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

In summary, 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 is 1.5 x 10^8 N/m^2. If a force of this magnitude is applied compressively, by how much does the 22.0 cm long bone shorten?
  • #1
blueantihero
3
0
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.
 
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  • #2
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?
 
  • #3
blueantihero said:
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.
 
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  • #4
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?
 
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  • #5
blueantihero said:
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.
 
  • #6
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?
 
  • #7
blueantihero said:
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.
 

What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It represents the ratio of stress (force per unit area) to strain (deformation) in a material under tension or compression.

How is Young's Modulus calculated?

Young's Modulus is calculated by dividing the stress by the strain in a material under tension or compression. It is represented by the symbol E and is expressed in units of force per unit area, such as N/m² or Pa (Pascals).

What factors affect Young's Modulus?

The main factors that affect Young's Modulus are the type of material, its composition and microstructure, temperature, and the presence of impurities or defects in the material. For example, a material with a higher degree of crystallinity will have a higher Young's Modulus compared to a more amorphous material.

Why is Young's Modulus important in materials science?

Young's Modulus is an important property in materials science as it helps engineers and scientists understand the behavior of materials under stress and how they will respond to different loads. It is also used in the design and testing of materials for various applications, such as building materials, aerospace components, and medical devices.

How is Young's Modulus used in real-world applications?

The knowledge of Young's Modulus is used in a variety of real-world applications, such as designing and testing of bridges, aircraft wings, and other structures to ensure they can withstand the expected loads. It is also used in the development of new materials with specific properties for different applications, such as lightweight and strong materials for use in the automotive industry.

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