Blocks and balls
Q. In lecture and in DR, we saw two balls crash into two wooden blocks. One ball was like a superball and the other was made out of clay. The block that the superball hit fell over, while the block that the clay ball hit did not. I don't get it -- what happened?
A. Check out this movie that I made:
Blocks and balls movie, quicktime format
Blocks and balls movie, avi format
Play around with the movie, and watch carefully what happens when the balls crash into the blocks. I personally notice two things:
The superball rebounds farther after it hits the block. It's hard to see this, since you have to account for the perspective.
The collision with the clay ball lasts a lot longer than the collision with the superball.
We can use the concept of impulse to understand what happens here. The impulse that each ball transfers to the block is equal to the change in momentum of the ball; let's call that change in momentum Dp. That impulse must be equal to the force that the ball exerts on the ball (call that force F) multiplied by the time of the collision (call that dt). So, we have Dp=F x dt, or F=Dp / dt. For the collision with the superball, dt is small and Dp is big (since it rebounds farther we know that the velocity is higher after the collision), so the force is higher compared with the collision with the clay ball. The superball exerts a strong enough force to knock over the block, while the clay ball does not!
If you look even more carefully at the movie, you'll notice something quite neat. Each block really rotates around the edge in contact with the table. In the collision with the clay ball, the torque associated with the force from the ball is not large enough to cause the block to rotate far enough to tip over.