The formalism of the Young€™s modulus is sometimes used to calculate the reversible work involved in extending or compressing an elastic material. Assume a force F is applied to an elastic rod of cross-sectional area A₀ and length L₀. As a result of this force, the rod changes in length by ΔL. The Young€™s modulus E is defined as 

a. Relate k in Hooke€™s Law to the Young€™s modulus expression just given.

b. Using your result in part (a), show that the magnitude of the reversible work involved in changing the length L₀ of an elastic cylinder of cross-sectional area A₀ by ΔL is w = ½(ˆ†L/L₀)² EA₀L₀.

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tensile stress 4 - FL. E = tensile strain A% A0AL