Mechanics Exam

Figure 1 shows a particle A of mass 0.2kg held at rest on a smooth roof inclined at 30 degrees to the horizontal. Particle A is attached to one end of a light inextensible string which passes over a smooth pulley at the edge of the roof. A particle B of mass 0.3kg is attached to the other end of the string and hangs freely at rest. Particle A is 3.8m from the pulley and particle B is 2m above the horizontal ground.

The System is released from rest.

The acceleration of each particle when the string remains taut is 7.84

The speed with which B strikes the flood is 5.6

Now assuming that B is brought to rest when it strikes the floor, I have to find the speed with which A reaches the pulley.

According to the answers the speed should be 7.

I would be a grateful for a solution.

Reply 1

Hingie

The speed at which B strikes the floor is the same speed as particle A at the same moment. However, when B is brought to rest, the tension in the string becomes 0, so the only force acting on A thereafter is its weight. By this point, A has travelled 2m, leaving just 1.8m between it and the pulley. Use F = ma to find out A's deceleration; now, you have A's initial velocity, you have the distance it travels to reach the pulley, you have its deceleration, and that's all you need to work out its final velocty once it's reached the pulley.