Secondary 3 Physics Semestral Assessment 2 (End of Year) Paper 4

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TuitionGoWhere Exam Practice (AI) - Physics Secondary 3

Assessment: SA2 (Version 4 of 5)

Subject: Physics
Level: Secondary 3
Paper: Structured Questions
Duration: 1 hour 30 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.
4. Use $g = 10\text{ m s}^{-2}$ where necessary.
5. Use significant figures appropriate to the data provided.

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Section A: Kinematics and Dynamics

Question 1 A toy car of mass $0.5\text{ kg}$ starts from rest and accelerates uniformly to a velocity of $4\text{ m s}^{-1}$ in $2.0\text{ s}$. (a) Calculate the acceleration of the toy car. [1]

(b) Calculate the resultant force acting on the car during this period. [1]

(c) If the car then travels at a constant velocity of $4\text{ m s}^{-1}$ for another $3.0\text{ s}$, sketch the velocity-time graph for the entire $5.0\text{ s}$ journey. [2]


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Question 2 A climber of mass $70\text{ kg}$ slides down a vertical rope. He decelerates from an initial speed of $2.0\text{ m s}^{-1}$ to a stop over a distance of $1.5\text{ m}$. (a) State the direction of the frictional force acting on the climber. [1]

(b) Calculate the magnitude of the average frictional force between the climber and the rope. [3]


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Question 3 A block of mass $2.0\text{ kg}$ is pulled up a rough inclined plane at a constant speed by a force of $15\text{ N}$ parallel to the plane. The block moves a distance of $4.0\text{ m}$ along the plane, resulting in a vertical height increase of $1.2\text{ m}$. (a) Calculate the work done by the pulling force. [1]

(b) Calculate the increase in the gravitational potential energy of the block. [1]

(c) Determine the energy dissipated as heat due to friction. [2]

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Question 4 A metal ring is suspended in equilibrium by two strings. String A makes an angle of $40^\circ$ and String B makes an angle of $50^\circ$ with the horizontal. The ring has a mass of $0.2\text{ kg}$. (a) Draw a free-body diagram of the ring, labeling all forces acting on it. [2]

(b) Explain why the tensions in the two strings are not equal. [2]

(c) Calculate the vertical component of the resultant force provided by the two strings. [1]

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Question 5 A spacecraft of mass $1.2 \times 10^6\text{ kg}$ is orbiting a planet of mass $6.0 \times 10^{24}\text{ kg}$. The distance between the centers of the spacecraft and the planet is $7.0 \times 10^6\text{ m}$. (a) Calculate the gravitational force between the spacecraft and the planet. [2]

(b) If the distance between the centers is doubled, state the new gravitational force in terms of the original force $F$. [1]

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Section B: Energy, Power, and Pressure

Question 6 A ball is released from rest at point A at the top of a circular track of radius $2.0\text{ m}$. (a) State the principle of conservation of energy. [1]

(b) Assuming no energy loss, calculate the minimum initial speed required at point A for the ball to just reach the top of the loop (point C), where the height is $4.0\text{ m}$. [4]



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Question 7 A hydraulic jack consists of two pistons. The smaller piston has an area of $0.02\text{ m}^2$ and the larger piston has an area of $0.5\text{ m}^2$. (a) A force of $100\text{ N}$ is applied to the smaller piston. Calculate the pressure transmitted through the oil. [2]

(b) Calculate the maximum force that can be exerted by the larger piston. [2]

(c) Explain why the oil is used instead of air in a hydraulic system. [2]

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Question 8 A diver descends to a depth of $25\text{ m}$ in a lake. The density of water is $1000\text{ kg m}^{-3}$. (a) Calculate the pressure exerted by the water at this depth. [2]

(b) If the atmospheric pressure is $1.0 \times 10^5\text{ Pa}$, calculate the total pressure acting on the diver. [1]

(c) Explain why the diver feels more pressure in the ears as they go deeper. [2]

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Question 9 An electric motor is used to lift a load of $50\text{ kg}$ to a height of $10\text{ m}$ in $20\text{ s}$. (a) Calculate the work done by the motor. [2]

(b) Calculate the power output of the motor. [1]

(c) If the electrical power input is $300\text{ W}$, calculate the efficiency of the motor. [2]

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Question 10 A block of mass $5\text{ kg}$ is pushed across a smooth horizontal surface by a force $F_1 = 20\text{ N}$ to the right. After $2\text{ s}$, a second force $F_2 = 20\text{ N}$ is applied to the left. (a) Describe the motion of the block during the first $2\text{ s}$. [2]

(b) Describe the motion of the block immediately after $F_2$ is applied. [2]

(c) Calculate the velocity of the block at $t = 4\text{ s}$. [2]


