Question

1. Suppose we have two blocks of masses m1 and m2. The block with mass m1 is moving towards block m2 at speed v. After the collision, we measure the total kinetic energy and find that the total kinetic energy after the collision is m2/(m1+m2) less than the kinetic energy before the collision. Find the final speeds of the two blocks. What type of collision is this?

2. Explain, in words, how we know that a freely spinning asteroid in space is rotating about an axis that passes through its center of mass?

3. You are handed a rod that is three times as dense on one end as it is on the other end. Find the moment of inertia when the axis of rotation is about the heavy end, and find the moment of inertia when the axis of rotation is about the light end.

Please answer all parts, Thank you!

Answer 1

1. Let the final speeds be

Momentum conservation gives

Relation between K.E.s

2 equations and 2 variables. Solving them simultaneously,

and thus, it is an inelastic collision.

2. There are many ways to do this. I can tell you one of them. Drop a particle on the object and see if it moves toward the edge. If it does its rotating otherwise not.

3. Exact variation would be needed for MOI calculation. But assume that the linear mass density varies from to linearly. So that,

where x is the distance from the lighter end and L is the rod length. MOI about the lighter end

In terms of total mass

Similarly from the heavier end

Replace in the density function.