A bullet of mass 0.012 kg and horizontal speed 70 m strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceilling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced to the block.
Here, mass of bullet m =0.012 kg, initial speed of bullet « = 70 m, mass of wood block M =0.4 kg.
As on collision, the bullet comes to rest w.r.t. block, it means that after collision bullet and block are moving with a common speed v.
From conservation law of momentum mu = (M + m)v
v = mu / (M + m) = 0.012 x 70 / (0.4 + 0.012) = 2.04 m
If the block now rises to a maximum height of h, then using conservation law of mechanical energy, we have
h = 0.212m = 21.2 cm