# Femur Compression/Young's Modulus

• Student in Need
In summary, the femur of a 73 kg runner will compress by 4.5*10-5 m when the normal force of the ground on the foot is three times the runner's body weight.
Student in Need

## Homework Statement

By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2×10-4 m2 and its Young's modulus is 1.6×1010 N/m2.

Express your answer to two significant figures and include the appropriate units.

## Homework Equations

Stress on femur = F/A
Strain = delta L/L = (1/Y)(F/A)

## The Attempt at a Solution

F/A = (73 kg * 9.8 m/ss)/(5.2 * 10-4 m2) = 1375769.231 N/m2

deltaL/L = (1/1.6×1010 N/m2)(1375769.231 N/m2) = 8.598557692 * 10-5

(8.598557692 * 10-5) * 0.52 m = 4.47125 * 10-5 m = 4.5 * 10-5 m

I'm not sure what I'm doing wrong; any help would be appreciated!

Last edited:
Student in Need said:

## Homework Statement

By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2×10-4 m2 and its Young's modulus is 1.6×1010 N/m2.

Express your answer to two significant figures and include the appropriate units.

## Homework Equations

Stress on femur = F/A
Strain = delta L/L = (1/Y)(F/A)

## The Attempt at a Solution

F/A = (73 kg * 9.8 m/ss)/(5.2 * 10-4 m2) = 1375769.231 N/m2

deltaL/L = (1/1.6×1010 N/m2)(1375769.231 N/m2) = 8.598557692 * 10-5

(8.598557692 * 10-5) * 0.52 m = 4.47125 * 10-5 m = 4.5 * 10-5 m

I'm not sure what I'm doing wrong; any help would be appreciated!
What makes you think you're doing anything wrong?

BTW, the femur is one of the biggest and strongest bones in the human body. It's not supposed to shrink or stretch very much under normal use.

Unless you're this guy:

billy_joule
This was a problem on MasteringPhysics and when I submitted this answer, it was incorrect. :(

Student in Need said:
This was a problem on MasteringPhysics and when I submitted this answer, it was incorrect. :(
Your problem statement seems to start in the middle. It's asking you to calculate by what amount the femur compresses "in this moment", but it is not clear what that means. Your calculation assumes that all the static weight of the runner is supported by one femur. Is that what the problem is really asking you? When someone is running, dynamic loadings on the legs can easily exceed the loads present when one is standing still.

There was also this bit of information in the problem that I assumed wasn't important:

"The normal force of the ground on the foot can reach three times a runner's body weight when the foot strikes the pavement."

Should I be multiplying the force by 3?

Student in Need said:
Should I be multiplying the force by 3?
Well, what do you think? If the force is three times what it would be in a static situation, don't you think this affects by how much the bone will compress?

BTW, the Rules at PF ask that HW posters provide a "complete" problem statement. That way, you don't have to worry about what is or is not important, because the HW helpers are working from the same information as the HW posters, which is only fair.

Thank you! And I'll make sure I keep that in mind next time.

## What is femur compression?

Femur compression is a type of force that occurs when an object or force is pressing down on the femur bone, which is the thigh bone in the human body.

## What is Young's Modulus?

Young's Modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It is the ratio of stress to strain within the material, and is typically measured in units of force per area, such as N/m² or lbs/in².

## How is femur compression related to Young's Modulus?

Femur compression and Young's Modulus are related because Young's Modulus is a measure of how much a material can resist deformation under a compressive force, such as the femur bone. It is used to determine the strength and resilience of the bone.

## What factors can affect femur compression?

There are several factors that can affect femur compression, including the shape and size of the bone, the direction and intensity of the force applied, and the density and strength of the bone tissue.

## Why is understanding femur compression and Young's Modulus important?

Understanding femur compression and Young's Modulus is important for several reasons. It can help in the diagnosis and treatment of bone-related injuries and diseases, as well as in the design of medical devices and implants. It can also provide insight into the overall health and strength of an individual's bones.

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