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 ($g = 9.81\ \text{m s}^{-2}$).

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

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

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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]

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

Image pending generation: graph for Q3.

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

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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]

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

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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]

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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]

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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]

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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]

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

Image pending generation: graph for Q10.

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

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

Image pending generation: graph for Q20.

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End of Paper

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

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

Total Marks: 80

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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].

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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]

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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.