Roller coasters are great examples the concept of conservation of energy. Using the knowledge that the initial energy should equal the final energy, we can use the equation Ui + KEi = Uf+ KEf . An example of a real life roller coaster that this equation works with is the Ride of Steel.
The website gives the information that it is a 205 ft drop (62.5 m) but the total height of the ride is 208 ft (63.4). Even though the max speed of about 75 mph (33.5 m/s) is listed on the website, we want to confirm that information through the use of conservation of energy. We are looking for the max speed at the bottom of the first large hill. For this problem, we are going to say that the velocity at the top of the hill is about 0 m/s.
mgh+(1/2)mv2=mgh+(1/2)mv2 ----mass cancels out---> gh+(1/2)v2=gh+(1/2)v2 -----plug in variables-----> (9.8 m/s2)(63.4 m)+(1/2)(0m/s)2=(9.8 m/s2)(.9 m)+(1/2)(v)2 -----solve for v-----> v=35 m/s
Because some values were rounded to make the math easier, the velocity for the Ride of Steel does appear to be around 75 mph.
Until next time,