Question

A vertical solid steel post of diameter d = 20 cmand length L = 2.80 m is required to support a load of mass m = 8500 kg . You can ignore the weight of the post. Take free fall acceleration to be g=9.8m/s2.

A) What is the stree in the post?

B) What is the strain in the post?

C) What is the change in the post's length when the load is applied?

(Express all answers using 2 sigfigs)

Answer 1

given data

A vertical solid steel post of diameter d = 20 cm

and length L = 2.80 m

load of mass m = 8500 kg .

A vertical solid steel post 20 cm in diameter and 2.80m long is required to support a load of 8500 kg. You may ignore the weight of the post.

The stress is the ratio of the external force to the cross sectional area.
The strain is the ratio of the change of length to the original length.
Young’s modulus = stress/ strain

A)What is the stress in the post when the load is applied?
The weight of the 7900 kg load is the force = 8500 * 9.8
Area = π * r^2 = π * 0.10^2
Stress = (8500 * 9.8) ÷ (π * 0.10^2) = 2.65* 10^6 Pascals
So, stress is pressure!

B)What is the strain in the post when the load is applied?
Strain = stress ÷ Young’s modulus = 2.65* 10^6 ÷ 200 * 10^9 = 1.325*10^-5

C)What is the change in the post's length when the load is applied?
The strain is the ratio of the change of length to the original length.
Increase of length = Original length * strain = 2.8 * 1.325*10^-5 = 3.71* 10^-5 m