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Phys105_ps9_2009

Phys105_ps9_2009 - Physics 105 Problem Set 9 Due Thursday...

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Physics 105, Problem Set 9 Due: Thursday, December 3, 2009, 3 PM. Reading: For waves, chapters 20-21 of Knight’s “Physics for scientists and engineers” textbook (the PHY103 book), which are posted in E-reserves on the 105 Blackboard site. (This does not seem to download properly with Firefox, but works in Explorer.) Starting Nov. 30, we will cover thermodynamics, from Sections 1-14 of Fermi’s book. See also Chapters 16-19 of Knight, which are posted. Problem 1. Consider a long string of mass density μ and under tension T s . One end, let’s call its position x = 0, is held by a support. Initially, the string is at rest, with the transverse displacement D ( x, t ) = 0 for all t < 0 at all positions along the string, x 0. Then the support is moved transversely by a small amount so D ( x = 0 , t ) = A sin ( πt/τ ) during the time interval 0 t τ . The support is then held at the original position ( D = 0) after time τ . This launches a wave pulse down the string. (a) What is the resulting displacement of the string D ( x, t )? Assume the wave does not reach the other end of the string. (b) How much total kinetic energy due to the motion of the string is contained in this wave at time t , for t > τ ? (c) How much total potential energy due to stretching the string is contained in this wave at time t , for t > τ ?
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