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

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Questions

TuitionGoWhere Practice Paper - Physics Secondary 3

TuitionGoWhere Secondary School (AI)

Subject: Physics
Level: Secondary 3
Paper: SA2 Practice Paper (Version 4)
Duration: 1 hour 30 minutes
Total Marks: 60

Name: _________________________
Class: _________________________
Date: _________________________

Instructions to Candidates

This paper consists of three sections: Section A, Section B, and Section C.
Answer all questions.
Write your answers in the spaces provided.
Show all working clearly for calculation questions. Marks are awarded for correct method even if the final answer is wrong.
Take gravitational acceleration, g = 10 m/s² unless otherwise stated.
The number of marks is given in brackets [ ] at the end of each question or part question.
You may use a scientific calculator.

Section A: Multiple Choice (10 marks)

Answer all questions in this section. Circle the correct answer for each question.

1. A student pushes a box across a rough floor at constant speed. Which statement about the forces acting on the box is correct?

A. The pushing force is greater than the friction force.
B. The pushing force equals the friction force.
C. The pushing force is less than the friction force.
D. No friction force acts on the box.

[1 mark]

2. An object of mass 5.0 kg is placed on a smooth horizontal surface. A force of 15 N acts on it to the right, and a force of 5.0 N acts on it to the left. What is the acceleration of the object?

A. 1.0 m/s²
B. 2.0 m/s²
C. 3.0 m/s²
D. 4.0 m/s²

[1 mark]

3. A ball is thrown vertically upwards. At the highest point of its motion, which of the following is true?

A. Its velocity is zero and its acceleration is zero.
B. Its velocity is zero and its acceleration is 10 m/s² downwards.
C. Its velocity is maximum and its acceleration is zero.
D. Its velocity is maximum and its acceleration is 10 m/s² downwards.

[1 mark]

4. A uniform metre rule is pivoted at its 50 cm mark. A 2.0 N weight is hung at the 20 cm mark. At which mark should a 1.0 N weight be hung to balance the rule?

A. 10 cm
B. 30 cm
C. 70 cm
D. 90 cm

[1 mark]

5. A car of mass 800 kg accelerates uniformly from rest to 20 m/s in 8.0 seconds. What is the average power developed by the engine during this time? (Ignore resistive forces.)

A. 10 kW
B. 20 kW
C. 40 kW
D. 80 kW

[1 mark]

6. A hydraulic press has a small piston of area 0.020 m² and a large piston of area 0.50 m². A force of 40 N is applied to the small piston. What is the force exerted by the large piston?

A. 1.6 N
B. 40 N
C. 500 N
D. 1000 N

[1 mark]

7. A block slides down a frictionless inclined plane. Which energy transformation occurs?

A. Kinetic energy → gravitational potential energy
B. Gravitational potential energy → kinetic energy
C. Chemical energy → kinetic energy
D. Kinetic energy → thermal energy

[1 mark]

8. A student investigates the relationship between force and extension for a spring. The spring obeys Hooke's Law. Which graph best represents the relationship?

A. Force (y-axis) vs. extension (x-axis): a straight line through the origin
B. Force (y-axis) vs. extension (x-axis): a curve flattening at high extension
C. Extension (y-axis) vs. force (x-axis): a straight line through the origin
D. Extension (y-axis) vs. force (x-axis): a curve flattening at high force

[1 mark]

9. A submarine is at a depth of 200 m in seawater of density 1030 kg/m³. What is the pressure due to the seawater at this depth? (Atmospheric pressure = 1.0 × 10⁵ Pa)

A. 2.06 × 10⁵ Pa
B. 2.06 × 10⁶ Pa
C. 2.16 × 10⁶ Pa
D. 3.06 × 10⁶ Pa

[1 mark]

10. Two forces, 3.0 N and 4.0 N, act on an object at right angles to each other. What is the magnitude of the resultant force?

A. 1.0 N
B. 5.0 N
C. 7.0 N
D. 12 N

[1 mark]

Section B: Structured Questions (30 marks)

Answer all questions in this section. Write your answers in the spaces provided.

