Question

A bullet of mass m is traveling to the left with a speed v when it embeds itself in a block of mass M. The block sits on a frictionless surface and is connected to a spring of stiffness k. What is the compression s of the spring when the bullet and block come to rest?

Answer 1

given,

mass of the bullet = m

velocity of the bullet = v

mass of block = M

spring constant = k

compression of spring = ?

According to law of conservation

m v + M × 0 = ( m + M )×V

`V = (m)/(m+M)v`

from law of conservation of energy

`(1)/(2)(M+m)v^2 = (1)/(2)kx^2`

`x = \sqrt{(m+M)/(k)}v`