Question

Lecture 16, W.L asks two questions to think about.
About KE of wall and that when we use 5 balls on the cradle. This is my solution, Please confirm:
momentum=p, KE=p^2/2m. since m>>p, KE->0
consider an inertial frame where the 5 balls are at rest, makes sense?

Answer 1

The wall has no KE but it must have moment p=2mv. Here the value of m refers to the ball's mass, NOT the wall's mass and v refers to the ball's speed, NOT the wall's (remember that momentum conservation here means the wall must have a momentum numerically equal to twice the ball's initial momentum). We have:\[p _{wall}=Mv _{wall}=2mv _{ball}\]Thus,\[v _{wall}=\frac{2mv _{ball}}{M}\]Now, the KE of the wall is:\[KE=\frac{1}{2}Mv _{wall}^2=\frac{1}{2}M \frac{4m^2v _{ball}^2}{M^2}\]Finally:\[KE=\frac{2m^2v _{ball}^2}{M}\]As M===>infinity, KE===>0.

Answer 2

Thank you,