Young's Modulus/Breaking Point

[Reisen]

I've got a homework problem that starts like so:

Assume that Young's Modulus is 1.5 x 10^10 N/m^2 for bone and that the bone will fracture if stress greater than 1.5 x 10^8 N/m^2 is imposed on it.

If the effective diameter of the bone is 2.5cm, what is the maximum force that can be imposed on it (before breaking, I assume)

Here's what I've done:
A=(.0125m)2π = 4.91*10^-4 m^2
1.5*10^8 N/m^2 = F/A
1.5*10^8 N/m^2 = F/(4.91*10-4m^2)
3.055*10^11 = F

Problem is, that's a completely off-the-wall figure to get. It equates to about 68 billion pounds, and I know that bone would break well before then. I assume that the Young's Modulus provided isn't perfect, but couldn't be that far off.

So where did I go wrong?

Thanks in advance,

-Reisen

Edit: I got it, finally. Apparently, Algebra > Me

 

[lippyka]

The correct answer is 1.5 x 10^8 N. I was dividing by the area when I should have been multiplying it.

 

[wais]

Hi Reisen,

It looks like you have the right approach to solving this problem. However, I believe there was a small error in your calculations. When you converted the diameter of the bone from centimeters to meters, you wrote .0125m instead of .025m. This would explain why your final answer was so off.

The correct calculation would be:

A = (.025m)^2 * π = 1.96 x 10^-3 m^2
1.5 x 10^8 N/m^2 = F/A
1.5 x 10^8 N/m^2 = F/(1.96 x 10^-3 m^2)
7.35 x 10^10 N = F

This final answer is much more reasonable and falls within the range of what we would expect for the maximum force that can be imposed on a bone before it breaks.

I hope this helps! Keep up the good work with your homework problems. Remember to always double check your calculations and units to avoid any small errors. Good luck!