Question

A bullet of mass m moving with a horizontal velocity u strikes a stationary wooden block of mass M suspended by a string of length L=50 cm.The bullet emerges out the block with the speed u/4.If M=6m, the minimum value of u so that the block can complete the vertical circle?

Answer 1

The speed to go round the circle:

$$v=\sqrt {gL}.$$

Apply conservation of momentum:

$$mu=m\frac u4+Mv,\\\space\\ u=\frac{4M}{3m}v=\frac{4M}{3m}\sqrt {gL}=17.7\text{ m/s}.$$