Answer to Question #162416 in Mechanical Engineering for Nachikethas K

Question

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?

Answer 1

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