11. A student investigates the motion of a trolley on a horizontal track. The trolley is pulled by a falling mass connected by a string over a pulley. The student records the following data:

Time / s	Displacement / m
0.0	0.0
0.5	0.10
1.0	0.40
1.5	0.90
2.0	1.60
2.5	2.50

(a) Plot a displacement-time graph for the trolley's motion on the grid below. Label both axes clearly. [3 marks]

(Grid space provided)

(b) Describe the motion of the trolley. Explain how you can tell from the graph. [2 marks]

(c) Calculate the average velocity of the trolley between t = 1.0 s and t = 2.0 s. [2 marks]

(d) The mass of the trolley is 0.80 kg. Calculate the resultant force acting on the trolley during the motion described. [2 marks]

12. A construction worker uses a uniform plank of length 4.0 m and weight 200 N as a ramp to load a heavy crate onto a truck. The plank is placed with one end on the ground and the other end on the truck bed at a height of 1.2 m.

(a) Calculate the angle the plank makes with the horizontal. [1 mark]

(b) A crate of weight 600 N is pulled up the plank at constant speed. The frictional force between the crate and the plank is 100 N.

(i) Draw a free-body diagram showing all the forces acting on the crate as it moves up the plank. Label each force clearly. [3 marks]

(Space provided for diagram)

(ii) Calculate the force required to pull the crate up the plank at constant speed. [3 marks]

(c) The worker pulls the crate a distance of 4.0 m along the plank. Calculate:

(i) The work done by the pulling force. [2 marks]

(ii) The gain in gravitational potential energy of the crate. [2 marks]

(iii) The energy dissipated as thermal energy due to friction. [1 mark]

13. A student investigates the principle of moments using a metre rule pivoted at its centre. The metre rule has a mass of 100 g.

(a) State the principle of moments. [1 mark]

(b) A 200 g mass is hung at the 15 cm mark on the left side of the pivot. A 150 g mass is hung at the 80 cm mark on the right side of the pivot.

(i) Calculate the moment due to the 200 g mass about the pivot. State whether it is clockwise or anticlockwise. [2 marks]

(ii) Calculate the moment due to the 150 g mass about the pivot. State whether it is clockwise or anticlockwise. [2 marks]

(iii) Determine whether the metre rule is balanced. If not, state which side will move downwards. [1 mark]

(c) The student now hangs an additional mass at the 90 cm mark to balance the rule. Calculate the mass required. [3 marks]

Section C: Data-Based and Application Questions (20 marks)

Answer all questions in this section. Write your answers in the spaces provided.

14. A skydiver of mass 70 kg jumps from a stationary helicopter. The graph below shows how the skydiver's velocity changes with time during the first 60 seconds of the fall.

Image pending generation for this question.

(Graph shows velocity increasing from 0, curving to approach a terminal velocity of approximately 55 m/s after about 15 seconds. At t = 30 s, the parachute opens and velocity decreases rapidly to a new terminal velocity of about 5 m/s.)

(a) Using the graph, determine:

(i) The terminal velocity of the skydiver before the parachute opens. [1 mark]

(ii) The time at which the parachute opens. [1 mark]

(iii) The terminal velocity after the parachute opens. [1 mark]

(b) Explain, in terms of forces, why the skydiver reaches a terminal velocity before the parachute opens. [3 marks]

(c) Calculate the weight of the skydiver. [1 mark]

(d) When the parachute opens, the skydiver experiences a large upward force. Explain why the skydiver does not immediately start moving upwards. [2 marks]

(e) Calculate the distance fallen by the skydiver during the first 10 seconds. State any assumption you make. [3 marks]

15. A student investigates the relationship between force, mass, and acceleration using the apparatus shown below.

(Diagram shows a trolley on a horizontal track connected by a string over a pulley to a hanging mass. A motion sensor is positioned to measure the trolley's acceleration.)

