A solid sphere of mass m and radius r rolls without slipping along the track shown 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 th (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (Use R, m, r, and gravity g, as necessary.) h = 2.70R for R >> r (b) What are the force components on the sphere at the point P if h = 3R? 5 7 Fx = Fy mg 20 -mg X X N N

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
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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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A solid sphere of mass m and radius r rolls without slipping along the track shown 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.
(a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (Use R, m, r, and gravity g, as necessary.)
h = 2.70R
Fx
m
=
(b) What are the force components on the sphere at the point P if h = 3R?
5
7mg
Fy =
h
20
7
-mg
X
for R >> r
X
N
N
Transcribed Image Text:A solid sphere of mass m and radius r rolls without slipping along the track shown 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. (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (Use R, m, r, and gravity g, as necessary.) h = 2.70R Fx m = (b) What are the force components on the sphere at the point P if h = 3R? 5 7mg Fy = h 20 7 -mg X for R >> r X N N
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