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I am trying to solve the following question but I don't understand what the assumption of instantaneous collision is for.

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A ball of mass $M$ moving with velocity $V_0$ on a frictionless plane strikes the first of two identical balls, each of mass $m$, connected by a massless spring with spring constant $k$ as shown in the figure above. Consider the collision to be central, elastic and essentially instantaneous. (Others are omitted for the sake of simplicity)

I understood the purpose of the assumption of central and elastic collision but not the last one, instantaneous. What is it for? And what happens when the assumption is not given? Does it affect the equations of motion for each ball?

Qmechanic
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D G
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1 Answers1

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The conservation of linear momentum can only be used if the external forces are zero.
In this example you are considering horizontal motion and the system consisting of the left ball and middle ball.
There is a potential problem in that the spring might exert a horizontal force during the collision and hence invalidate the conservation equation.
An "instantaneous" collision would result in the spring not having time to be compressed and thus it would not exert a horizontal force on the system.

Another way to make an assumptions is to say that the impulses between the two balls when they are colliding are much larger than the impulses between the middle ball and the spring as explained in an answer to the post, Can linear momentum be conserved before and after collision in the presence of an external force?

Farcher
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