Item NG086002: Assuming no energy transfer between a roller coaster car and the track it is moving in or between the car and the air around it, all of the hills that a roller coaster car can get over must be lower than the height of the starting point.

An engineer is building a roller coaster and wants the roller coaster car to go over two hills.  In order for the roller coaster car to make it over both hills, should the first hill be higher or lower than the second hill?  (Assume that no energy is transferred between the roller coaster car and the track or between the roller coaster car and the air around it.)

  1. The first hill has to be higher than the second hill because the roller coaster car will lose energy as it rolls along the track, so it will not be able to get over a second hill that is as high as the first hill.
  2. The first hill can be lower than the second hill because the roller coaster car will gain enough energy as it rolls along the track to get over a second hill that is higher than the first hill.
  3. It doesn’t matter which hill is higher as long as they are both lower than the starting point because no energy is lost as the roller coaster car rolls along the track, so it can get over any hill that is lower than the starting point.
  4. It doesn’t matter which hill is higher because even though the total amount of energy that the roller coaster car has will decrease going uphill, it will increase enough going downhill to get over any size hill.