What should the tensile strength of a cylindrical steel cable with radius 3 cm be to support a mass of 1000 kg on Earth.

Expert Answers
justaguide eNotes educator| Certified Educator

The tensile strength of a steel cable is the maximum stress or force per unit area that it can withstand before it starts to stretch and form a neck.

If the steel cable is a cylinder with a radius equal to 3 cm, the area of cross section is pi*r^2 = (22/7)*(3/100)^2 = (22/7)*(9/10000) m^2 = 2.8286*10^-3 m^2.

On Earth, the acceleration due to gravity is equal to 9.81 m/s^2. When a mass of 1000 kg is suspended using the cable the force applied on the cable due to the mass is equal to 9.81*1000 = 9810 N. The stress on the cable is equal to 9810/2.8286*10^-3 N/m^2 = 9810000/2.8286 = 3468181.81 N/m^2 = 3.4681 MPa

A cylindrical steel cable with a radius of 3 cm should have a tensile strength of 3.4681 MPa if it has to support a mass of 1000 kg.