Question

A bullet of mass 81gm and moving with a velocity of 300m/sec is fired into a log of wood and it penetrates to a depth of 10cm. If the bullet moving with the same velocity were fired into a similar piece of wood 5cm thick, with what velocity would it emerge? Find also the force of resistance assuming it to be uniform.

Answer 1

Given that: 

m = 81gm = 0.081Kg, u = 300m/sec, s = 10cm = 0.1m, v = 0 

As the force of resistance is acting in the opposite direction of motion of bullet, hence force of resistance will produce retardation on the bullet, 

Apply, V² = u² – 2as

0 = 300² – 2a(0.1)

a = 450000m/sec²

Let F is the force of resistance offered by wood to the bullet.

Using equation, F = ma

F = 0.081 X 450000

F = 36450N

Let v = velocity of bullet with which the bullet emerges from the piece of wood of 5cm thick, 

U = 300m/sec, a = 450000m/sec², s = 0.05m 

Using equation, V² = u² – 2as

V² = 300² – 2 X 450000 X 0.05

V = 212.132m/sec