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Let's say two objects are sitting adjacent (in contact) to each other. If we start pushing one of them, we know that both the objects move, remaining in contact to each other. But let's now consider imparting an impulse to one of the objects, instead of a steady force. I expect the two objects to start moving, but this time with different velocities, and thus developing a separation between them.

As a test case, let's say that we push the object which has mass $M$, and the other object has mass $m$; where $M > m$.

I expect the smaller mass to move off with a higher velocity.

But I can't find a mathematical description for it.

Assuming that the force is large enough, we have $F dt$ as the impulse on the combination. On the mass $M$, the impulse is $(F-N) dt$, where $N$ is the contact force between the two masses. Also, $N dt$ is the impulse on the object of mass $m$.

How can I calculate the velocities of the two masses, knowing that both the masses were at rest before the impulse.

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  • $\begingroup$ "Impulse" is the world for the transferred momentum $\int F \mathrm{d}t$ during the exertion of a force. I'm not sure what you are asking. $\endgroup$ – ACuriousMind Jul 21 '14 at 15:04
  • $\begingroup$ What are the respective velocities of the two masses after the application of the impulse? $\endgroup$ – Sidd Jul 21 '14 at 15:08
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You can analyze this by imagining a tiny tiny gap between the two masses. Physically we have exactly that, as the electrons at the surface of the first block are certainly not in contact with the electrons at the surface of the second block. Then we have a series of two collisions: the first is the initial impulse, the second is the collision between the two objects.

The answer will differ, of course, depending on the degree of elasticity of the collision.

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  • $\begingroup$ I tried to use an alternative, and it worked out. I am not sure though if it was the right thing to do. I assumed that the impulse is imparted by another imaginary mass, whose purpose was to provide the impulsive force. Thus, I was able to conserve energy, and the final answer for the velocities of the two objects came out to be independent of the mass of this imaginary object (which I used as a representation of the impulse). I hope I was write in doing so. $\endgroup$ – Sidd Jul 22 '14 at 10:59
  • $\begingroup$ That sounds fine (assuming I'm understanding you correctly!) $\endgroup$ – garyp Jul 22 '14 at 14:46

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