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Secondary 4 Pure Physics Mechanics Quiz

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Questions

Secondary 4 Pure Physics Quiz - Mechanics

Name: __________________________
Class: __________________________
Date: __________________________
Score: ________ / 45

Duration: 45 minutes
Total Marks: 45

Instructions:

Answer all questions.
Write your answers in the spaces provided.
Show all working clearly. Marks may be awarded for correct working even if the final answer is incorrect.
Take the acceleration due to gravity, $g = 10 \text{ m/s}^2$ .

Section A: Kinematics and Dynamics (Questions 1–5)

1. A car travels along a straight road. It accelerates uniformly from rest to a velocity of $20 \text{ m/s}$ in $5.0 \text{ s}$ . It then maintains this constant velocity for $10 \text{ s}$ before decelerating uniformly to rest in $4.0 \text{ s}$ .

(a) Calculate the acceleration of the car during the first $5.0 \text{ s}$ .
[2]

(b) Calculate the total distance travelled by the car during the entire journey.
[3]

2. Define the term inertia.
[1]

3. A box of mass $12 \text{ kg}$ is pushed across a horizontal floor with a horizontal force of $50 \text{ N}$ . The box accelerates at $2.5 \text{ m/s}^2$ .

(a) Calculate the resultant force acting on the box.
[1]

(b) Calculate the magnitude of the frictional force acting on the box.
[2]

4. State Newton’s Third Law of motion.
[2]

5. A skydiver jumps from a stationary helicopter. Explain, in terms of forces, why the skydiver eventually reaches a constant terminal velocity.
[3]

Section B: Turning Effects and Pressure (Questions 6–10)

6. State the Principle of Moments.
[2]

7. A uniform metre rule is pivoted at the $50 \text{ cm}$ mark. A weight of $4.0 \text{ N}$ is hung at the $20 \text{ cm}$ mark. Calculate the weight $W$ that must be hung at the $80 \text{ cm}$ mark to balance the rule horizontally.
[3]

8. A hydraulic press consists of two pistons connected by an oil-filled tube. The small piston has an area of $0.02 \text{ m}^2$ and the large piston has an area of $0.80 \text{ m}^2$ . A force of $100 \text{ N}$ is applied to the small piston.

(a) Calculate the pressure transmitted through the oil.
[2]

(b) Calculate the output force exerted by the large piston.
[2]

9. A diver is swimming at a depth of $15 \text{ m}$ below the surface of the sea. The density of sea water is $1030 \text{ kg/m}^3$ . Atmospheric pressure is $100,000 \text{ Pa}$ .

Calculate the total pressure acting on the diver.
[3]

10. Explain why a sharp knife cuts through meat more easily than a blunt knife, assuming the same force is applied.
[2]

Section C: Energy, Work and Power (Questions 11–15)

11. Define power.
[1]

12. A crane lifts a load of mass $500 \text{ kg}$ vertically through a height of $20 \text{ m}$ in $10 \text{ s}$ .

(a) Calculate the work done by the crane against gravity.
[2]

(b) Calculate the useful power output of the crane.
[2]

13. A ball of mass $0.5 \text{ kg}$ is dropped from a height of $10 \text{ m}$ . Air resistance is negligible.

(a) State the principle of conservation of energy.
[1]

(b) Calculate the speed of the ball just before it hits the ground.
[3]

14. A motor has an input power of $2000 \text{ W}$ and an efficiency of $75\%$ .

(a) Calculate the useful output power.
[2]

(b) Calculate the energy wasted by the motor in $1 \text{ minute}$ .
[2]

15. Describe the energy changes that occur when a pendulum swings from its highest point to its lowest point.
[2]

Section D: Mixed Mechanics Applications (Questions 16–20)

16. A vector quantity has both magnitude and direction. Give one example of a vector quantity and one example of a scalar quantity.
[2]

Vector: __________________________
Scalar: __________________________

17. Two forces act on an object: $3 \text{ N}$ to the North and $4 \text{ N}$ to the East.

(a) Draw a vector diagram to show how to find the resultant force.
[2]

(b) Calculate the magnitude of the resultant force.
[2]

18. A car of mass $1000 \text{ kg}$ is travelling at $15 \text{ m/s}$ . The driver applies the brakes, and the car stops in $3.0 \text{ s}$ .

