Answer to Question #228208 in Physics for Ekott jnr

Question

A horizontal force of 0.80N is required to pull a 5kg block across a table top at a constant speed. With the block initially at rest, a 20g bullet fired horizontally into the block causes the block to slide 1.5m before coming to rest again. Determine the speed v of the bullet , where the bullet is assumed to be embedded in the block.

Answer 1

Given:

$M=5.0\:\rm kg$

$m=0.02\:\rm kg$

$F=0.80\:\rm N$

$d=1.5\:\rm m$

The law of conservation of momentum gives

$$mu=(M+m)v$$

The energy-work theorem gives

$$\frac{(M+m)v^2}{2}=Fd$$

Finally, the initial speed of a bullet

$$u=\frac{M+m}{m}\sqrt{\frac{2Fd}{M+m}}$$

$$u=\frac{5.0+0.02}{0.02}\sqrt{\frac{2*0.8*1.5}{5.0+0.02}}=174\:\rm m/s$$