Question

A block of mass m moving with velocity V, collides
with another stationary block of mass Mas
shown. The maximum compression in the spring is
(Assume all surfaces to be smooth and spring
constant isK
answer:v root mM/K(M+m)
please help​

Answer 1

The spring attached with block of mass M will compress untill both the particles starts to move together.

as external force acting on the system = 0,

so, initial momentum = final momentum

or, $mv_0=(m+M)v$

or, $v=\frac{mv_0}{(m+M)}$

let maximum compression is x

from law of conservation of energy,

initial kinetic energy = spring potential energy + kinetic energy of system of blocks.

$or,\frac{1}{2}mv_0^2=\frac{1}{2}Kx^2+\frac{1}{2}(m+M)\left(\frac{mv_0}{(m+M)}\right)^2$

or,$v_0^2\left[m-\frac{m^2}{(m+M)}\right]=Kx^2$

or, $x^2=\frac{mM}{(m+M)K}v_0^2$

or, $x=\sqrt{\frac{mM}{(m+M)K}}v_0$

hence, answer is $x=\sqrt{\frac{mM}{(m+M)K}}v_0$

Answer 2

Answer:

Explanation: i hope