Question

Two blocks A and B of mass 2m and m respectively are connected to a massless spring of force constant K as shown in the figure. A and B are moving on the horizontal frictionless surface with velocity v to right with undeformed spring. If B collides with a block C of mass M elastically, then the maximum compression of the spring is​

Answer 1

Given :

Block A :

mass = 2m

initial velocity = v

Block B :

mass = m

initial velocity = v

Block C

mass = m

initially at rest

To find :

Maximum compression of the string after collision with Block C.

Solution :

As we know that the collision is elastic.

If the collision is elastic and the objects are of equal mass and also one of the object is initially at rest.

Then, the velocities of both the objects will get interchanged.

Therefore,

Before collision :-

Velocity of Block A = v

Velocity of Block B = v

Velocity of Block C = 0

After collision :-

Velocity of Block A = v

Velocity of Block B = 0

Velocity of Block C = v

Then we will apply law of conservation of momentum.

That is, Initial Momentum = Final Momentum

And finally we will apply law of conservation of energy.

That is, Initial KE + Initial PE = Final KE + Final PE

We will finally get the maximum compression i.e., $\sqrt{\frac{2m}{3k} } v$