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Impulsive Forces in Collision

two blocks of...

Question

two blocks of masses m1 and M with speeds v1 and v2 (v1 is greater than v2) in the same direction on the friction less surface respectively, M being ahead of m. An ideal spring of force constant k is attached to the backside of M. the maximum compression of the spring when the block collides is :

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Solution

Dear student,
According to hooke's law F=-Kx
Kinetic energy of mass m moving with velocity $v_{1}$ is 1/2m ${v_{1}^{2}}^{}$ and is transferred to another mass M and force exerted on that is 1/2 m $\frac{v_{1}^{2}}{x}$ where x is compression in the spring
Using Hooke's law and this expression for force
compression comes out to be
$\sqrt{\frac{m}{k}}$ $v_{1}$
With Regards
Tanvi Mahajan

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