(1) Brachistochrone vs. Straight Track
(2) Brachistochrone vs. Brachistochrone at Different Start Positions
1. Conservation of Energy
If the car is released from rest from the top of the lowest left step (the second peg from the bottom is the first step; see Configuration 1), the car will make it over the hill without flying off the hill. If the car is released from higher up on the right side, the car will fly off the hill. The speed of the car at the top of the hill can be measured with a photogate; the kinetic energy can be calculated and compared to the predicted value given by conservation of energy. The normal force atthe top of the hill can also be calculated.
Compare the potential energy at the top of the step to the kinetic energy at the bottom of the step (Use the setup in Configuration 2).