Secondary 3 Physics Semestral Assessment 2 (End of Year) Paper 1

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TuitionGoWhere Exam Practice (AI) - Physics Secondary 3

Subject: Physics
Level: Secondary 3
Paper: SA2 (Version 1)
Duration: 1 hour 45 minutes
Total Marks: 60

Name: __________________________ Class: __________ Date: __________

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Instructions to Candidates:

1. Answer all questions.
2. Write your answers in the spaces provided.
3. For calculations, show all working clearly. Use $g = 10\text{ m s}^{-2}$ unless otherwise stated.
4. Use a calculator where necessary.

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Section A: Multiple Choice Questions (10 Marks)

Each question carries 1 mark.

1. An object moves along a straight line. Which of the following represents a vector quantity? A. Distance B. Speed C. Displacement D. Time

2. A ball is thrown vertically upwards. At the highest point of its trajectory, the acceleration of the ball is: A. $0\text{ m s}^{-2}$ B. $10\text{ m s}^{-2}$ downwards C. $10\text{ m s}^{-2}$ upwards D. Dependent on the initial velocity

3. A block of mass $2\text{ kg}$ is pushed across a smooth horizontal surface with a constant force of $10\text{ N}$. The acceleration of the block is: A. $5\text{ m s}^{-2}$ B. $10\text{ m s}^{-2}$ C. $20\text{ m s}^{-2}$ D. $0\text{ m s}^{-2}$

4. Which of the following is a non-contact force? A. Tension in a string B. Friction between two surfaces C. Normal reaction force D. Gravitational force

5. A diver of mass $60\text{ kg}$ jumps from a platform. If the diver's acceleration is $8\text{ m s}^{-2}$ downwards, the resistive force acting on the diver is: A. $120\text{ N}$ B. $480\text{ N}$ C. $600\text{ N}$ D. $1080\text{ N}$

6. The principle of moments states that for a body in equilibrium, the sum of clockwise moments about any pivot is equal to: A. The total force acting on the body B. The sum of anticlockwise moments about the same pivot C. The weight of the body D. Zero

7. A rectangular block has a mass of $400\text{ g}$ and dimensions $2\text{ cm} \times 5\text{ cm} \times 10\text{ cm}$. The density of the block is: A. $4\text{ g cm}^{-3}$ B. $8\text{ g cm}^{-3}$ C. $40\text{ g cm}^{-3}$ D. $80\text{ g cm}^{-3}$

8. A hydraulic press has a small piston of area $0.01\text{ m}^2$ and a large piston of area $0.1\text{ m}^2$. If a force of $100\text{ N}$ is applied to the small piston, the force exerted by the large piston is: A. $10\text{ N}$ B. $100\text{ N}$ C. $1,000\text{ N}$ D. $10,000\text{ N}$

9. A $0.5\text{ kg}$ ball is dropped from a height of $20\text{ m}$. Ignoring air resistance, the kinetic energy of the ball just before it hits the ground is: A. $10\text{ J}$ B. $100\text{ J}$ C. $200\text{ J}$ D. $400\text{ J}$

10. A machine is used to lift a load. If the total energy input is $500\text{ J}$ and the useful work done is $300\text{ J}$, the efficiency of the machine is: A. $60\%$ B. $1.67\%$ C. $167\%$ D. $200\text{ J}$

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Section B: Structured Questions (50 Marks)

Question 11 (5 marks) A car of mass $1200\text{ kg}$ accelerates uniformly from rest to a velocity of $20\text{ m s}^{-1}$ in $8\text{ seconds}$. (a) Calculate the acceleration of the car. [2] \vfill (b) Calculate the resultant force acting on the car during this acceleration. [3] \vfill

Question 12 (6 marks) A wooden block of mass $2\text{ kg}$ is pulled up a rough inclined plane at a constant speed by a force of $30\text{ N}$ acting parallel to the plane. The distance moved along the plane is $4\text{ m}$, and the vertical height gained is $1.5\text{ m}$. (a) Calculate the work done by the pulling force. [2] \vfill (b) Calculate the gain in gravitational potential energy of the block. [2] \vfill (c) Determine the energy lost to friction as the block moves up the plane. [2] \vfill

Question 13 (7 marks) A uniform meter rule is pivoted at the $40\text{ cm}$ mark. A mass of $100\text{ g}$ is placed at the $10\text{ cm}$ mark to keep the rule in horizontal equilibrium. (a) State the principle of moments. [1] \vfill (b) Calculate the anticlockwise moment about the pivot. (Take $g = 10\text{ m s}^{-2}$) [3] \vfill (c) Determine the weight of the meter rule and explain where its weight acts. [3] \vfill

Question 14 (8 marks) A ring of mass $0.5\text{ kg}$ is suspended by two strings, $S_1$ and $S_2$. String $S_1$ makes an angle of $45^\circ$ with the horizontal, and string $S_2$ makes an angle of $60^\circ$ with the horizontal. (a) Draw a free-body diagram of the ring, labeling all forces acting on it. [3] \vfill (b) Explain why the horizontal components of the tension in $S_1$ and $S_2$ must be equal in magnitude. [2] \vfill (c) Describe the effect on the tensions if the mass of the ring is increased. [3] \vfill

Question 15 (7 marks) A cylinder of density $800\text{ kg m}^{-3}$ floats in water (density $1000\text{ kg m}^{-3}$). (a) Define density. [1] \vfill (b) Explain, in terms of forces, why the cylinder floats. [3] \vfill (c) Calculate the fraction of the cylinder's volume that is submerged. [3] \vfill

