M1 January 2007 Q2
2.
A uniform plank \(AB\) has weight 120 N and length 3 m. The plank rests horizontally in equilibrium on two smooth supports \(C\) and \(D\), where \(AC = 1\) m and \(CD = x\) m, as shown in Figure 2. The reaction of the support on the plank at \(D\) has magnitude 80 N. Modelling the plank as a rod,
(a) show that \(x = 0.75\) (3)
A rock is now placed at \(B\) and the plank is on the point of tilting about \(D\).
Modelling the rock as a particle, find
(b) the weight of the rock, (4)
(c) the magnitude of the reaction of the support on the plank at \(D\). (2)
(d) State how you have used the model of the rock as a particle. (1)
| Scheme | Marks |
|---|---|
| M(\(C\)) \(80 \times x = 120 \times 0.5\) | M1 A1 |
| \(x = 0.75\) * cso | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| Using reaction at \(C = 0\) | B1 |
| M(\(D\)) \(120 \times 0.25 = W \times 1.25\) ft their \(x\) | M1 A1 |
| \(W = 24\) (N) | A1 |
| (4) |
| Scheme | Marks |
|---|---|
| \(\uparrow\) \(X = 24 + 120 = 144\) (N) ft their \(W\) | M1 A1ft |
| (2) |
| Scheme | Marks |
|---|---|
| The weight of the rock acts precisely at \(B\). | B1 |
| (1) | |
| (10 marks) |