I would Like step by step solutions please. I REALLY NEED STEP BY STEP A 3.20-in

Question

I would Like step by step solutions please. I REALLY NEED STEP BY STEP

A 3.20-in long slab of granite rests 011 two supporting columns, labeled A and B in the diagram. Column A is made of wood (E = 1.00 Times 109 N/m2), and column B is made of steel (E = 200.0 Times 109 N/m2). Both columns have a circular cross-section with a radius of 20.0 cm. Column A was originally 1.0000 m tall, before the slab was placed on the columns. The slab is horizontal, and has a weight of 8.00 Times 104 N. What was the original height of column B? (Note: you must report your answer to 5 significant figures.)

Explanation / Answer

for the column A:

Y = (F/A)/(dL/L)

F = W/2 = 8e4/2 = 4e4 N

A = pi R^2 = 3.1416*0.20*0.20 = 0.125664 m2

==> dL = (F/A)/(Y/L)

==> dL = (4e4/0.125664)/(1e9/1)

==> dL = 3.183091e-4 m

==> final length of the column A = L - dL = 1 - 3.183091e-4 = 0.9996816909 m

final length of the column B is equal to the final length of the column A; therefore:

For the column B:

Y = (F/A)/(dL/L)

F = W/2 = 8e4/2 = 4e4 N

A = pi R^2 = 3.1416*0.20*0.20 = 0.125664 m2

Y = (F/A)/(dL/L)

L = 0.9996816909 + dL

==> Y = (F/A)/(dL/(0.9996816909+dL))

==> 200e9 = (4e4/0.125664)/(dL/(0.9996816909+dL))

==> dL = 1.59104e-6 m

==> initial length of the column B = 0.9996816909 + 1.59104e-6 = 0.99968328 m

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