College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Consider a solid uniform ball of mass m and radius R rolling
without slipping near the bottom of a frictionless
hemispherical fishbowl of radius r as shown. The ball
oscillates about the center of the fishbowl. Set the
gravitatio nal potential energy to be zero at the bottom of the
bowl.
r(1- cos 0)
A.
Express the total energy of the ball as a function of the ball's distance from the center x and its
velocity.
Hint 1: Since the ball is rolling without slipping, its angular velocity can be expressed in terms of its linear
velocity, and it has translational and rotational energy.
Hint 2: In writing gravitational potential U, use the approximation cos 0 ~ 1 –, then use SOH-CAH-TOA
to rewrite 0 in terms of x and r, then use sin 0 ~ 0 to eliminate the variable 0.
`Find the oscillation frequency of the ball.
Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t)) follows a certain form.
Also, since the energy of the system is conserved, then dE/dt = 0.
B.
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