June 2025 Paper 2 Q18
18 In this question use \(g = 9.81\ \text{m s}^{-2}\)
A uniform platform \(AD\) has length 2.5 metres and weight 400 newtons.
The platform is attached to a chain at \(A\). The other end of the chain is fixed to the floor.
The platform rests on a support at a point \(B\) which is 0.6 metres from \(A\)
The support exerts an upwards reaction force on the platform.
A child of mass 30 kilograms stands at a point \(C\)
The point \(C\) is 0.2 metres from \(D\), as shown in the diagram.
The system is in equilibrium with the platform resting horizontally.
State what happens to the reaction force at \(B\) during this movement.
[1 mark]State what happens to the tension in the chain during this movement.
[1 mark]| Scheme | Marks | AO |
|---|---|---|
| Obtains one of the following moments about A. \(\pm 2.3 \times 30g\) OE \(\pm 1.25 \times 400\) OE PI AWRT 1960 or AWRT 1983 | B1 | 3.3 |
| Forms a three term moments equation about A with at least one correct term. Must be dimensionally correct. PI 0.6R = AWFW [1176, 1177] or 0.6R = 1190 | M1 | 3.3 |
| Forms a fully correct moments equation about A. PI AWRT 1960 or AWRT 1983 | A1 | 1.1b |
| Obtains \(1960\ \text{N}\) Must include units | A1 | 3.2a |
| (4) |
Typical solution
clockwise: \(2.3 \times 30 \times 9.81 + 1.25 \times 400\)
anticlockwise: \(0.6\mathbf{R}\)
\[0.6\mathbf{R} = 2.3 \times 30 \times 9.81 + 1.25 \times 400\]\[\mathbf{R} = \frac{2.3 \times 30 \times 9.81 + 1.25 \times 400}{0.6}\]\[\mathbf{R} = 1960\ \text{N}\]| Scheme | Marks | AO |
|---|---|---|
| (i) States that the reaction force decreases with no other incorrect reasoning. | E1 | 3.5a |
| (1) | ||
| (ii) States that the tension in the chain does not change. | E1 | 3.5a |
| (1) | ||
| (6 marks) |
Typical solution
(b)(i)
As the child walks towards \(B\) the reaction force at \(B\) decreases.
(b)(ii)
The tension in the chain does not change.