# 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:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$, 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:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

99% (392 ratings) ###### 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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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Motion Along Curved Paths concept. You can view video lessons to learn Motion Along Curved Paths. Or if you need more Motion Along Curved Paths practice, you can also practice Motion Along Curved Paths practice problems.

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