Work and energy: Rollercoasters are energy at work!

One of the most interesting and fun demonstrations of the conservation of energy can be found in amusement parks. Rollercoaster designers often utilize the principles of physics to ensure that a minimal amount of resources is pooled into the system, often by taking advantage of gravitational potential energy. This is fiscally beneficial for the owner of the park, as it is not necessary to propel the cart through the use of an engine.

An amusement park owner is developing one of these new rides. The coaster’s track begins with a 320kg cart starting from rest and rolling 34 meters down an incline. The cart then moves up a 21m tall ramp and eventually is stopped by a spring with a spring constant of 1325 N/m. Visitors will then exit the coaster and it will be manually returned to its starting position.

Assume that no energy is lost to heat or dissipated by friction or air resistance.

Figure 1. A rough diagram of the cart’s projected path.