Question

A copper wire is 1.6 m long and its diameter is 1.1 mm. If the wire hangs vertically, how much weight (in N) must be added to its free end in order to stretch it 2.8 mm?

Answer 1

Weight required = 194.51 N

Step-by-step explanation:

The elongation is given by

`\Delta L=(PL)/(AE)`

Length , L= 1.6 m

Diameter, d = 1.1 mm

Area

`A=(\pi d^2)/(4)=(\pi * (1.1* 10^(-3))^2)/(4)=9.50* 10^(-7)m^2`

Change in length, ΔL = 2.8 mm = 0.0028 m

Young's modulus of copper, E = 117 GPa = 117 x 10⁹ Pa

Substituting,

`\Delta L=(PL)/(AE)\\\\0.0028=(P* 1.6)/(9.50* 10^(-7)* 117* 10^9)\\\\P=194.51N`

Weight required = 194.51 N