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When a block of mass M is suspended by a long wire of length L,elastic pot. energy stored in wire is {1/2.stress.strain.volum}.Show that this is equal to 1/2Mgl where l is extension.The loss in gravitational pot. energy of mass-earths system is Mgl.Where does the remaining 1/2Mgl energy goes???????? PLZ EXPLAIN........ANY SORT OF HELP WILL BE APPRECIATED!!!


When a block of mass M is suspended by a long wire of length L,elastic pot. energy stored in wire is {1/2.stress.strain.volum}.Show that this is equal to 1/2Mgl where l is extension.The loss in gravitational pot. energy of mass-earths system is Mgl.Where does the remaining 1/2Mgl energy goes????????

PLZ EXPLAIN........ANY SORT OF HELP WILL BE APPRECIATED!!!

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

consider the behaviour of the wire to be similar to that of a spring of spring constant 'k'. at equilibrium, kl =Mg,

k=Mg/l, elastic potential energy = (k/2)l2 =Mgl/2.

when the unextended wire is released, it is stretched by 2l before it starts moving upward and exhibits damped simple harmonic motion. the lost energy ends up as thermal energy of the wire, the amplitude of SHM keeps decreasing till static equilibrium at an extension of 'l'

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