Calculate the average braking force.
[3]

19. A student investigates the relationship between the extension of a spring and the load applied. The spring obeys Hooke’s Law.

(a) State Hooke’s Law.
[1]

(b) If a load of $10 \text{ N}$ causes an extension of $5 \text{ cm}$ , calculate the spring constant $k$ in $\text{N/m}$ .
[2]

20. Explain why the centre of gravity of a double-decker bus is designed to be as low as possible.
[2]

End of Quiz

Answers

Secondary 4 Pure Physics Quiz - Mechanics (Answer Key)

1. Kinematics (a) Acceleration $a = \frac{v - u}{t}$
$a = \frac{20 - 0}{5} = 4.0 \text{ m/s}^2$
[1 for formula/substitution, 1 for answer with unit]

(b) Distance = Area under velocity-time graph.
Area 1 (Acceleration): $\frac{1}{2} \times 5 \times 20 = 50 \text{ m}$
Area 2 (Constant): $10 \times 20 = 200 \text{ m}$
Area 3 (Deceleration): $\frac{1}{2} \times 4 \times 20 = 40 \text{ m}$
Total Distance = $50 + 200 + 40 = 290 \text{ m}$
[1 for each correct area calculation, 1 for final sum]

2. Inertia Inertia is the resistance of an object to change its state of rest or uniform motion.
[1 for correct definition]

3. Dynamics (a) Resultant Force $F = ma$
$F = 12 \times 2.5 = 30 \text{ N}$
[1 for answer]

(b) Resultant Force = Applied Force - Friction
$30 = 50 - f$
$f = 50 - 30 = 20 \text{ N}$
[1 for equation, 1 for answer]

4. Newton’s Third Law For every action, there is an equal and opposite reaction.
OR
If body A exerts a force on body B, then body B exerts a force of equal magnitude and opposite direction on body A.
[1 for "equal magnitude", 1 for "opposite direction" / acting on different bodies]

5. Terminal Velocity

Initially, weight is greater than air resistance, so the skydiver accelerates downwards.
As speed increases, air resistance increases.
Eventually, air resistance equals weight. The resultant force is zero, so acceleration is zero and velocity becomes constant.
[1 for each point]

6. Principle of Moments For a body in rotational equilibrium, the sum of clockwise moments about any pivot is equal to the sum of anticlockwise moments about the same pivot.
[1 for "sum clockwise = sum anticlockwise", 1 for "about the same pivot/equilibrium"]

7. Moments Calculation Pivot at $50 \text{ cm}$ .
Force 1: $4.0 \text{ N}$ at $20 \text{ cm}$ . Distance from pivot $d_1 = 50 - 20 = 30 \text{ cm} = 0.3 \text{ m}$ .
Force 2: $W$ at $80 \text{ cm}$ . Distance from pivot $d_2 = 80 - 50 = 30 \text{ cm} = 0.3 \text{ m}$ .
Clockwise Moment = Anticlockwise Moment
$4.0 \times 0.3 = W \times 0.3$
$1.2 = 0.3 W$
$W = 4.0 \text{ N}$
[1 for distances, 1 for equation, 1 for answer]

8. Hydraulics (a) Pressure $P = \frac{F}{A}$
$P = \frac{100}{0.02} = 5000 \text{ Pa}$ (or $\text{N/m}^2$ )
[1 for formula/sub, 1 for answer]

(b) Output Force $F_{out} = P \times A_{large}$
$F_{out} = 5000 \times 0.80 = 4000 \text{ N}$
[1 for substitution, 1 for answer]

