Secondary 3 Physics Mechanics Quiz

Secondary 3 Physics Quiz - Mechanics: Answer Key

Total Marks: 50

Section A: Multiple Choice

1. C — displacement [1]

Displacement is a vector quantity because it has both magnitude and direction. Mass, speed, and time are scalar quantities with magnitude only.

2. C — 10 m/s [1]

Using $v = u + at$, where $u = 0$, $a = 2.0$ m/s², $t = 5.0$ s: $v = 0 + (2.0)(5.0) = 10$ m/s.

3. C — The net force on the object is zero [1]

Newton's First Law: constant velocity (including rest) means zero net force. Frictional forces may balance applied forces.

4. B — velocity is zero and acceleration is downward [1]

At the highest point, instantaneous velocity is zero (momentarily at rest), but acceleration due to gravity (g = 10 m/s² downward) continues to act throughout the flight.

5. B — 100 N [1]

Weight on Moon = $\frac{1}{6} \times 600$ N = 100 N. Weight depends on gravitational field strength; mass stays constant.

6. C — 20 N [1]

Constant velocity means zero acceleration, so net force is zero (Newton's First Law). Therefore frictional force equals applied force: 20 N, acting opposite to motion.

7. (Accept: graph showing straight line with negative gradient from positive velocity to zero) [1]

Deceleration to rest is represented by a straight line with negative slope reaching v = 0. The gradient of a velocity-time graph equals acceleration.

8. A — gravitational potential energy to kinetic energy [1]

As the bob falls, its height decreases (GPE decreases) and speed increases (KE increases). Total mechanical energy is conserved if air resistance is negligible.

9. B — 5 N [1]

Using Pythagoras: $R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ N. The resultant of perpendicular vectors is found using $R = \sqrt{a^2 + b^2}$.

10. C — 4000 W [1]

Work done = force × distance = mg × h = (500)(10)(8) = 40 000 J. Power = $\frac{40 000}{10}$ = 4000 W.

Section B: Structured Questions

11. Acceleration is the rate of change of velocity with respect to time. [1]
The SI unit is m/s² (metres per second squared). [1]

Key concept: Acceleration measures how quickly velocity changes, including changes in speed or direction. The unit comes from (m/s) ÷ s = m/s².

12. (a) Total distance = 1200 + 800 = 2000 m [1]

Distance is the total path length travelled, regardless of direction.

(b) Displacement = 1200 m (north) − 800 m (south) = 400 m north [2]

Displacement is the straight-line distance from start to finish with direction. North is positive; south subtracts. [1 mark for magnitude 400 m, 1 mark for direction north]

(c) Average speed = $\frac{\text{total distance}}{\text{total time}} = \frac{2000}{200}$ = 10 m/s [2]

[1 mark for formula/state use of total distance not displacement, 1 mark for correct answer with unit]

13. (a) Acceleration = gradient = $\frac{\Delta v}{\Delta t} = \frac{10 - 0}{5 - 0}$ = 2 m/s² [2]

[1 mark for identifying gradient method or correct substitution, 1 mark for answer with unit]

(b) Distance = area under graph
= Area of triangle (0–5 s) + Area of rectangle (5–12 s) + Area of triangle (12–20 s) [1]

= $\frac{1}{2} \times 5 \times 10 + (12-5) \times 10 + \frac{1}{2} \times (20-12) \times 10$
= 25 + 70 + 40 [1]

= 135 m [1]

Each phase: acceleration phase = triangle, constant velocity = rectangle, deceleration = triangle. Area under velocity-time graph equals displacement/distance for linear motion.

(c) The train is decelerating uniformly (at constant rate) to rest. [1]

Velocity decreases linearly from 10 m/s to 0 in 8 s. The negative gradient indicates negative acceleration (deceleration).

14. (a) Terminal velocity [1]

(Accept: constant velocity in free fall when air resistance equals weight)

(b) Weight = $mg = 70 \times 10$ = 700 N [1]

(c) By Newton's First Law: constant velocity means zero resultant force [1]
The upward air resistance equals the downward weight (700 N) [1]
These two forces balance, so there is no acceleration [1]

At terminal velocity, the skydiver is in dynamic equilibrium. Initially, air resistance < weight, so acceleration downward. As speed increases, air resistance increases until it equals weight.

