A solid sphere of mass m and radius r rolls without slipping (v = rw) along the track shown in the figure below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. What is the minimum value of h (in terms of R) such that the sphere completes the loop? The moment of inertia of a sphere is I = mr². Hint: You will need to draw a free-body diagram of the ball at the top of the loop and you will need to find the minimum speed the ball needs to complete the loop. Recall that the centripetal acceleration is ac = v² /R. Answer: h= (27/10) R = 2.7 R. Solid sphere of mass m and radius r << R. R P

A solid sphere of mass m and radius r rolls without slipping (v = rw) along the track shown in the figure below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. What is the minimum value of h (in terms of R) such that the sphere completes the loop? The moment of inertia of a sphere is I = mr². Hint: You will need to draw a free-body diagram of the ball at the top of the loop and you will need to find the minimum speed the ball needs to complete the loop. Recall that the centripetal acceleration is ac = v² /R. Answer: h= (27/10) R = 2.7 R. Solid sphere of mass m and radius r << R. R P

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 83P: A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.83....

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