A Level H2 Physics Practice Paper 1

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TuitionGoWhere Exam Practice (AI)

Subject: Physics H2 | Level: A-Level | Paper: Practice Paper 1 (Version 1) Duration: 2 hours | Total Marks: 80 Name: ____________________ Class: __________ Date: __________

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Instructions to Candidates

1. Answer all questions.
2. Write your answers in the spaces provided.
3. Use a calculator where necessary.
4. Physical constants:
   • Acceleration of free fall, $g = 9.81 \text{ m s}^{-2}$
   • Speed of light, $c = 3.00 \times 10^8 \text{ m s}^{-1}$

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Section A: Structured Questions (40 Marks)

Question 1 (a) State the principle of conservation of linear momentum. [2]

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(b) A trolley of mass $0.50 \text{ kg}$ moving at $2.0 \text{ m s}^{-1}$ collides head-on with a stationary trolley of mass $1.50 \text{ kg}$. The two trolleys stick together after the collision. (i) Calculate the common velocity of the trolleys immediately after the collision. [2]

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(ii) Determine whether the collision is elastic or inelastic. Justify your answer by calculating the change in kinetic energy of the system. [3]

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Question 2 A mass $m$ is attached to a horizontal spring of spring constant $k$ and is pulled to a displacement $X_0$ from its equilibrium position, then released. The mass undergoes simple harmonic motion (SHM). (a) Show that the maximum acceleration of the mass is given by $a_{\max} = \omega^2 X_0$. [2]

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(b) Given $k = 25 \text{ N m}^{-1}$, $m = 0.20 \text{ kg}$, and $X_0 = 0.10 \text{ m}$: (i) Calculate the angular frequency $\omega$ of the oscillation. [2]

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(ii) Calculate the maximum acceleration of the mass. [2]

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Question 3 A small sphere of mass $0.10 \text{ kg}$ is suspended by a light inextensible string of length $0.50 \text{ m}$ and whirled in a horizontal circle at a constant speed. The string makes an angle of $30^\circ$ with the vertical. (a) Draw a free-body diagram of the sphere, labeling all forces. [2]

(b) Calculate the tension in the string. [3]

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(c) Calculate the speed of the sphere in its circular path. [3]

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Question 4 An experiment is conducted to determine the acceleration of free fall $g$ by measuring the time of fall of a steel ball from various heights $h$. (a) Describe how the apparatus should be set up to minimize systematic errors in the measurement of $h$. [3]

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(b) State three precautions that would be taken to improve the accuracy and safety of this experiment. [6]

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Question 5 A block of mass $2.0 \text{ kg}$ is pushed across a rough horizontal surface with an initial velocity of $5.0 \text{ m s}^{-1}$. It comes to rest after sliding $3.0 \text{ m}$. (a) Calculate the initial kinetic energy of the block. [2]

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(b) Calculate the average frictional force acting on the block. [3]

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(c) Calculate the coefficient of kinetic friction $\mu_k$ between the block and the surface. [2]

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Section B: Long Structured Questions (40 Marks)

Question 6 Two particles, A and B, of masses $m_A = 1.0 \text{ kg}$ and $m_B = 2.0 \text{ kg}$ respectively, move towards each other along a straight line. Particle A has a velocity of $4.0 \text{ m s}^{-1}$ and particle B has a velocity of $2.0 \text{ m s}^{-1}$. (a) Calculate the total momentum of the system before the collision. [2]

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(b) After a perfectly elastic collision, particle A rebounds with a velocity of $1.0 \text{ m s}^{-1}$ in the opposite direction. Calculate the final velocity of particle B. [3]

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(c) Verify that the total kinetic energy of the system is conserved in this collision. [4]

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Question 7 A satellite of mass $M_s$ orbits a planet of mass $M_p$ in a circular orbit of radius $r$. (a) Derive an expression for the orbital period $T$ of the satellite in terms of $G, M_p,$ and $r$. [5]

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(b) If the radius of the orbit is doubled, by what factor does the orbital period change? [3]

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(c) Explain why the satellite does not fall into the planet despite the gravitational attraction. [3]

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Question 8 A block of mass $m$ is released from rest at the top of a smooth incline of angle $\theta$ and length $L$. (a) Calculate the acceleration of the block down the incline. [3]

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(b) Find an expression for the velocity of the block at the bottom of the incline. [3]

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(c) If the incline were rough with a coefficient of friction $\mu$, explain how this would affect the time taken to reach the bottom. [3]

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Question 9 A mass $m$ is attached to a vertical spring. When the mass is hung, the spring extends by $e$. The mass is then pulled down further by a distance $x$ and released. (a) State the condition for the mass to undergo simple harmonic motion. [2]

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(b) Calculate the period of oscillation if $m = 0.5 \text{ kg}$ and $e = 0.1 \text{ m}$. [4]

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(c) Discuss the effect on the period if the mass $m$ is doubled. [3]

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TuitionGoWhere Exam Practice - Physics H2 A-Level (Version 1)

