M1 June 2005 Q6
6.
A uniform beam \(AB\) has mass 12 kg and length 3 m. The beam rests in equilibrium in a horizontal position, resting on two smooth supports. One support is at the end \(A\), the other at a point \(C\) on the beam, where \(BC = 1\) m, as shown in Figure 3. The beam is modelled as a uniform rod.
(a) Find the reaction on the beam at \(C\). (3)
A woman of mass 48 kg stands on the beam at the point \(D\). The beam remains in equilibrium. The reactions on the beam at \(A\) and \(C\) are now equal.
(b) Find the distance \(AD\). (7)
| Scheme | Marks |
|---|---|
| M(\(A\)): \(12g \times 1.5 = R \times 2\) | M1 A1 |
| \(R = 9g\) or 88.2 N | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| R(\(\uparrow\)) \(2S = 48g + 12g\) \(S = 30g\) | M1 A1 |
| M(\(A\)): \(S \times 2 = 12g \times 1.5 + 48g \times x\) | M1 A2,1,0 |
| Sub for \(S\) and solve for \(x\): \(x = 7/8\) or 0.875 or 0.88 m | M1 A1 |
| (7) | |
| (10 marks) |