Motion Along Curved Paths Video Lessons

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Problem: A roller coaster car with a mass of 700 Kg starts from rest at h1 above the ground and slides along a track. The car encounters a loop of a radius of 12 m. The bottom of the loop is a height of h2 = 5 m from the ground. What would be the max height of release h1 for the roller coaster car if the amount of thermal energy produced between the point of release and the top of the loop should not exceed 15% of the initial mechanical energy and the normal force at the top should be no more than 580 N? Answer in meters

FREE Expert Solution

Law of conservation of energy:

Ki+Ui+Wnc=Kf+Uf, where Wnc is the work done by non-conservative forces such as friction.

Since we don't have the non-conservative forces acting on the roller coaster car:

Ki+Ui=Kf+Uf

Kinetic energy:

K=12mv2

Potential energy:

U=mgh

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Problem Details

A roller coaster car with a mass of 700 Kg starts from rest at h1 above the ground and slides along a track. The car encounters a loop of a radius of 12 m. The bottom of the loop is a height of h2 = 5 m from the ground. What would be the max height of release h1 for the roller coaster car if the amount of thermal energy produced between the point of release and the top of the loop should not exceed 15% of the initial mechanical energy and the normal force at the top should be no more than 580 N? 

Answer in meters

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Based on our data, we think this problem is relevant for Professor Almaraz-Calderon & Capstick's class at FSU.