The student keeps the hanging mass constant at 0.10 kg and varies the mass of the trolley by adding masses to it. The following results are obtained:

Mass of trolley + added masses / kg	Acceleration / m/s²	1/Mass / kg⁻¹
0.50	1.67	2.00
0.75	1.18	1.33
1.00	0.91	1.00
1.25	0.74	0.80
1.50	0.63	0.67

(a) State the independent variable and the dependent variable in this investigation. [2 marks]

(b) Explain why the hanging mass is kept constant. [1 mark]

(c) Plot a graph of acceleration (y-axis) against 1/mass (x-axis) on the grid below. Draw the best-fit straight line. [4 marks]

(Grid space provided)

(d) Using your graph, determine the force causing the acceleration. Explain how you obtained your answer. [3 marks]

(e) The student notices that the graph does not pass exactly through the origin. Suggest a reason for this observation. [1 mark]

--- End of Paper ---

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Answers

TuitionGoWhere Practice Paper - Physics Secondary 3

SA2 Practice Paper (Version 4) - ANSWER KEY AND MARKING SCHEME

Total Marks: 60

Section A: Multiple Choice (10 marks)

Question	Answer	Marks
1	B	1
2	B	1
3	B	1
4	D	1
5	B	1
6	D	1
7	B	1
8	A	1
9	C	1
10	B	1

Marking notes for Section A:

Award 1 mark per correct answer.
No half marks; no marks deducted for incorrect answers.

Section B: Structured Questions (30 marks)

Question 11 (9 marks)

(a) Plot displacement-time graph. [3 marks]

Marking:

1 mark: Both axes correctly labelled (Time/s on x-axis, Displacement/m on y-axis) with appropriate scales.
1 mark: All six data points plotted correctly (± half small square).
1 mark: Smooth curve drawn through points (curve should show increasing gradient, indicating acceleration).

(b) Describe the motion of the trolley. [2 marks]

Expected answer: The trolley is accelerating / moving with increasing velocity. [1 mark]

Explanation: The gradient of the displacement-time graph is increasing / the displacement increases by larger amounts in equal time intervals. [1 mark]

Accept: "The trolley is undergoing uniform acceleration" if justified by reference to the curve shape.

(c) Calculate average velocity between t = 1.0 s and t = 2.0 s. [2 marks]

Working:

At t = 1.0 s, displacement = 0.40 m
At t = 2.0 s, displacement = 1.60 m
Change in displacement = 1.60 - 0.40 = 1.20 m [1 mark]
Time interval = 2.0 - 1.0 = 1.0 s
Average velocity = 1.20 / 1.0 = 1.2 m/s [1 mark]

Accept: 1.20 m/s. Award 1 mark for correct method even if arithmetic error.

(d) Calculate resultant force on trolley. [2 marks]

Working:

From graph, acceleration can be found from gradient of v-t graph, or using s = ut + ½at².
Using data: at t = 2.0 s, s = 1.60 m, u = 0.
1.60 = 0 + ½ × a × (2.0)²
1.60 = 2.0a
a = 0.80 m/s² [1 mark for correct acceleration]
F = ma = 0.80 × 0.80 = 0.64 N [1 mark]

Alternative method: Find acceleration from any valid kinematic calculation. Award 1 mark for correct method, 1 mark for correct answer with unit.

Question 12 (12 marks)

(a) Calculate angle of plank with horizontal. [1 mark]

Working:

sin θ = opposite/hypotenuse = 1.2/4.0 = 0.30
θ = sin⁻¹(0.30) = 17.5° (or 17° or 18°)

Award 1 mark for correct angle. Accept 17° to 18°.

(b)(i) Free-body diagram. [3 marks]

Expected forces (all must be present and correctly labelled):

Weight (W or mg) acting vertically downwards from centre of crate [1 mark]
Normal reaction (N or R) acting perpendicular to the plank surface [1 mark]
Pulling force (F or P) acting up the plank, parallel to surface
Friction (f or F_f) acting down the plank, parallel to surface [1 mark for both pulling force and friction correctly shown]

Deduct 1 mark if any force is missing or incorrectly directed. Arrows must show correct directions.

