Calculate Maximum Force & Shortening of Femur Bone | Young's Modulus Help

[blueantihero]

Assume that Young's Modulus for bone is 1.50x10^10 N/m^2 and that the bone will fracture if more than 1.50x10^8 N/m^2 is exerted.

(a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.60 cm?

(b) If a force of this magnitude is applied compressively, by how much does the 22.0 cm long bone shorten?

Y=F/A is what I tried for Part A but I am not sure if I', using the right area. Without the first part I can't even attempt B.

 

[alphysicist]

Hi blueantihero,

I believe the maximum force would be related to the fracturing stress of 1.5 x 10^8 N/m^2, not the Young's modulus (which is related to how much stretch or compression that bone undergoes in response to an applied stress). What numbers are you using and getting?

 

[CrazyIvan]

Y=F/A is what I tried for Part A.

F/A is the pressure needed to break the bone. Why would you set it equal to Young's Modulus? Although Young's Modulus has the same units as pressure, they are conceptually different.

 

[blueantihero]

Young's Modulus

F/A=Y(deltaL/L)

That's the full Young's modulus expression. I'm not sure what to do with it since I'm missing the force and deltaL (change in length). And I'm not sure what area to use since I should be able to find a before b and i need the length of the bone for the area. (pi)r^2h for the area right?

 

[CrazyIvan]

F/A=Y(deltaL/L)

That's the full Young's modulus expression. I'm not sure what to do with it since I'm missing the force and deltaL (change in length). And I'm not sure what area to use since I should be able to find a before b and i need the length of the bone for the area. (pi)r^2h for the area right?

Yes, that is the full expression. And yes, you're right, you're missing both force and deltaL, so you need to do more than just use the one equation you posted above.

What about that other number you were given? How can that help you solve for one of your unknowns?


Also, area = pi * r^2. Not pi * r^2 * h.

 

[blueantihero]

The data in the original post is all I was given. And for the area since young's modulus is stretching or conpressing an object, I assumed I would need to account for the full bone area (not the ends of course) and the area for that would be (pi)r^2h. The shear modulus would be if the bone was breaking because of bending, but this is for pressure from both ends or stretching...right?

 

[CrazyIvan]

The data in the original post is all I was given. And for the area since young's modulus is stretching or conpressing an object, I assumed I would need to account for the full bone area (not the ends of course) and the area for that would be (pi)r^2h. The shear modulus would be if the bone was breaking because of bending, but this is for pressure from both ends or stretching...right?

(pi)r^2h is the volume of the bone (assuming the bone is cylindrical). You only need the cross-sectional area.

Young's Modulus relates how much an object stretches or compresses to the pressure on that object.

What is the pressure on the bone?


Regarding shear modulus and bending moments and whatnot, you do not need any of that. It is a bone in compression, and the information you're given in the problem statement is enough.