Abullet of mass 0.012 kg and horizontal speed 70 ms^–1strikes a block of wood of mass 0.4 kg and instantly comes to restwith respect to the block. The block is suspended from the ceiling bymeans of thin wires. Calculate the height to which the block rises.Also, estimate the amount of heat produced in the block.

Massof the bullet, m= 0.012 kg

Initialspeed of the bullet, u_b= 70 m/s

Massof the wooden block, M= 0.4 kg

Initialspeed of the wooden block, u_B= 0

Finalspeed of the system of the bullet and the block = ν

Applyingthe law of conservation of momentum:

For thesystem of the bullet and the wooden block:

Massof the system, m'= 0.412 kg

Velocityof the system = 2.04 m/s

Heightup to which the system rises = h

Applyingthe law of conservation of energy to this system:

Potentialenergy at the highest point = Kinetic energy at the lowest point

=0.2123 m

The woodenblock will rise to a height of 0.2123 m.

Heatproduced = Kinetic energy of the bullet – Kinetic energy of thesystem

= 29.4 – 0.857 = 28.54 J