(b)(ii) Calculate force required to pull crate at constant speed. [3 marks]

Working:

At constant speed, net force = 0.
Forces along the plane: Pulling force F = component of weight down plane + friction
Component of weight down plane = mg sin θ = 600 × (1.2/4.0) = 600 × 0.30 = 180 N [1 mark]
Friction = 100 N [given]
Total force required: F = 180 + 100 = 280 N [2 marks for correct total]

Alternative: Calculate angle first, then use F = mg sin θ + friction. Award marks proportionally.

(c)(i) Work done by pulling force. [2 marks]

Working:

Work = Force × distance moved in direction of force
W = 280 × 4.0 = 1120 J [1 mark for formula/substitution, 1 mark for correct answer with unit]

Accept: 1100 J (if using rounded values).

(c)(ii) Gain in gravitational potential energy. [2 marks]

Working:

GPE = mgh = 600 × 1.2 = 720 J [1 mark for formula/substitution, 1 mark for correct answer with unit]

(c)(iii) Energy dissipated as thermal energy due to friction. [1 mark]

Working:

Energy dissipated = Work done by friction = friction force × distance
= 100 × 4.0 = 400 J

Or: Energy dissipated = Work input - GPE gain = 1120 - 720 = 400 J

Award 1 mark for 400 J.

Question 13 (9 marks)

(a) State the principle of moments. [1 mark]

Expected answer: For an object in equilibrium, the sum of clockwise moments about a pivot equals the sum of anticlockwise moments about the same pivot.

Accept: "Total clockwise moment = total anticlockwise moment" or equivalent wording.

(b)(i) Moment due to 200 g mass. [2 marks]

Working:

Mass = 200 g = 0.200 kg; Weight = 0.200 × 10 = 2.0 N
Distance from pivot (at 50 cm mark) = 50 - 15 = 35 cm = 0.35 m
Moment = Force × perpendicular distance = 2.0 × 0.35 = 0.70 N m [1 mark]
Direction: Anticlockwise [1 mark]

Accept: 0.7 N m.

(b)(ii) Moment due to 150 g mass. [2 marks]

Working:

Mass = 150 g = 0.150 kg; Weight = 0.150 × 10 = 1.5 N
Distance from pivot = 80 - 50 = 30 cm = 0.30 m
Moment = 1.5 × 0.30 = 0.45 N m [1 mark]
Direction: Clockwise [1 mark]

(b)(iii) Is the metre rule balanced? [1 mark]

Answer: No, the rule is not balanced. The anticlockwise moment (0.70 N m) is greater than the clockwise moment (0.45 N m), so the left side will move downwards.

Award 1 mark for correct conclusion with reasoning.

(c) Calculate mass required at 90 cm mark to balance rule. [3 marks]

Working:

For balance: Total anticlockwise moment = Total clockwise moment
Anticlockwise moment = 0.70 N m (from 200 g mass)
Clockwise moment from 150 g mass = 0.45 N m
Additional clockwise moment needed = 0.70 - 0.45 = 0.25 N m [1 mark]
Distance of 90 cm mark from pivot = 90 - 50 = 40 cm = 0.40 m
Let required weight = W; then W × 0.40 = 0.25 [1 mark]
W = 0.25 / 0.40 = 0.625 N
Mass = W/g = 0.625 / 10 = 0.0625 kg = 62.5 g [1 mark]

Accept: 62.5 g or 0.0625 kg. Award marks for correct method even with arithmetic errors.

