Two trucks \(A\) and \(B\), moving in opposite directions on the same horizontal railway track, collide. The mass of \(A\) is 600 kg . The mass of \(B\) is \(m \mathrm {~kg}\). Immediately before the collision, the speed of \(A\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after the collision, the trucks are joined together and move with the same speed \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The direction of motion of \(A\) is unchanged by the collision. Find
- the value of \(m\),
- the magnitude of the impulse exerted on \(A\) in the collision.
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A lever consists of a uniform steel \(\operatorname { rod } A B\), of weight 100 N and length 2 m , which rests on a small smooth pivot at a point \(C\) of the rod. A load of weight 2200 N is suspended from the end \(B\) of the rod by a rope. The lever is held in equilibrium in a horizontal position by a vertical force applied at the end \(A\), as shown in Fig. 1. The rope is modelled as a light string.
Given that \(B C = 0.2 \mathrm {~m}\),