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A uniform elastic string has length a1 when tension is T1 and length a2 when tension is T2 . The amount of work done in streching it from its natural length to (a1+a2) is ?

A uniform elastic string has length a1 when tension is T1 and length a2 when tension is T2 . The amount of work done in streching it from its natural length to (a1+a2) is ?

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
When Tension is T1=> the elongation let x1.
then 
l + x1 =a1 
and T1 = kx1 = k(a1 – l)
 
When Tension is T2=> the elongation let x2.
then 
l + x2 = a2 
and T2 = kx2 = k(a2 – l)
Work done,
dW = – k(x1 + x2)dx => -k(a1 + a2 – 2l)dx
Integerating both sides, from (a1 + a2) to l. we get,
W = -k[3a1l – a2l – a1^2 – a2^2 -2a1a2 – 2l^2] J. 

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