Answered: wwww X = 0 (a) wwww A = -KAR (b) F =…

Name: Consider a linear spring, as in Figure 7.7(a), with mass M uniformly d
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Description: Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x = 0, is moving with speed v in the x-direction. What is the total

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

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 29P

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Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x = 0, is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)

wwww
X = 0
(a)
wwww A = -KAR
(b)
F = -kAx
(c)
Figure 7.7 (a) The spring exerts no force at its equilibrium
position. The spring exerts a force in the opposite direction to
(b) an extension or stretch, and (c) a compression.

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