Physics Help. The 2 m copper wire with square cross section of 1mm by 1mm stretched 1.67 mm when it supports a 10kg mass.

Question

Cut a length of this wire 0.2m long and hang a 10kg mass from it. How much will this short wire stretch?

Answer 1

x = amount stretched

F = applied axial force

L = length of wire

A = cross sectional area of wire

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)(1.67 x 10^-3 m) = 1.67 x 10^-4 m