You have applied for a great summer job working with a special effects team at a

Question

You have applied for a great summer job working with a special effects team at a movie studio. As part of your interview you have been asked to evaluate the design for a stunt in a new Indiana Jones production. A large spherical boulder starts from rest and rolls down an inclined track. At the bottom, the track curves up into a vertical circle so that the boulder can roll around on the inside of the circle and come back to ground level. It is important that the boulder not fall off the track at the top of the circle and crush the star standing below. You have been asked to determine the relationship between the height of the boulder's starting point on the ramp (measured from the center of the boulder) and the maximum radius the circular part of the track. You can determine the mass and the radius of the boulder should you need to know them. You have also been told that the moment of inertia of a sphere is 2/5 that of a ring of the same mass and radius. After some thought you decide that the boulder will stay moving in a vertical circle if its radial acceleration at the top is just that provided by gravity. Please write what physics principle is used for this problem and draw any diagrams for clarification. Please write the equation that is going to be used first.

Explanation / Answer

so at top of the loop

mg = mv^2/r

so v^2 = gr

now conservation of energy

m g h = m g 2r + 1/2 mv^2 + 1/2 I w^2

m g h = m g 2r + 1/2 mv^2 + 1/2 2/5 m R^2 w^2
use that Rw = v
g h = g 2 r + 1/2 v^2 + 1/5 v^2

g h = 2 g r + 7/10 gr

h = 27 r/10

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