Section C: Data-Based and Application Questions (20 marks)

Question 14 (12 marks)

(a)(i) Terminal velocity before parachute opens. [1 mark]

Answer: 55 m/s (accept 54-56 m/s from graph reading)

(a)(ii) Time at which parachute opens. [1 mark]

Answer: 30 s

(a)(iii) Terminal velocity after parachute opens. [1 mark]

Answer: 5 m/s (accept 4.5-5.5 m/s from graph reading)

(b) Explain why skydiver reaches terminal velocity before parachute opens. [3 marks]

Expected answer:

As the skydiver falls, air resistance (drag force) increases with speed. [1 mark]
The weight of the skydiver remains constant (mg = 700 N). [1 mark]
When air resistance becomes equal to the weight, the net force is zero. According to Newton's First Law, the skydiver continues at constant velocity (terminal velocity). [1 mark]

Accept any answer that correctly identifies: (1) air resistance increases with speed, (2) weight is constant, (3) terminal velocity occurs when forces balance.

(c) Calculate weight of skydiver. [1 mark]

Working:

W = mg = 70 × 10 = 700 N

Award 1 mark for 700 N.

(d) Explain why skydiver does not immediately move upwards when parachute opens. [2 marks]

Expected answer:

When the parachute opens, the upward force (air resistance) becomes much larger than the weight, producing a net upward force. [1 mark]
However, the skydiver is still moving downwards. The net upward force causes a deceleration (reduction in downward velocity), not an immediate reversal of direction. The skydiver continues moving downwards but at a decreasing speed until a new, lower terminal velocity is reached. [1 mark]

Key point: The skydiver has downward momentum/velocity; the net upward force decelerates but does not instantly reverse the motion.

(e) Calculate distance fallen in first 10 seconds. [3 marks]

Working:

Assumption: For the first 10 seconds, the graph is approximately a straight line, indicating roughly constant acceleration (or: air resistance is negligible in the first 10 s). [1 mark for stated assumption]
From graph, at t = 10 s, velocity ≈ 50 m/s (accept 48-52 m/s)
Average velocity ≈ (0 + 50)/2 = 25 m/s [1 mark]
Distance = average velocity × time = 25 × 10 = 250 m [1 mark]

Alternative: Use area under v-t graph (approximate as triangle). Award marks proportionally. Accept 240-260 m depending on graph reading.

Question 15 (8 marks)

(a) Independent and dependent variables. [2 marks]

Answer:

Independent variable: Mass of trolley (or 1/mass) [1 mark]
Dependent variable: Acceleration [1 mark]

(b) Why hanging mass is kept constant. [1 mark]

Answer: To keep the force causing acceleration constant, so that the relationship between mass and acceleration can be investigated. (Since F = ma, if F is constant, a ∝ 1/m.)

Award 1 mark for "to keep force constant" or equivalent.

(c) Graph of acceleration vs. 1/mass. [4 marks]

Marking:

1 mark: Axes correctly labelled (Acceleration / m/s² on y-axis; 1/Mass / kg⁻¹ on x-axis) with appropriate scales.
1 mark: All five data points plotted correctly (± half small square).
1 mark: Best-fit straight line drawn (should pass through or near origin).
1 mark: Line is straight and reasonably fits the trend of points.

(d) Determine force causing acceleration from graph. [3 marks]

Working:

From Newton's Second Law: F = ma, rearranged as a = F × (1/m)
Therefore, the gradient of the a vs. 1/m graph equals the force F. [1 mark]
Gradient calculation: Choose two points on best-fit line, e.g., (0.5, 0.45) and (2.0, 1.80)
Gradient = (1.80 - 0.45) / (2.0 - 0.5) = 1.35 / 1.5 = 0.90 N [1 mark for correct gradient calculation]
Force = 0.90 N [1 mark]

Accept: 0.85-0.95 N depending on graph line drawn. Award 1 mark for stating gradient = force, 1 mark for method, 1 mark for answer with unit.

Alternative: Use F = hanging mass × g = 0.10 × 10 = 1.0 N. The graph gives approximately 0.9 N due to friction in the system. Accept either answer with justification.

(e) Reason why graph does not pass exactly through origin. [1 mark]

Answer: There is friction in the system (between trolley and track, or in the pulley) that opposes motion, so a small force is needed before acceleration begins. / Systematic error in the measurements. / The hanging mass also accelerates, so not all its weight contributes to accelerating the trolley.

Award 1 mark for any reasonable suggestion.

--- End of Answer Key ---