Physics H2
Level: A-Level
Paper: Practice Paper 2 (Mechanics Topic Set)
Version: 2 of 5
Duration: 75 minutes
Total Marks: 80
Name: ___________________________
Class: ___________________________
Date: ___________________________

Instructions:

Answer all questions in the spaces provided.
Show all working clearly. Use SI units and appropriate significant figures.
Diagrams are not drawn to scale unless stated.
A data sheet is NOT provided; use standard constants where needed ( $g = 9.81\ \text{m s}^{-2}$ ).

Section A: Foundations of Mechanics (Questions 1–5) — [20 marks]

1. State the principle of conservation of linear momentum. [2]

2. A block of mass $4.0\ \text{kg}$ is pulled along a horizontal frictionless surface by a constant force of $12\ \text{N}$ acting at $30^\circ$ above the horizontal. (a) Resolve the force into horizontal and vertical components. [2] (b) Calculate the acceleration of the block. [2]

3. A car travels along a straight road. The variation of its velocity with time is shown below.

Graph for Q3 (ALEVEL Physics H2)

Generated graph for Q3.

(a) Calculate the total distance travelled by the car. [2] (b) Determine the average acceleration during the first 4 s. [1]

4. A uniform rod of length $1.2\ \text{m}$ and weight $20\ \text{N}$ is pivoted at one end. A force of $15\ \text{N}$ is applied vertically upward at the other end. Calculate the net moment about the pivot. [2]

5. Explain why the weight of an object is considered a vector quantity but mass is a scalar. [2]

Section B: Motion, Collisions and Circular Motion (Questions 6–13) — [32 marks]

6. A projectile is launched from level ground with initial speed $25\ \text{m s}^{-1}$ at an angle of $40^\circ$ to the horizontal. (a) Calculate the initial horizontal and vertical components of velocity. [2] (b) Find the maximum height reached. [2] (c) Calculate the horizontal range. [2]

7. A ball of mass $0.20\ \text{kg}$ moving at $3.0\ \text{m s}^{-1}$ collides head-on with a stationary ball of mass $0.30\ \text{kg}$ . After the collision the $0.20\ \text{kg}$ ball moves at $1.0\ \text{m s}^{-1}$ in the same direction. (a) State the principle of conservation of momentum as applied here. [1] (b) Calculate the velocity of the $0.30\ \text{kg}$ ball after collision. [3] (c) Determine whether the collision is elastic. Show your reasoning. [3]

8. A particle moves in a horizontal circle of radius $0.50\ \text{m}$ with constant speed $4.0\ \text{m s}^{-1}$ . (a) Calculate the angular velocity. [1] (b) Calculate the centripetal acceleration. [2] (c) State the direction of the centripetal force. [1]

9. A stone of mass $0.050\ \text{kg}$ is tied to a string of length $0.80\ \text{m}$ and whirled in a vertical circle. At the lowest point its speed is $5.0\ \text{m s}^{-1}$ . Calculate the tension in the string at this point. [3]

10. The graph shows the force acting on a $0.10\ \text{kg}$ object over a time interval.

Graph for Q10 (ALEVEL Physics H2)

Generated graph for Q10.

Calculate the impulse on the object and its final velocity assuming it starts from rest. [3]

11. A satellite orbits Earth at a height where gravitational field strength is $6.0\ \text{N kg}^{-1}$ . The satellite has mass $500\ \text{kg}$ . (a) Calculate the gravitational force on it. [1] (b) State one condition for a stable circular orbit. [1]

12. A disc rotates with angular velocity $8.0\ \text{rad s}^{-1}$ . A point on its rim is $0.10\ \text{m}$ from the centre. Calculate the linear speed and the centripetal acceleration of the point. [3]

13. A $2.0\ \text{kg}$ mass is dropped from rest and falls freely. After $3.0\ \text{s}$ , calculate: (a) its velocity, [1] (b) the distance fallen, [2] (c) its kinetic energy at that instant. [2]

Section C: Oscillations and Gravitation (Questions 14–20) — [28 marks]

