# Mechanics problem

If a rigid homogeneous rectangular crate of mass m and height h slides on its base of w, while traveling a velocity v, it stikes a low, immovable curb. What is the angular velocity of the crate immediately after the impact, in terms of m,w,h,v; and under what condition (in m,w,h,v) will the crate fall over on its side?

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#### Solution Preview

the problem is simpler than how it looks like:

<br>you can imagine the curb as a small ball of infinite mass (see the attached picture1), and the collision as an inelastic collision (the two bodies will stick together).

<br>In this case energy doesn't conserve (inelastic collision), while linear momentum and angular momentum conserve.

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<br>CONVERVATION OF MOMENTUM:

<br>you expect that the final body (the crate stuck to the ball of infinite mass) will have no velocity, because of the mass of the ball... let's work out the formulas:

<br>mv=(m+M)v1, where v1 is the total momentum after the collision.

<br>as M goes to infinity, v1 has to go to zero, as expected. good.

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<br>CONSERVATION OF ANGULAR ...