The formalism of young\'s modulus is sometimes used to calculate thereversible w

Question

The formalism of young's modulus is sometimes used to calculate thereversible work involved in extending or compressing an elasticmaterial. Assume a force F is applied to an elastic rod of crosssectional area Ao and length Lo. As a resultof this force the rod changes in length by L. The young'smodulus E is defined as E=tensile stress/tensilestrain=F/Ao/L/Lo=FLo/Ao L                                      a)Relate K in Hooke's law to the young's modulus expression givenabove. .........b)using your result in part (a) show that themagnitude of the reversible work involved in changing the lengthLo of an elastic cylinder of cross sectional areaAo by L is w=1/2(L/L0)2 EAo L0 .

Explanation / Answer

a) E = FLo/Ao L F = (EAo/Lo) L = K L so K = EAo/Lo b) W = K(L)2/2 = EAo/Lo(L)2/2 = EAoLo(L/Lo)2/2

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