What is the stress within the column?

[mathcrzy]

Homework Statement

A marble column of cross-sectional area 1.7 m2 supports a mass of 30,000 kg.
(a) What is the stress within the column?
(b) What is the strain?

Elastic modulus for marble E (N/m^2) 50e9
shear modulus (G)

Homework Equations

a)stress=F/A=N/m^2
b) don't know

The Attempt at a Solution

a) 30000*9.8/1.7=172941 N/m^2 (this is right)
b)

 

[hotcommodity]

The strain will be given by the change in the length of the column divided by its initial length: $$\frac{\Delta L}{L_0}$$.

Its relation to the stress is given by: $$\frac{F}{A} = Y \frac{\Delta L}{L_0}$$. That is, the stress is equal to the modulus times the strain. Now its just algebra.

 

[mathcrzy]

how do you find the length of the column?

 

[hotcommodity]

You don't need it. You can just treat $$\frac{\Delta L}{L_0}$$ as a single term, does that make sense?

 

[mathcrzy]

so just solve for that term then? what would Y be? the elastic or shear modulus?

F=30000*9.8
A=1.7
Y=?

 

[hotcommodity]

You would use the elastic modulus, we're speaking in terms of tensile stress and strain. If we were using shear stress and strain, we would use the shear modulus.

 

[mathcrzy]

so-

(30000*9.8/1.7)/50e9=3.5e-6

 

[hotcommodity]

Looks good to me, don't forget to put your answer for part a into significant figures.