Explanation Given: A stunt motorcycle is going through a loop-the-loop. Formula used: The relation between the energy and force is given by, E = F d cos θ The relation between the net change in energy and energy at different position is given by, Δ E net = E a + E b + E c + E d Calculation: The stuntman drives the motorcycle through a loop-the-loop. The gravitational force acts in vertical downward direction, which is parallel to the displacement of the bike rider. The following figure-(1) shows the motorcycle on four different position of the loop. Figure-(1) At position (a), the gravitational force act towards the downward direction and the displacement of the motorcycle is towards the left direction which means the angle between the force and displacement is 3 π 2 rad . The energy at position (a) is calculated as, E = F d cos θ E a = F d ( cos 3 π 2 ) = F d ( 0 ) = 0 J At position (b), the gravitational force act towards the downward direction and the displacement of the motorcycle is in the upward direction which means the angle between the force and displacement is π rad . The energy at position (b) is calculated as, E = F d cos θ E b = F d ( cos π ) = F d ( − 1 ) = − F d At position (c), the gravitational force act towards the downward direction and the displacement of the motorcycle is towards the right which means the angle between the force and displacement is π 2 rad

OER 2016 Edition

ISBN: 9781947172173

Author: OpenStax

Publisher: OpenStax College

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Chapter 7, Problem 18TP

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The graph of the loop versus the distance traveled around the loop and an explanation for the change in energy.

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The graph of the loop versus the distance traveled around the loop and an explanation for the change in energy.

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