Elascticity question

[DisabledDoctor]

The question reads:

When subjected to a force of compression the length of bone decreases 2.7e-5m. When this same bone is subjected to a tensile force of the same magnitude by how much does it stretch?

There are some values given:
Bone compression modulus=9.4e9 N/m2
Tension 1.6e10 N/m2
"A compressional force in excess of 6.8e4 N will fracture this bone" (from homework)
Femur bone minimum cross-section area about 4e-4 m2

In order to solve this question I figure I need the following:
a) Original L
b) A lot of patience

Part by part

a) Find the original L by solving for compression. I set it up as:
y=F/A / delta L/L --> 9.4e9=6.8e4/4E-4 / 2.7e-5/L
Solving for L (I hope) I got 2.538e-4m

Now to find the stretch delta L, I figure I just set up the equation again and try to solve for delta L. My confusion is thus- it says that the strech (tensile) force is the same magnitude. I assume that means the F and not y. So I should set it up as

1.6e10=6.8e4N/4e-10m2 / delta L/2.538e-4m

and solve for delta L.

Does this make sense?! Thank you!!!!!

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[DisabledDoctor]

I set up the stretch formula to be:

delta L=FL/YA=(6.8e4N)(2.538e-4m)/(1.6e10N/m2)(4e-4m2)
delta L=2.69e-6m

This seems to make sense as the stretch is less distance than the compression and also less by two orders of magnitude than the cross-sectional area.

My only question is if I did it right. If my numbers aren't correct is at least my reasoning? Thank you!

 

[ilovemcat]

The typical equation for these types of questions goes something like this:
Force / Area = Modulus x (Change in Length / Original Length)

Now ask yourself, what remains the same for both conditions?

(Force/Area) x Original Length does.

So if that stays the same for both conditions, then all you have to do is equate the (Moduli x Change in Length) to each other and solve for the unknown.

Moduli (compression) x Change in Length (compression) = Moduli (tensile) x Change in Length (tensile)

Re-arranging this we get: Change in Length = Moduli (compression) x Change in Length (compression) / Moduli (tensile)
Change in Length = (9.4e9 N/m2 x 2.7e-5m) / (1.6e10 N/m2)
Change in Length = 1.58e-5 m

 

[DisabledDoctor]

Ok, I am workign through this!!!

 

[DisabledDoctor]

Cool I got the same answer. It appears you have a much stronger sense of how to solve these questions than I do. I did it by:
a) Finding the L based upon the compression
b) Using the L to find the stretch based upon the y given for tensile

I came up with 1.58e-5m. Same as you!! Thanks!