A vertical solid steel post of diameter d = 26cmand length L = 2.40m is required

Question

A vertical solid steel post of diameter d = 26cmand length L = 2.40m is required to support a load of mass m = 7800kg . You can ignore the weight of the post. Take free fall acceleration to be g=9.8m/s2.

Part A

What is the stress in the post?

Express your answer using two significant figures.

Part B

What is the strain in the post?

Express your answer using two significant figures.

Part C

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

Express your answer using two significant figures.

Explanation / Answer

(a) Stress = F/A = mg / pi.r2

= 7800 x 9.8 / pi x 0.13 x 0.13

= 1.44 *106 N/m2 or Pa.

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(b) Young's modulus Y = Stress/strain

Strain = Stress / Y =1.44 * 106 / 200x109

= 7.19 x 10-6m

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(c) Change in length,

deltaL = strain x L = 7.19 x10-6 x 2.40

=  17.2 * 10-6 m = 17.2 mu.m

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