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Answer Key - Physics Secondary 3 SA2 (Version 4)

Q1: Kinematics (a) $a = \frac{v-u}{t} = \frac{4-0}{2} = 2.0\text{ m s}^{-2}$ [1] (b) $F = ma = 0.5 \times 2 = 1.0\text{ N}$ [1] (c) Graph: Straight line from $(0,0)$ to $(2,4)$, then horizontal line from $t=2$ to $t=5$ at $v=4$. [2]

Q2: Vertical Motion/Friction (a) Upwards [1] (b) $F_{net} = ma \implies mg - f = ma$ $a = \frac{v^2 - u^2}{2s} = \frac{0 - 2^2}{2(1.5)} = -1.33\text{ m s}^{-2}$ (magnitude $1.33$) $f = mg - ma = 70(10) - 70(-1.33)$ ... Wait, if decelerating downward, $a$ is upward. $f - mg = ma \implies f = m(g+a) = 70(10 + 1.33) = 793.1\text{ N}$ OR using energy: $W_{friction} = \Delta KE \implies f \times 1.5 = \frac{1}{2}(70)(2^2) - 0 \implies f = \frac{140}{1.5} = 93.3\text{ N}$ (This is the net force; friction must also overcome weight). Correct approach: $f - mg = ma \implies f = 70(10) + 70(1.33) = 793.1\text{ N}$. [3]

Q3: Inclined Plane (a) $W = F \times d = 15 \times 4.0 = 60\text{ J}$ [1] (b) $\Delta PE = mgh = 2.0 \times 10 \times 1.2 = 24\text{ J}$ [1] (c) Energy loss = $W_{applied} - \Delta PE = 60 - 24 = 36\text{ J}$ [2]

Q4: Suspended Ring (a) Diagram showing Weight ($W$) down, $T_A$ at $40^\circ$ to horizontal, $T_B$ at $50^\circ$ to horizontal. [2] (b) The angles are different; to maintain horizontal equilibrium, the horizontal components must cancel ($T_A \cos 40^\circ = T_B \cos 50^\circ$), requiring different magnitudes. [2] (c) Vertical component = Weight = $0.2 \times 10 = 2.0\text{ N}$ [1]

Q5: Gravitation (a) $F = \frac{Gm_1m_2}{r^2} = \frac{(6.67 \times 10^{-11})(1.2 \times 10^6)(6.0 \times 10^{24})}{(7.0 \times 10^6)^2} = 9.8 \times 10^6\text{ N}$ [2] (b) $F \propto \frac{1}{r^2}$. If $r$ doubles, $F$ becomes $\frac{1}{4}F$ or $0.25F$. [1]

Q6: Energy Conservation (a) Energy cannot be created or destroyed, only transformed from one form to another. [1] (b) At top of loop (C), $v_C = \sqrt{gr} = \sqrt{10 \times 2} = 4.47\text{ m s}^{-1}$. Energy at A = Energy at C $\frac{1}{2}mv_0^2 = \frac{1}{2}mv_C^2 + mgh$ $\frac{1}{2}v_0^2 = \frac{1}{2}(20) + (10 \times 4) = 10 + 40 = 50$ $v_0^2 = 100 \implies v_0 = 10\text{ m s}^{-1}$ [4]

Q7: Hydraulics (a) $P = \frac{F}{A} = \frac{100}{0.02} = 5000\text{ Pa}$ [2] (b) $F = P \times A = 5000 \times 0.5 = 2500\text{ N}$ [2] (c) Oil is incompressible (unlike air), ensuring pressure is transmitted instantly and efficiently. [2]

Q8: Pressure (a) $P = h\rho g = 25 \times 1000 \times 10 = 250,000\text{ Pa}$ [2] (b) $P_{total} = 250,000 + 100,000 = 350,000\text{ Pa}$ [1] (c) Pressure increases with depth; the external water pressure exceeds the internal air pressure in the ear, pushing the eardrum inward. [2]

Q9: Power/Efficiency (a) $W = mgh = 50 \times 10 \times 10 = 5000\text{ J}$ [2] (b) $P = \frac{W}{t} = \frac{5000}{20} = 250\text{ W}$ [1] (c) $\text{Eff} = \frac{250}{300} \times 100\% = 83.3\%$ [2]

Q10: Opposing Forces (a) Constant acceleration to the right. $a = \frac{20}{5} = 4\text{ m s}^{-2}$. [2] (b) Net force becomes $20 - 20 = 0$. The block continues to move at a constant velocity (zero acceleration). [2] (c) $v$ at $t=2\text{s}$: $v = 0 + (4 \times 2) = 8\text{ m s}^{-1}$. From $t=2$ to $t=4$, $a=0$, so $v$ remains $8\text{ m s}^{-1}$. [2]