Question

A steel cable of diameter 3.0 cm supports a load of 2.0kN. What is the fractional length increase of the cable compared with the length when there is no load if Y=2.0 x 10^11 Pa?

Answer 1

1.429*10^-5 m

Step-by-step explanation:

From the question, we are given that

Diameter of the cable, d = 3 cm = 0.03 m

Force on the cable, F = 2 kN

Young Modulus, Y = 2*10^11 Pa

Area of the cable = πd²/4 = (3.142 * 0.03²) / 4 = 0.0028 / 4 = 0.0007 m²

The fractional length = Δl/l

Δl/l = F/AY

Δl/l = 2000 / 0.0007 * 2*10^11

Δl/l = 2000 / 1.4*10^8

Δl/l = 1.429*10^-5 m

Therefore, the fractional length is 1.429*10^-5 m long