Secondary 4 Pure Physics Mechanics Quiz

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

1. Initially, weight is greater than air resistance, so the skydiver accelerates downwards.
2. As speed increases, air resistance increases.
3. 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]