A Level H2 Physics Practice Paper 1

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TuitionGoWhere Practice Paper - Physics H2 A-Level

TuitionGoWhere Practice Paper (AI) - Version 1

Subject: Physics H2
Level: A-Level
Paper: Structured Questions (Mechanics Focus)
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 $g = 9.81 \text{ m s}^{-2}$ and the constants provided in the data booklet.
4. Show all working clearly.

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Section A: Kinematics and Dynamics (30 Marks)

Question 1 A projectile is launched from ground level with an initial velocity of $40 \text{ m s}^{-1}$ at an angle of $35^\circ$ to the horizontal. (a) Calculate the maximum height reached by the projectile. [3]


(b) Determine the horizontal range of the projectile. [3]


(c) Explain, with reference to acceleration, why the horizontal component of the velocity remains constant throughout the flight. [2]

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Question 2 A block of mass $2.5 \text{ kg}$ is placed on a rough plane inclined at $30^\circ$ to the horizontal. The coefficient of static friction between the block and the plane is $0.40$. (a) Calculate the magnitude of the normal reaction force acting on the block. [2]

(b) Determine whether the block will slide down the plane from rest. Justify your answer with a calculation. [4]


(c) If the block is pushed up the plane with a constant velocity, calculate the magnitude of the force applied parallel to the plane. [4]

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Question 3 A car of mass $1200 \text{ kg}$ accelerates from rest to $25 \text{ m s}^{-1}$ over a distance of $150 \text{ m}$. (a) Calculate the average acceleration of the car. [3]

(b) Calculate the average net force acting on the car during this acceleration. [2]

(c) If the engine provides a constant driving force of $3500 \text{ N}$, calculate the average resistive force acting on the car. [3]

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Question 4 State Newton's Second Law of Motion in terms of momentum. [3]

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Section B: Energy, Momentum, and Circular Motion (30 Marks)

Question 5 Two trolleys, A and B, of masses $1.0 \text{ kg}$ and $2.0 \text{ kg}$ respectively, are moving towards each other on a frictionless track. Trolley A moves at $3.0 \text{ m s}^{-1}$ and Trolley B moves at $1.5 \text{ m s}^{-1}$. They collide and stick together. (a) State the Principle of Conservation of Linear Momentum. [2]

(b) Calculate the final velocity of the combined mass after the collision. [4]

(c) Calculate the loss in kinetic energy during the collision. [4]

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Question 6 A small sphere of mass $0.15 \text{ kg}$ is attached to a string of length $0.80 \text{ m}$ and whirled in a vertical circle. (a) Calculate the minimum velocity required at the highest point of the circle to keep the string taut. [3]

(b) Determine the tension in the string when the sphere is at the lowest point of the circle, assuming it maintains the velocity found in (a) throughout the motion (ignore air resistance). [5]


(c) Explain why the tension in the string is greater at the bottom than at the top. [3]

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Question 7 A block of mass $0.5 \text{ kg}$ is pushed against a horizontal spring (spring constant $k = 200 \text{ N m}^{-1}$), compressing it by $0.12 \text{ m}$. The block is then released and slides across a rough surface with a coefficient of kinetic friction $\mu = 0.20$. (a) Calculate the initial potential energy stored in the spring. [2]

(b) Calculate the distance the block travels before coming to a stop. [5]

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Section C: Gravitational Fields (20 Marks)

Question 8 A satellite of mass $m$ orbits a planet of mass $M$ and radius $R$ at a height $h$ above the surface. (a) Show that the orbital period $T$ is given by $T = 2\pi \sqrt{\frac{(R+h)^3}{GM}}$. [6]


(b) If the height $h$ is increased, state and explain the effect on the orbital speed of the satellite. [3]

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Question 9 The gravitational field strength at the surface of a planet is $4.5 \text{ N kg}^{-1}$ and its radius is $3.4 \times 10^6 \text{ m}$. (a) Calculate the mass of the planet. [4]

(b) Calculate the escape velocity from the surface of the planet. [4]


(c) Define "gravitational potential" at a point in a field. [3]

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TuitionGoWhere Practice Paper - Physics H2 A-Level (Answers)

Version 1 - Marking Scheme

Section A: Kinematics and Dynamics

Question 1 (a) $v_{iy} = 40 \sin(35^\circ) = 22.94 \text{ m s}^{-1}$. $H = v_{iy}^2 / 2g = (22.94)^2 / (2 \times 9.81) = 26.7 \text{ m}$. [3] (b) $t_{flight} = 2 v_{iy} / g = 4.68 \text{ s}$. $v_{ix} = 40 \cos(35^\circ) = 32.77 \text{ m s}^{-1}$. Range $= 32.77 \times 4.68 = 153 \text{ m}$. [3] (c) There are no horizontal forces acting on the projectile (neglecting air resistance). According to Newton's First Law, the horizontal acceleration is zero, thus velocity remains constant. [2]