Question 16 (7 marks) A ball is released from the top of a smooth hemispherical bowl of radius $2\text{ m}$. (a) State the principle of conservation of energy. [2] \vfill (b) Calculate the speed of the ball when it reaches the bottom of the bowl. [3] \vfill (c) If the bowl were rough, how would the speed at the bottom be affected? Explain your answer. [2] \vfill

Question 17 (10 marks) (a) A $0.2\text{ kg}$ block is pushed across a smooth horizontal surface by a force $F_1 = 15\text{ N}$ to the right. Calculate its acceleration. [2] \vfill (b) After $2\text{ seconds}$, an opposing force $F_2 = 15\text{ N}$ is applied to the left while $F_1$ continues to act. Describe the motion of the block for the next $2\text{ seconds}$. [4] \vfill (c) Calculate the total distance traveled by the block from the moment $F_1$ was first applied until the end of the second $2\text{-second}$ interval. [4] \vfill

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Answer Key - Physics Secondary 3 SA2 (Version 1)

Section A: MCQ

1. C (Displacement has magnitude and direction)
2. B (Gravity $g$ always acts downwards regardless of velocity)
3. A ($a = F/m = 10/2 = 5\text{ m s}^{-2}$)
4. D (Gravitational force acts over a distance)
5. A ($W - f = ma \Rightarrow 600 - f = 60 \times 8 \Rightarrow f = 600 - 480 = 120\text{ N}$)
6. B (Definition of equilibrium for moments)
7. A ($\text{Vol} = 2 \times 5 \times 10 = 100\text{ cm}^3$; $\text{Density} = 400/100 = 4\text{ g cm}^{-3}$)
8. C ($P = F_1/A_1 = F_2/A_2 \Rightarrow 100/0.01 = F_2/0.1 \Rightarrow F_2 = 1000\text{ N}$)
9. B ($GPE = mgh = 0.5 \times 10 \times 20 = 100\text{ J}$. By conservation, $KE = 100\text{ J}$)
10. A ($\text{Eff} = 300/500 \times 100\% = 60\%$)

Section B: Structured

Question 11 (a) $a = (v - u)/t = (20 - 0)/8 = 2.5\text{ m s}^{-2}$ [2] (b) $F = ma = 1200 \times 2.5 = 3000\text{ N}$ [3]

Question 12 (a) $W = F \times d = 30 \times 4 = 120\text{ J}$ [2] (b) $\Delta GPE = mgh = 2 \times 10 \times 1.5 = 30\text{ J}$ [2] (c) $\text{Energy loss} = W_{\text{applied}} - \Delta GPE = 120 - 30 = 90\text{ J}$ [2]

Question 13 (a) For a body in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot. [1] (b) $\text{Force} = 0.1 \times 10 = 1\text{ N}$. $\text{Distance} = 40 - 10 = 30\text{ cm} = 0.3\text{ m}$. $\text{Moment} = 1 \times 0.3 = 0.3\text{ Nm}$ [3] (c) Weight acts at the center of gravity ($50\text{ cm}$ mark). $\text{Distance to pivot} = 50 - 40 = 10\text{ cm} = 0.1\text{ m}$. $\text{Clockwise moment} = \text{Anticlockwise moment} \Rightarrow W \times 0.1 = 0.3 \Rightarrow W = 3\text{ N}$ [3]

Question 14 (a) Diagram showing: Weight ($W$) acting downwards, Tension $T_1$ at $45^\circ$ up-left, Tension $T_2$ at $60^\circ$ up-right. [3] (b) Since the ring is in equilibrium and there is no horizontal acceleration, the net horizontal force must be zero. Thus, the leftward component of $T_1$ must equal the rightward component of $T_2$. [2] (c) Increased mass increases the downward weight. To maintain equilibrium, the vertical components of $T_1$ and $T_2$ must increase, which requires the magnitude of the tensions in both strings to increase. [3]

Question 15 (a) Density is the mass per unit volume of a substance. [1] (b) The cylinder floats because the upthrust (buoyancy force) exerted by the water is equal to the weight of the cylinder. [3] (c) $\text{Fraction submerged} = \rho_{\text{object}} / \rho_{\text{fluid}} = 800 / 1000 = 0.8$ or $80\%$ [3]

Question 16 (a) Energy cannot be created or destroyed, only transformed from one form to another. The total energy of an isolated system remains constant. [2] (b) $mgh = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh} = \sqrt{2 \times 10 \times 2} = \sqrt{40} \approx 6.32\text{ m s}^{-1}$ [3] (c) Speed would be lower. Some gravitational potential energy is converted into thermal energy due to work done against friction. [2]

Question 17 (a) $a = 15 / 0.2 = 75\text{ m s}^{-2}$ [2] (b) Net force $F_{\text{net}} = 15 - 15 = 0\text{ N}$. According to Newton's First Law, the block will continue to move at a constant velocity (uniform motion) because there is no resultant force. [4] (c) Phase 1: $v = u + at = 0 + 75(2) = 150\text{ m s}^{-1}$. $s_1 = \frac{1}{2}at^2 = 0.5 \times 75 \times 4 = 150\text{ m}$. Phase 2: $v = 150\text{ m s}^{-1}$ (constant). $s_2 = v \times t = 150 \times 2 = 300\text{ m}$. Total distance $= 150 + 300 = 450\text{ m}$. [4]