My son is working on a roller coaster physics project. One of his experiments involved running a marble down a 30 foot length of PVC tubing with about a 1" diameter. In trial A, the top of the pipe (the starting point of the marble's journey) was located at a height of about 7 feet from the ground. The pipe had a straight slope to the ground. In the trial B, the pipe had the exact same starting point, but we introduced a curve into the track. Thus, the marble's initial descent down the track was steeper than in trial A. The steep drop was followed by a gentle uphill climb and a gentle final descent down the hill. The same exact length of pipe and the same marble was used in both trials.
As we understand it, a roller coaster's potential energy at the starting point of the first hill, the lift hill, is slowly lost over the course of the roller coaster's track through friction, wind, and braking. (In his experiment, we simulated a lift hill by simply starting the marble at the opening of the pipe that we held 80 inches off the ground).
Here is one explanation we read online:
"When a coaster is at the highest point of its track, it has high potential energy (energy of position). As the coaster accelerates down the hill, that potential energy changes into kinetic energy (energy of motion). Each time the coaster goes up another hill, the kinetic energy becomes potential energy again, and the cycle continues. Ideally, the total amount of energy would remain the same, but some is lost to friction between the wheels and the rails, wind drag along the train, and friction applied by the brakes. Because of this energy loss, each successive hill along a coaster track must be smaller than the previous hill in order for the train to continue along the course. " (http://www.essortment.com/roller-coaste ... 31074.html
Our "coaster" did not have brakes or wind (the tube was enclosed), so only friction would affect the speed of the marble through the track, in theory.
We also ran another set of trials, C and D. In those trials, the pipe was kept straight (no curves / hills) but the slope of the track was changed. We had a low starting point (C, 30 inches off the ground) and a medium starting point (D, 55 inches).
For each trial, Matt ran the marble through the track about 10-12 times and recorded the speed through the track with a stop watch. As one might expect, the marble ran slowest through C and fastest through A. We think we understand why...what seems obvious is that the steeper slope makes you go faster because of the acceleration of gravity. My son says it's just like skiing, the steeper the run, the faster you go.
But here is what we can't quite figure out....why was trial B slower than A? The starting point height was the same. The marble was the same. The pipe used was the same. Wouldn't the friction then also be identical? The only difference was the curve in the pipe. Is there somehow less friction going uphill than downhill? In Trial B, in theory, the marble starts out faster since it has a steeper drop immediately. Then it slows as it goes up the hill and recovers speed as it goes down the hill to the end of the track. But adding it all up...why would the marble be slower in Trial B than A, since the friction is the same, the starting height the same and the marble and pipe the same.
What are we not understanding?
Thanks for your help!
Courtney and Matt