14. A mass on a spring performs simple harmonic motion with amplitude $0.040\ \text{m}$ and period $1.2\ \text{s}$ . (a) Calculate the angular frequency. [1] (b) Calculate the maximum acceleration. [2] (c) State the phase difference between displacement and velocity. [1]

15. The displacement of an oscillator is given by $x = 0.05 \sin(10t)$ where $x$ is in metres and $t$ in seconds. (a) State the amplitude. [1] (b) Calculate the maximum velocity. [2] (c) Write the expression for acceleration $a$ in terms of $x$ . [2]

16. A pendulum of length $1.0\ \text{m}$ performs s.h.m. with small amplitude. (a) Calculate its period. ( $g = 9.81\ \text{m s}^{-2}$ ) [2] (b) Explain why the motion is simple harmonic for small angles. [2]

17. Two masses $m_1 = 4.0\times10^{3}\ \text{kg}$ and $m_2 = 6.0\times10^{3}\ \text{kg}$ are separated by $2.0\ \text{m}$ . Calculate the gravitational force between them. ( $G = 6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}$ ) [3]

18. A planet has mass $M = 6.0\times10^{24}\ \text{kg}$ and radius $R = 6.4\times10^{6}\ \text{m}$ . (a) Calculate the gravitational field strength at its surface. [2] (b) Calculate the gravitational potential at the surface. [2]

19. A geostationary satellite orbits Earth at radius $4.2\times10^{7}\ \text{m}$ from the centre. (a) State one characteristic of a geostationary orbit. [1] (b) Calculate its orbital speed if its period is 24 h. [3]

20. A $0.10\ \text{kg}$ mass on a spring oscillates with $x = 0.02\cos(5t)$ . (a) State the initial displacement. [1] (b) Calculate the maximum kinetic energy. [3] (c) Sketch a graph of kinetic energy against time for one cycle. [2]

Graph for Q20 (ALEVEL Physics H2)

Generated graph for Q20.

End of Paper

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Answers

TuitionGoWhere Exam Practice (AI) — Physics H2 A-Level

Practice Paper: Mechanics (Version 2 of 5) — Answer Key

Total Marks: 80

Section A: Foundations of Mechanics (Q1–5) — [20 marks]

Q1. [2 marks] Principle: In a closed/isolated system, total momentum before an event equals total momentum after, provided no net external force acts.

1 mark: system/closed condition stated
1 mark: before = after momentum stated Teaching note: Momentum is a vector; external impulses change total momentum. Do not confuse with energy conservation.

Q2. [4 marks] (a) $F_x = 12\cos30^\circ = 10.4\ \text{N}$ ; $F_y = 12\sin30^\circ = 6.0\ \text{N}$ [2] (b) Net horizontal force = $10.4\ \text{N}$ ; $a = F_x/m = 10.4/4.0 = 2.6\ \text{m s}^{-2}$ [2] Common mistake: Using full 12 N without resolving.

Q3. [3 marks] (a) Distance = area under graph = ½(4)(8) + (4)(8) + ½(4)(8) = 16+32+16 = 64 m [2] (b) $a_{avg} = (8-0)/4 = 2.0\ \text{m s}^{-2}$ [1]

Q4. [2 marks] Moment of weight = $20 \times (1.2/2) = 12\ \text{N m}$ clockwise. Applied moment = $15 \times 1.2 = 18\ \text{N m}$ anticlockwise. Net = $18 - 12 = 6.0\ \text{N m}$ anticlockwise. [2]

Q5. [2 marks] Weight = $mg$ , direction toward Earth's centre → vector [1]. Mass is amount of matter, no direction → scalar [1].

Section B: Motion, Collisions and Circular Motion (Q6–13) — [32 marks]

Q6. [6 marks] (a) $v_x = 25\cos40^\circ = 19.2\ \text{m s}^{-1}$ ; $v_y = 25\sin40^\circ = 16.1\ \text{m s}^{-1}$ [2] (b) $h_{max} = v_y^2/(2g) = (16.1)^2/(2\times9.81) = 13.2\ \text{m}$ [2] (c) $t_{flight} = 2v_y/g = 3.28\ \text{s}$ ; range = $v_x t = 19.2\times3.28 = 62.9\ \text{m}$ [2]