Question 2 (a) $F_N = mg \cos(30^\circ) = 2.5 \times 9.81 \times 0.866 = 21.2 \text{ N}$. [2] (b) Driving force $F_d = mg \sin(30^\circ) = 2.5 \times 9.81 \times 0.5 = 12.3 \text{ N}$. Max static friction $f_{s,max} = \mu F_N = 0.40 \times 21.2 = 8.5 \text{ N}$. Since $F_d > f_{s,max}$, the block will slide. [4] (c) $F_{applied} - mg \sin(30^\circ) - \mu mg \cos(30^\circ) = 0$. $F_{applied} = 12.3 + (0.20 \times 21.2)$ (assuming $\mu_k$ is same as $\mu_s$ or specified). $F_{applied} = 12.3 + 8.5 = 20.8 \text{ N}$. [4]

Question 3 (a) $v^2 = u^2 + 2as \implies 25^2 = 0 + 2(a)(150) \implies a = 625 / 300 = 2.08 \text{ m s}^{-2}$. [3] (b) $F_{net} = ma = 1200 \times 2.08 = 2500 \text{ N}$. [2] (c) $F_{net} = F_{drive} - F_{resistive} \implies 2500 = 3500 - F_r \implies F_r = 1000 \text{ N}$. [3]

Question 4 The rate of change of momentum of a body is directly proportional to the net force acting on it and takes place in the direction of the force. $\vec{F} = \frac{d\vec{p}}{dt}$. [3]

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Section B: Energy, Momentum, and Circular Motion

Question 5 (a) In a closed system, the total linear momentum before an event is equal to the total linear momentum after the event, provided no external forces act. [2] (b) $m_1u_1 + m_2u_2 = (m_1+m_2)v \implies (1.0)(3.0) + (2.0)(-1.5) = (3.0)v \implies 3.0 - 3.0 = 3v \implies v = 0 \text{ m s}^{-1}$. [4] (c) $KE_{initial} = 0.5(1)(3^2) + 0.5(2)(1.5^2) = 4.5 + 2.25 = 6.75 \text{ J}$. $KE_{final} = 0$. Loss $= 6.75 \text{ J}$. [4]

Question 6 (a) $T=0$ at top: $mg = mv^2/r \implies v = \sqrt{gr} = \sqrt{9.81 \times 0.80} = 2.80 \text{ m s}^{-1}$. [3] (b) $T - mg = mv^2/r \implies T = m(g + v^2/r) = 0.15(9.81 + 2.8^2/0.8) = 0.15(9.81 + 9.8) = 2.94 \text{ N}$. [5] (c) At the bottom, the tension must provide the centripetal force AND overcome the weight of the sphere. At the top, weight assists in providing the centripetal force. [3]

Question 7 (a) $E_p = 0.5 k x^2 = 0.5 \times 200 \times (0.12)^2 = 1.44 \text{ J}$. [2] (b) Work done by friction = Initial Energy. $f_k \times d = E_p \implies (\mu mg) d = 1.44 \implies (0.20 \times 0.5 \times 9.81) d = 1.44 \implies 0.981 d = 1.44 \implies d = 1.47 \text{ m}$. [5]

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Section C: Gravitational Fields

Question 8 (a) $F_c = F_g \implies mv^2/r = GMm/r^2$ where $r = R+h$. $v^2 = GM/(R+h)$. Since $v = 2\pi r / T$, then $(2\pi(R+h)/T)^2 = GM/(R+h) \implies T^2 = 4\pi^2(R+h)^3/GM \implies T = 2\pi \sqrt{(R+h)^3/GM}$. [6] (b) Orbital speed $v = \sqrt{GM/r}$. As $h$ increases, $r$ increases, so $v$ decreases. [3]

Question 9 (a) $g = GM/R^2 \implies M = gR^2/G = (4.5 \times (3.4 \times 10^6)^2) / (6.67 \times 10^{-11}) = 7.8 \times 10^{23} \text{ kg}$. [4] (b) $v_{esc} = \sqrt{2GM/R} = \sqrt{2 \times 6.67 \times 10^{-11} \times 7.8 \times 10^{23} / 3.4 \times 10^6} = 5520 \text{ m s}^{-1}$. [4] (c) The work done per unit mass in bringing a small test mass from infinity to that point. [3]