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Question

an elastic spring of unstretched lenght L and force constant K is stretched by a small length C it is further stretched by a small length Y the qork done in seconh stretching is


Solution

Work done in second stretching = Potential energy  after second streching - Potential energy after first stretching 
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Potential energy stored, when it is extended by x, is
U1= (1/2) k *x²

Potential energy stored, when it is further extended by y, is
U2 = (1/2) k* (x+y)²

Work done = U2 - U1

= (1/2) k [x² +y² + 2xy - x²]

= (1/2) k*y ( 2x +y)

Answer : (1/2)ky(2x+y)

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