15. (a) Initial KE = $\frac{1}{2}mu^2 = \frac{1}{2}(1200)(5)^2 = 15 000$ J [1]
Final KE = $\frac{1}{2}mv^2 = \frac{1}{2}(1200)(25)^2 = 375 000$ J [1]
Change in KE = 375 000 − 15 000 = 360 000 J (or 360 kJ) [1]

(b) Power = $\frac{\text{work done (or energy change)}}{\text{time}} = \frac{360 000}{10}$ = 36 000 W (or 36 kW) [2]

[1 mark for correct formula and substitution, 1 mark for answer with unit]

16. (a) Resultant force = 0 N [1]
The block is at rest (not accelerating), so by Newton's First/Second Law, net force must be zero [1]

(b) Frictional force = 15 N, acting horizontally opposite to the applied force (to the left) [2]

[1 mark for magnitude 15 N, 1 mark for correct direction]

(c) Resultant force = $ma = 1200 \times 0.5$ — Wait: mass not stated in Q16. Using F = ma with given acceleration...

Recalculating: The question states block weight 50 N, so mass = 5 kg.
Resultant force = $ma = 5 \times 0.5$ = 2.5 N [2]

[1 mark for correct mass from weight, 1 mark for F = ma calculation]

Common error: Using 1200 kg from Q15. Each question is independent.

17. (a) Vertical motion: $s = ut + \frac{1}{2}at^2$
45 = $0 \times t + \frac{1}{2}(10)t^2$ [1]
$t^2 = 9$, so $t$ = 3.0 s [1]

Vertical initial velocity is zero (launched horizontally). Only gravity acts vertically.

(b) Horizontal distance = horizontal velocity × time = $20 \times 3.0$ = 60 m [2]

[1 mark for identifying horizontal velocity is constant, 1 mark for calculation]

(c) The horizontal velocity remains constant (at 20 m/s). [1]

No horizontal force (air resistance negligible), so by Newton's First Law, horizontal velocity is unchanged. Vertical and horizontal motions are independent.

18. (a) Using geometry: $h = L - L\cos\theta = 1.0 - 1.0\cos30°$ [1]
$h = 1.0 - 0.866$ = 0.134 m (or 0.13 m) [1]

Height difference comes from the vertical component: at angle θ, vertical drop from maximum height is L(1 − cos θ).

(b) GPE lost = $mgh = (0.20 \times 10) \times 0.134 = 2.0 \times 0.134$ = 0.268 J (or 0.27 J) [2]

[1 mark for correct weight/mg, 1 mark for calculation]

(c) By conservation of energy: GPE lost = KE gained
$\frac{1}{2}mv^2 = mgh$ [1]
$v^2 = 2gh = 2 \times 10 \times 0.134 = 2.68$ [1]
$v = \sqrt{2.68}$ = 1.64 m/s (or 1.63 m/s using g = 10 exactly) [1]

Alternative: $v = \sqrt{2 \times 10 \times 0.134} = \sqrt{2.68}$. Using exact values, accept 1.6–1.7 m/s range.

19. (a) Weight = $mg = 0.30 \times 10$ = 3.0 N [1]

(b) Taking moments about pivot (50 cm mark): [1]
Clockwise moment = anticlockwise moment
$m \times 10 \times (70-50) = 3.0 \times (50-20)$ [1]
$m \times 10 \times 20 = 3.0 \times 30$
$200m = 90$
$m$ = 0.45 kg [1]

Moment = force × perpendicular distance from pivot. The 0.30 kg mass is 30 cm from pivot; unknown mass is 20 cm from pivot.

(c) The rule would rotate clockwise (tip down on the right side) [1]
The clockwise moment would increase (greater distance from pivot), making it larger than the anticlockwise moment [1]

At 80 cm: moment arm = 30 cm vs 20 cm. Clockwise moment = 4.5 N × 0.30 m = 1.35 Nm; anticlockwise = 3.0 N × 0.30 m = 0.90 Nm. Not balanced.

20. (a) Principle of conservation of linear momentum:
The total linear momentum of a system remains constant provided no external resultant force acts on the system. [2]

[1 mark for statement about constant total momentum, 1 mark for condition about no external force]

(b) Taking direction of A's initial motion as positive:
Total momentum before = total momentum after [1]
$(2.0)(3.0) + (4.0)(0) = (2.0)(-1.0) + (4.0)(v_B)$
$6.0 = -2.0 + 4.0v_B$ [1]
$8.0 = 4.0v_B$
$v_B$ = 2.0 m/s in the original direction of trolley A [1]

A rebounds (negative velocity), so momentum is conserved by B moving forward. Direction must be stated.

(c) KE before = $\frac{1}{2}(2.0)(3.0)^2 + 0 = 9.0$ J [1]
KE after = $\frac{1}{2}(2.0)(1.0)^2 + \frac{1}{2}(4.0)(2.0)^2 = 1.0 + 8.0 = 9.0$ J [1]
Since total KE before = total KE after, the collision is elastic [1]

In elastic collisions, both momentum and kinetic energy are conserved. Inelastic collisions lose KE to other forms (heat, sound, deformation).

END OF ANSWER KEY