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

Answer:

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

$V = \dfrac{m}{m+M}v$

from law of conservation of energy

$\dfrac{1}{2}(M+m)v^2 = \dfrac{1}{2}kx^2$

$x = \sqrt{\dfrac{m+M}{k}}v$