Question

a bullet of mass m strikes a block of mass M connected to a light spring of stiffness k,with a speed V if the bullet gets embedded in block,the maximum compression in the spring is

Answer 1

@ryanvarghese12790 @GTXMUQSIT @firefox @quantun PLS..HLP

Answer 2

I think that you have to use conservation of momentum fist, then apply conservation of energy. So, when the bullet first strikes the block, we use conservation of momentum knowing that both the bullet and the block have the same velocity after the bullet hits it.

\[p_i=p_f\]
\[mV = (M+m)v\]
\[v=\frac{mV}{(M+m)}\]

Next we can use conservation of energy to see how far the spring is displaced. If the bullet-block has only kinetic energy to start, and then at max displacement has only spring potential energy, we can say.
\[E_i=E_f\]
\[K=U_{spring}\]
\[\frac{(M+m)v^2}{2} = \frac{kx^2}{2}\]
\[(m+M) \Bigg( \frac{mV}{(M+m)} \Bigg)^2 = kx^2\]
\[\Bigg( \frac{(mV)^2}{k(M+m)} \Bigg) = x^2\]
therefore the max compression of the spring is
\[x= mV \sqrt{\frac{1}{k(M+m)}} \]

^_^