
Conservation Laws 71
1/2mv
2
bot
= mgh
or
v
bot
= √2gh
This is our answer, which took us a few lines of simple algebra. Note that the nal
answer does not depend on the shape of the track or the mass of the car, m. The mass
cancels out since it appears in both the kinetic and potential energy.
We can also use our roller coaster example to highlight what we might call a
physics-biology problem. Let us imagine that the roller coaster operator made a mis-
take such that at the top of the track he backed up off the track (the dashed car in
Figure 8.3), causing the car to drop straight down to the ground. A physicist in the
car decides he better quickly ...