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posted by  soconfused on 6/4/2007 12:41:24 PM  |  status: Live  

HW problem. Need Help

Course Textbook Chapter Problem
Algebra Based Physics N/A N/A N/A
Question Details:
A wire of length L, Young's modulus Y, and cross-sectional area A is stretched elastically by an amount ΔL. The restoring force is given by Hooke's aw as kΔL.
Show that the work done in stretching the wire must be
 

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posted by HungryHungryHippo on 6/4/2007 1:50:52 PM  |  status: Live
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soconfused's comment:
"Is there a way to figure it out without using integration?"
Response Details:
The work being done can be found by integrating the force done over the distance:

W = ∫ F dx = ∫ kx dx

The stiffness constant, k, would be k = YA/L in this problem:
Hope I have helped.  Anyone feel free to correct any mistake I may have made.
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posted by HungryHungryHippo on 6/4/2007 3:16:38 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
The work being done will be equal to the potential energy stored in the spring:

k = YA/L
x = ΔL

W = PEspring = 1/2 kx2 = 1/2 (YA/L) (ΔL)2
Hope I have helped.  Anyone feel free to correct any mistake I may have made.
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