- #1
GregA
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Hi folks...can someone tell me where I'm going wrong with this question, or back me up if I'm right?
A string of natural length 2a and modulus of elasticity b has its ends attached to fixed points A and B where AB = 3a. Find the work done when the midpoint C of the string is pulled away from the line AB to a position where triangle ABC is equilateral. My attempt to solve is as follows:
I ignore B and focus just on A and C
if the natural length of the string = 2a then the midpoint represents half this length and therefore = a
AB = 3a, and so AC = 3a/2... the extention x = a/2
AC when streched to the equilateral triangle = 3a and so...x = 2a
The question asks me how much work is done from pulling the midpoint from its initial position on the line AB to its final position
Surely I want to subtract the work taken to pull the string to from its natural length to AC1 from the work required to pull the string to AC2..using Work = (b(x)^2)/2a...
(b((2a)^2-(a/2)^2)/2a = 15ab/8.
The books answer is given as 4ab however...I've tried to find a problem with my working and cannot.
A string of natural length 2a and modulus of elasticity b has its ends attached to fixed points A and B where AB = 3a. Find the work done when the midpoint C of the string is pulled away from the line AB to a position where triangle ABC is equilateral. My attempt to solve is as follows:
I ignore B and focus just on A and C
if the natural length of the string = 2a then the midpoint represents half this length and therefore = a
AB = 3a, and so AC = 3a/2... the extention x = a/2
AC when streched to the equilateral triangle = 3a and so...x = 2a
The question asks me how much work is done from pulling the midpoint from its initial position on the line AB to its final position
Surely I want to subtract the work taken to pull the string to from its natural length to AC1 from the work required to pull the string to AC2..using Work = (b(x)^2)/2a...
(b((2a)^2-(a/2)^2)/2a = 15ab/8.
The books answer is given as 4ab however...I've tried to find a problem with my working and cannot.
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