100 In Fig. 15-59, a solid cylinder attached to a horizontal spring (k = 3.00 N/m) rolls without slipping along a horizontal surface. If the sys- tem is released from rest when the м oo000d 00000 Figure 15-59 Problem 100. spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these condi- tions the cylinder's center of mass executes simple harmonic mo- tion with period ЗМ T = 27 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.)

100 In Fig. 15-59, a solid cylinder attached to a horizontal spring (k = 3.00 N/m) rolls without slipping along a horizontal surface. If the sys- tem is released from rest when the м oo000d 00000 Figure 15-59 Problem 100. spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these condi- tions the cylinder's center of mass executes simple harmonic mo- tion with period ЗМ T = 27 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.)

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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Question

100 In Fig. 15-59, a solid cylinder
attached to a horizontal spring (k =
3.00 N/m) rolls without slipping
along a horizontal surface. If the sys-
tem is released from rest when the
м
oo000d
00000
Figure 15-59 Problem 100.
spring is stretched by 0.250 m, find
(a) the translational kinetic energy
and (b) the rotational kinetic energy of the cylinder as it passes
through the equilibrium position. (c) Show that under these condi-
tions the cylinder's center of mass executes simple harmonic mo-
tion with period
ЗМ
T = 27
2k
where M is the cylinder mass. (Hint: Find the time derivative of the
total mechanical energy.)

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