Explanation Take the downward direction to be positive y direction. The free-body diagram at the top of the loop is shown in figure 1. Write the equation for the y-component of the net force on the car. Σ F y = m a (I) Here, Σ F y is the y-component of the net force on the car, m is the mass and a is the acceleration of the car. Write the equation for Σ F → y . Σ F y = n + F g Here, n is the normal force and F g is the force of gravity. Put the above equation in equation (I). n + F g = m a (II) Write the equation for F g . F g = m g Here, g is the acceleration due to gravity. Put the above equation in equation (II). n + m g = m a (III) The acceleration is centripetal acceleration. Write the equation for the acceleration of the car. a = v 2 r Here, v is the speed of the car and r is the radius of the loop-the -loop at the top. Put the above equation in equation (III)

4th Edition

ISBN: 9780135272947

Author: Wolfson

Publisher: VST

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Chapter 5, Problem 34E

To determine

The minimum speed of the roller-coaster car at the top of the loop if it is to stay on the track.

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Chapter 5, Problem 33E

Chapter 5, Problem 35E

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