A block of mass m moving with velocity v

Asked by admin @ 17/08/2021 in Physics viewed by 290 People

A block of mass m moving with velocity V, collides

with another stationary block of mass Masshown. The maximum compression in the spring is(Assume all surfaces to be smooth and springconstant isKanswer:v root mM/K(M+m)please help

Answered by admin @ 17/08/2021

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

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