Question

ii. x is the distance from the end of the plank to the point of application of force f
force f is now applied at various points nearer to the pivot so that x increases.
equilibrium is maintained all the time. on the axes provided sketch the relation
between force f and x. (2 marks)
(iii) give a reason for the answer in (ii) above (1 mark)

1. (a) a student is provided with five 20 g masses, a meter rule, a spring with a pointer, a stand, a boss

and a clamp.
(i) in the space provided, sketch a labelled diagram of the set up that may be used in
order to verify hookes law using these apparatus. (3 marks)

Explanation:

For part (II): The problem involves rotational equilibrium (torque balance). When equilibrium is maintained, the torque from force \( F \) (about the pivot) equals the opposing torque (from a fixed load). Torque is \( F \times X \), so \( F \times X = \text{constant} \). This means \( F \) is inversely proportional to \( X \), so the graph is a hyperbola (curved line decreasing as \( X \) increases).

For part (iii): The reason is that torque must be constant for equilibrium, leading to an inverse relationship between \( F \) and \( X \).

For 18(a)(i): To verify Hooke’s law, the setup needs the spring suspended vertically (clamped to the stand), masses hung from its end, and a meter rule to measure extension. The painter marks the spring’s position for each mass.

Answer:

(II) A curved line (hyperbola) starting high on the \( F \)-axis and decreasing as \( X \) increases (inverse proportionality graph).
(iii) Torque \( F \times X \) is constant for equilibrium, so \( F \propto 1/X \).
18(a)(i) A diagram showing:

• Stand with boss and clamp holding the spring vertically.
• Meter rule alongside the spring (fixed to the stand).
• Masses hung from the spring’s end.
• Painter on the spring to mark positions.

(Note: Diagrams are visual, but the key labeled components are as above.)