How Much Does a Marble Column Compress Under Load?

[Jbreezy]

Homework Statement

A marble column with cross sectional area of 45cm^2 supports a load of 8.5 x 10^4 Newtons.
The marble has a Young's modulus of 5.5 x 10^10 N/m^2 and a compressive strength of 1.8 x 10^8 Pa. If the column is 2.75m high, what is the change in length of the column?

Homework Equations

Y(ΔL/L) = F/A

Where Y is young modulus.

The Attempt at a Solution

Y(ΔL/L) = F/A
Solve the equation for ΔL and you get.
ΔL = (FL)/ (AY)
So plugging in the values you get.
ΔL = ((8.5 x 10^4 N)(2.75m)) / ((.45m^2)(5.5 x 10^10 N/m^2))
So ΔL = 9.44 x 10^-6
Can someone double check me? I don't understand why my instructor gave me this number
1.8 x 10^8 Pa.
Please confirm or deny my answer. Thanks very much.

 

[mfb]

45cm^2 is not .45m^2.

Can someone double check me? I don't understand why my instructor gave me this number
1.8 x 10^8 Pa.

Maybe to check if the column breaks down.

 

[Jbreezy]

OK. So with that correction

ΔL = ((8.5 x 10^4 N)(2.75m)) / ((0.0045 m^2)(5.5 x 10^10 N/m^2))
So ΔL = 9.44 x 10^-4

Is this correct now? Thanks for the help.

 

[mfb]

Looks fine

 

[Nickie]

I would first like to commend you for attempting to solve this problem using the correct equations. Your solution seems to be correct based on the given information and equations. However, it is always a good practice to double check your work and units to ensure accuracy.

Regarding the compressive strength of 1.8 x 10^8 Pa, this is the maximum stress that the marble column can withstand before it starts to deform or break. It is not directly related to the change in length of the column, but it does provide important information about the strength of the material.

In summary, your solution for the change in length of the column seems to be correct. Just make sure to double check your work and units to ensure accuracy.