I mentioned previously that we came across an old stroboscope down at the 'varsity, and that we were looking for some worthwile use for it. The picture below is probably the best and most interesting one we've produced so far. It might not be entirely obvious at first, but this is in fact a demonstration of a rather funky consequence of the conservation of momentum.
I you drop two objects from a height h
, one of mass m
and one of mass M
, and where m
, such that m
will land on top of M
immediately after M
hits the ground, m
can in principle bounce to a height of several times h
, in fact, if m
>0, and no energy is lost to friction.
At the left hand side, about halfway up the picture, one can see a pingpong ball, fastened on top of a golf ball with a minute amount of glue. There are several exposures of this, because I didn't manage to time it perfectly. Then, a little bit further down, one can see pingpong ball and the golf ball falling towards the ground, still glued together. At the bottom, still on the left hand side, the golfball has just hit the ground, and the pingpong ball has torn free of the glue. Proceeding to the right, one can see the pingpong ball bouncing to about 2.5h
So how do I know that 9h
is the upper limit for the height the pingpong ball could bounce to?
Just before the golf ball hits the ground, both objects are traveling downwards, with speed v
. Immediately after the golf ball hits the ground, but before the pingpong ball hits the golf ball, the pingpong ball is still traveling downwards with speed v
, whereas the golf ball is traveling upwards with the same speed, v
. If we now consider this from the frame of reference of the golf ball, it is at rest, while the pingpong ball is moving downwards with speed 2v
. Assuming that m
=0, the pingpong ball will just bounce off the golf ball as if it was a wall. Hence, after the collision, it will be moving upwards with speed 2v
(still in the frame of the golf ball).
We now know that the pingpong ball is moving upwards with a speed of 2v
in a frame that is itself moving upvards with speed v
as compared to the lab frame. Hence, the speed of the pingpong ball in the lab frame is 3v
. An increase in speed by a factor 3 means an increase in energy by a factor of 9. Thus, the pingpong ball could ideally bounce to a height of 9h