Answer to Question #162416 in Mechanical Engineering for Nachikethas K

Question #162416

A 2 m copper wire with square cross-section of 1 mm by 1 mm stretched 1.51 mm when it supported a 10 kg mass. Suppose you cut a length of this wire 0.2 m long and hang a 10 kg mass from it. How much will this shore wire stretch?

Expert's answer

x = amount stretched

F = applied axial force

L = length

A = cross-sectional area

E = modulus of elasticity of the material (copper in this problem)


For a linear elastic material,


x = FL / AE


x1 = stretching of 2 m wire, L1 = 2 m

x2 = stretching of 0.2 m wire, L2 = 0.2 m


Both wires have the same applied axial force F = mg, the same cross-sectional area A, and the same modulus E


x1 = FL1 / AE

x2 = FL2 / AE


Divide the 2 equations and get


x1/x2 = L1/L2


x2 = (L2/L1)x1 = (0.2 / 2)(1.51 x 10-3 m) = 1.51 x 10-4 m


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