Marking Scheme

Section A

Question 1 (a) In a closed system (or isolated system), the total momentum before an event equals the total momentum after the event, provided no external forces act. [2] (b) (i) $m_1v_1 + m_2v_2 = (m_1+m_2)v_f \Rightarrow (0.5)(2.0) + 0 = (0.5+1.5)v_f \Rightarrow 1.0 = 2.0v_f \Rightarrow v_f = 0.5 \text{ m s}^{-1}$. [2] (ii) $KE_{initial} = \frac{1}{2}(0.5)(2^2) = 1.0 \text{ J}$. $KE_{final} = \frac{1}{2}(2.0)(0.5^2) = 0.25 \text{ J}$. $\Delta KE = 0.75 \text{ J}$ loss. Inelastic because kinetic energy is not conserved. [3]

Question 2 (a) $F = -kx$ and $F = ma \Rightarrow ma = -kx \Rightarrow a = -\frac{k}{m}x$. Since $\omega^2 = \frac{k}{m}$, $a = -\omega^2 x$. Max acceleration occurs at $x=X_0$, so $a_{\max} = \omega^2 X_0$. [2] (b) (i) $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{25}{0.20}} = \sqrt{125} \approx 11.18 \text{ rad s}^{-1}$. [2] (ii) $a_{\max} = (11.18)^2 \times 0.10 = 12.5 \text{ m s}^{-2}$. [2]

Question 3 (a) Diagram showing Tension $T$ along the string and Weight $mg$ downwards. [2] (b) Vertical equilibrium: $T \cos 30^\circ = mg \Rightarrow T = \frac{0.1 \times 9.81}{\cos 30^\circ} = \frac{0.981}{0.866} \approx 1.13 \text{ N}$. [3] (c) Horizontal: $T \sin 30^\circ = \frac{mv^2}{r}$. $r = L \sin 30^\circ = 0.5 \times 0.5 = 0.25 \text{ m}$. $1.13 \times 0.5 = \frac{0.1 \times v^2}{0.25} \Rightarrow 0.565 = 0.4v^2 \Rightarrow v^2 = 1.4125 \Rightarrow v \approx 1.19 \text{ m s}^{-1}$. [3]

Question 4 (a) Use a fiducial marker at the release point and the landing point to ensure height is measured exactly from the bottom of the ball to the impact surface. [3] (b) Accuracy: (1) Use an electronic timer/light gates to reduce reaction time error. (2) Repeat measurements for the same height and average results to reduce random error. (3) Ensure the ball is dropped without initial velocity. Safety: Ensure a padded landing area to prevent the ball from bouncing or damaging the floor. [6]

Question 5 (a) $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2.0)(5.0^2) = 25 \text{ J}$. [2] (b) Work done by friction = $\Delta KE \Rightarrow F \times d = 25 \Rightarrow F \times 3.0 = 25 \Rightarrow F = 8.33 \text{ N}$. [3] (c) $F = \mu_k mg \Rightarrow 8.33 = \mu_k (2.0 \times 9.81) \Rightarrow \mu_k = \frac{8.33}{19.62} \approx 0.42$. [2]

Section B

Question 6 (a) $p_{total} = m_Av_A + m_Bv_B = (1.0)(4.0) + (2.0)(-2.0) = 4.0 - 4.0 = 0 \text{ kg m s}^{-1}$. [2] (b) $0 = m_A v_{Af} + m_B v_{Bf} \Rightarrow 0 = (1.0)(-1.0) + (2.0)v_{Bf} \Rightarrow 2v_{Bf} = 1.0 \Rightarrow v_{Bf} = 0.5 \text{ m s}^{-1}$. [3] (c) $KE_{initial} = \frac{1}{2}(1)(4^2) + \frac{1}{2}(2)(2^2) = 8 + 4 = 12 \text{ J}$. $KE_{final} = \frac{1}{2}(1)(-1^2) + \frac{1}{2}(2)(0.5^2) = 0.5 + 0.25 = 0.75 \text{ J}$. $12 \neq 0.75$. Kinetic energy is not conserved. [4]

Question 7 (a) $\frac{GM_p M_s}{r^2} = \frac{M_s v^2}{r} \Rightarrow v = \sqrt{\frac{GM_p}{r}}$. $T = \frac{2\pi r}{v} = \frac{2\pi r}{\sqrt{GM_p/r}} = 2\pi \sqrt{\frac{r^3}{GM_p}}$. [5] (b) $T \propto r^{3/2}$. If $r \to 2r$, $T \to 2^{3/2} T \approx 2.83 T$. Factor is 2.83. [3] (c) The gravitational force acts as the centripetal force, constantly changing the direction of the satellite's velocity, keeping it in orbit rather than pulling it straight down. [3]

Question 8 (a) $F_{net} = mg \sin \theta = ma \Rightarrow a = g \sin \theta$. [3] (b) $v^2 = u^2 + 2as \Rightarrow v^2 = 0 + 2(g \sin \theta)L \Rightarrow v = \sqrt{2gL \sin \theta}$. [3] (c) Frictional force $f = \mu mg \cos \theta$ opposes motion. $a = g(\sin \theta - \mu \cos \theta)$. Acceleration decreases, so time taken to reach the bottom increases. [3]

Question 9 (a) The restoring force must be proportional to the displacement from equilibrium and directed towards the equilibrium position. [2] (b) $mg = ke \Rightarrow k = \frac{0.5 \times 9.81}{0.1} = 49.05 \text{ N m}^{-1}$. $T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{0.5}{49.05}} \approx 2\pi \sqrt{0.0102} \approx 0.63 \text{ s}$. [4] (c) $T \propto \sqrt{m}$. If $m$ is doubled, $T$ increases by a factor of $\sqrt{2} \approx 1.41$. [3]