Most-appropriate topic codes (Cambridge IGCSE Co-ordinated Sciences 0654):
• Topic P1.5.2 — Turning effect of forces
• Topic P1.3 — Mass and weight
(a)(i) force × perpendicular distance from pivot
The moment of a force is a measure of its turning effect about a pivot. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the pivot to the line of action of the force.
(a)(ii) no resultant force ; no resultant moment
For an object to be in equilibrium, the net force acting on it must be zero and the net moment about any point must be zero. This means all forces and turning effects are balanced.
(b)(i) (W = mg) = 0.040 × 9.8 = 0.39 N
Weight is calculated by multiplying mass (in kg) by gravitational field strength. The mass of 40 g is converted to 0.040 kg.
(b)(ii) 0.24 N
Appreciation of weight acting from centre of ruler
0.39 × 17 = W × 28
W = 0.24 N
The weight of the ruler acts at its centre (50 cm from the end). Taking moments about the pivot: the 0.39 N weight at 17 cm from pivot balances the ruler’s weight at 28 cm from pivot.
Most-appropriate topic codes (Cambridge IGCSE Co-ordinated Sciences 0654):
• Topic P1.1 — Physical quantities and measurement techniques (Part (a)(i))
• Topic P1.2 — Motion (Parts (a)(ii) & (b))
• Topic P1.3 — Mass and weight (Part (c)(i))
• Topic P1.6.2 — Work / Kinetic energy (Part (c)(ii))
(a)(i) Vector quantities: gravitational field strength, weight.
Vector quantities have both magnitude and direction. Gravitational field strength and weight are vectors; energy, temperature, and time are scalars (magnitude only).
(a)(ii) Velocity is speed in a given direction.
Velocity is a vector quantity that describes the rate of change of displacement (distance travelled per unit time in a specific direction).
(b) Acceleration = 0.45 m/s².
Acceleration is the gradient of a speed-time graph. During the first 12 seconds, the speed increases from 0 to 5.4 m/s.
\(a = \frac{\Delta v}{\Delta t} = \frac{5.4 – 0}{12 – 0} = \frac{5.4}{12} = 0.45\text{ m/s}^2\)
(c)(i) Ratio = 3.6 (or –3.6).
\(\text{ratio} = \frac{35}{9.8} = 3.57 \approx 3.6\)
(The negative sign indicates deceleration/opposite direction.)
(c)(ii) Mass = 1200 kg.
\(E_k = \frac{1}{2}mv^2\)
\(470000 = \frac{1}{2} \times m \times 28^2\)
\(470000 = \frac{1}{2} \times m \times 784\)
\(470000 = 392m\)
\(m = \frac{470000}{392} = 1198.98 \approx 1200\text{ kg}\)
