How to find minimum possible mass

[ssarpal]

Homework Statement

A block of mass m moving at a speed 4 m/s collides with a block of mass 2 Kg initially at rest. The force during collision varies as the function F = A*sin^2(Bt). The collision lasts for 1 ms.

Find the minimum possible mass m?
$A = 10^4 N$

$B = 1000\pi \hspace{2mm} rad/sec$

Relevant Equations

Change in momentum is equal to the integral of force with respect to time.

Unfortunately, this is not the right answer.

 

[kuruman]

The integral gives you the impulse $J$ which is the momentum change of the unknown mass. After the collision, this mass will still be moving with velocity $v_1$ and the 2 kg will also be moving with velocity $v_2$ because it received impulse $J$ in the opposite direction. Do you see how to tie all this together?

 

[haruspex]

this is not the right answer.

Did it bother you that you were asked to find a minimum, but you did not go through such a step?

 

[ssarpal]

The integral gives you the impulse $J$ which is the momentum change of the unknown mass. After the collision, this mass will still be moving with velocity $v_1$ and the 2 kg will also be moving with velocity $v_2$ because it received impulse $J$ in the opposite direction. Do you see how to tie all this together?

I think that means
$mu_1 = mv_1 +m_2v_2$
where $u_1$ = 4 m/s and $m_2$ = 2 Kg
Am not sure if $v_1$ and $v_2$ are needed to solve this?

 

[ssarpal]

Did it bother you that you were asked to find a minimum, but you did not go through such a step?

Yes, was wondering where it could be used, am not sure how though.

 

[PeroK]

Yes, was wondering where it could be used, am not sure how though.

Perhaps you need to think about energy?

 

[Orodruin]

The first thing to ask oneself is: What are the possible final velocities of each object and what is the mass m for each of those velocities?