Roller Coasters Essay

Roller coasters are an exciting, popular and fun ride at amusement parks. The physics behind roller coasters are very interesting and captivating. This report will be about the energy changes involved during the ride, minimum energy required to make the ride safe but also ensuring that it is also exciting, forces involved in the ‘clothoid loop’ and the weight changes experienced by the rider during their ride through the loop.

First, the roller coaster’s energy are conserved and at the start of the ride they will need to have sufficient energy to complete the ride. This will help the ride to travel the vertical circle (loop) without extra energy injected. The energy involved with the roller coaster ride are gravitational potential energy (Ep=mgh)

Clothoid loop is a loop that has a small radius at the top and a larger radius at the bottom. Velocity can’t be changed easily because it is a function of the height of the carriage, but by changing the radius of the loop, smaller loop at the top of the loop means smaller velocity will help to produce a greater acceleration since when r decreases, a increases(ac=v²/r). As the carriage ascend the loop, the carriage’s velocity would be smaller therefore it would begin to slow down because increase in height would decrease kinetic energy and velocity. Which means that the carriage will have a larger velocity when it enters and leaves the loop and a smaller velocity when the carriage is at the top of the loop. No matter where the carriage is, the carriages’ centripetal acceleration will always be in the direction towards the center of the circle except that when the carriage is at the bottom of the loop the acceleration is in the upward direction while when the carriage reaches the top of the loop it is in the downward direction.

The roller coaster will experience two forces gravity force and support force, when we neglect friction and air resistance. At the bottom of the loop, the track push the carriage upwards with a support force, but at the top of the loop the support force is downwards since the track is above the car. Gravity force(Fgrav) will always act downwards on the carriage, which can be found by using the formula