Exercise 11.30 A vertical solid steel post of diameter d = 21 cmand length L = 2

Question

Exercise 11.30

A vertical solid steel post of diameter d = 21 cmand length L = 2.80 m is required to support a load of mass m = 8000 kg . You can ignore the weight of the post. Take free fall acceleration to beg=9.8m/s2.

Part B

What is the strain in the post?

Express your answer using two significant figures.

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Part C

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

Express your answer using two significant figures.

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Explanation / Answer

a)

youngs modulus of steel is = 200 * 10^9 N/m^2

E = stress/strain

200 * 10^9 = F / A * strain

200 * 10^9 = 8000 * 9.8 / ( 3.14 * 0.105^2) * strain

strain = (8000 * 9.8 ) / (3.14 * 0.105^2 * 200 * 10^9 )

strain = 1.13 * 10^-5

b)

by using the same formula

E = stress / strain

E = F * L / A * dL

200 * 10^9 = 8000 * 9.8 * 2.8 / ( 3.14 * 0.105^2 * dL)

dL = (8000 * 9.8 * 2.8 ) / ( 3.14 * 0.105^2 * 200 * 10^9)

dL = 3.1 * 10^-5 m

the change in the length is 3.1 * 10^-5 m

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