Q7. [7 marks] (a) Total momentum before = total after (no external force). [1] (b) $0.20(3.0) = 0.20(1.0) + 0.30v$ → $0.60 = 0.20 + 0.30v$ → $v = 1.33\ \text{m s}^{-1}$ [3] (c) KE before = ½(0.2)(9)=0.90 J; KE after = ½(0.2)(1)+½(0.3)(1.33²)=0.10+0.265=0.365 J. Not equal → inelastic. [3]

Q8. [4 marks] (a) $\omega = v/r = 4.0/0.50 = 8.0\ \text{rad s}^{-1}$ [1] (b) $a = v^2/r = 16/0.50 = 32\ \text{m s}^{-2}$ [2] (c) Toward centre. [1]

Q9. [3 marks] At lowest point: $T - mg = mv^2/r$ → $T = m(g+v^2/r) = 0.050(9.81 + 25/0.80) = 0.050(41.1) = 2.05\ \text{N}$ .

Q10. [3 marks] Impulse = area = $20 \times 0.04 = 0.80\ \text{N s}$ . $v = J/m = 0.80/0.10 = 8.0\ \text{m s}^{-1}$ .

Q11. [2 marks] (a) $F = mg_{field} = 500 \times 6.0 = 3000\ \text{N}$ [1] (b) Centripetal force provided by gravity; speed constant, radius constant. [1]

Q12. [3 marks] $v = r\omega = 0.10 \times 8.0 = 0.80\ \text{m s}^{-1}$ ; $a = v^2/r = 0.64/0.10 = 6.4\ \text{m s}^{-2}$ .

Q13. [5 marks] (a) $v = gt = 29.4\ \text{m s}^{-1}$ [1] (b) $s = ½gt^2 = 44.1\ \text{m}$ [2] (c) $E_k = ½mv^2 = ½(2.0)(29.4^2) = 864\ \text{J}$ [2]

Section C: Oscillations and Gravitation (Q14–20) — [28 marks]

Q14. [4 marks] (a) $\omega = 2\pi/T = 5.24\ \text{rad s}^{-1}$ [1] (b) $a_{max} = \omega^2 x_0 = (5.24)^2(0.040) = 1.10\ \text{m s}^{-2}$ [2] (c) $\pi/2$ (90°) [1]

Q15. [5 marks] (a) $0.05\ \text{m}$ [1] (b) $v_{max} = \omega x_0 = 10 \times 0.05 = 0.50\ \text{m s}^{-1}$ [2] (c) $a = -\omega^2 x = -100x$ [2]

Q16. [4 marks] (a) $T = 2\pi\sqrt{l/g} = 2\pi\sqrt{1.0/9.81} = 2.01\ \text{s}$ [2] (b) For small $\theta$ , $\sin\theta \approx \theta$ , restoring force ∝ displacement → s.h.m. [2]

Q17. [3 marks] $F = Gm_1m_2/r^2 = (6.67\times10^{-11})(4.0\times10^3)(6.0\times10^3)/(2.0^2) = 4.00\times10^{-4}\ \text{N}$ .

Q18. [4 marks] (a) $g = GM/R^2 = (6.67\times10^{-11})(6.0\times10^{24})/(6.4\times10^6)^2 = 9.77\ \text{N kg}^{-1}$ [2] (b) $\phi = -GM/R = -(6.67\times10^{-11})(6.0\times10^{24})/(6.4\times10^6) = -6.25\times10^7\ \text{J kg}^{-1}$ [2]

Q19. [4 marks] (a) Period = 24 h, above equator, fixed position. [1] (b) $v = 2\pi r/T = 2\pi(4.2\times10^7)/(86400) = 3.05\times10^3\ \text{m s}^{-1}$ [3]

Q20. [6 marks] (a) $x_0 = 0.02\ \text{m}$ at t=0 [1] (b) $E_{k,max} = ½m\omega^2 x_0^2 = ½(0.10)(25)(0.0004) = 5.0\times10^{-4}\ \text{J}$ [3] (c) Graph: sinusoidal-squared, period 1.26 s, peaks at 0.0005 J twice per cycle. [2] Image expected: axes labelled t(s), E_k(J); curve from 0 to max to 0 repeated; period marked.