9. Fluid Pressure Pressure due to water column $P_{water} = h \rho g$
$P_{water} = 15 \times 1030 \times 10 = 154,500 \text{ Pa}$
Total Pressure = $P_{atm} + P_{water}$
$P_{total} = 100,000 + 154,500 = 254,500 \text{ Pa}$
[1 for water pressure calc, 1 for adding atmospheric, 1 for final answer]

10. Pressure Application Pressure $P = \frac{F}{A}$ . A sharp knife has a smaller surface area ( $A$ ) at the edge compared to a blunt knife. For the same force ( $F$ ), a smaller area results in higher pressure, allowing it to cut through the meat more easily.
[1 for linking P=F/A and area, 1 for conclusion on higher pressure]

11. Power Power is the rate of doing work (or rate of energy transfer).
[1 for definition]

12. Work and Power (a) Work Done $W = F \times d = mgh$
$W = 500 \times 10 \times 20 = 100,000 \text{ J}$
[1 for formula/sub, 1 for answer]

(b) Power $P = \frac{W}{t}$
$P = \frac{100,000}{10} = 10,000 \text{ W}$ (or $10 \text{ kW}$ )
[1 for formula/sub, 1 for answer]

13. Conservation of Energy (a) Energy cannot be created or destroyed, only converted from one form to another.
[1 for correct statement]

(b) Loss in GPE = Gain in KE
$mgh = \frac{1}{2}mv^2$
$gh = \frac{1}{2}v^2 \Rightarrow v = \sqrt{2gh}$
$v = \sqrt{2 \times 10 \times 10} = \sqrt{200} \approx 14.1 \text{ m/s}$
[1 for equation, 1 for substitution, 1 for answer]

14. Efficiency (a) Efficiency = $\frac{\text{Useful Output Power}}{\text{Input Power}} \times 100\%$
$75 = \frac{P_{out}}{2000} \times 100$
$P_{out} = 0.75 \times 2000 = 1500 \text{ W}$
[1 for rearrangement, 1 for answer]

(b) Wasted Power = Input - Output = $2000 - 1500 = 500 \text{ W}$
Energy Wasted = Power $\times$ Time
$E = 500 \times 60 \text{ s} = 30,000 \text{ J}$
[1 for wasted power, 1 for energy calc]

15. Energy Changes Gravitational Potential Energy (GPE) is converted into Kinetic Energy (KE).
[1 for GPE decreases, 1 for KE increases]

16. Vectors and Scalars Vector: Force, Velocity, Acceleration, Displacement, Weight (Any one)
Scalar: Mass, Speed, Distance, Time, Energy (Any one)
[1 for each correct example]

17. Vector Addition (a) Diagram should show two vectors at right angles (head-to-tail or parallelogram method) with the resultant drawn from start to finish.
[1 for correct arrangement, 1 for resultant label]

(b) Magnitude $R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ N}$
[1 for Pythagoras, 1 for answer]

18. Braking Force Acceleration $a = \frac{v - u}{t} = \frac{0 - 15}{3} = -5 \text{ m/s}^2$
Force $F = ma = 1000 \times (-5) = -5000 \text{ N}$
Magnitude of braking force = $5000 \text{ N}$
[1 for acceleration, 1 for F=ma, 1 for magnitude]

19. Hooke’s Law (a) The extension of a spring is directly proportional to the load applied, provided the limit of proportionality is not exceeded.
[1 for proportionality, 1 for limit condition]

(b) $F = kx$
$10 = k \times 0.05$ (convert cm to m)
$k = \frac{10}{0.05} = 200 \text{ N/m}$
[1 for conversion/formula, 1 for answer]

20. Stability A lower centre of gravity increases stability. It requires a larger tilt angle to move the centre of gravity outside the base area, making the bus less likely to topple over.
[1 for link to stability/toppling, 1 for explanation of base/CG position]