Compression of human bone: forces

AI Thread Summary
The discussion focuses on calculating the compressive force on a human leg modeled as a cylinder when falling from a height. The bone can withstand a compressive stress of 1.7 × 10^8 N/m2 before breaking. An 80 kg man falling from 5 m generates a force, but confusion arises regarding the calculation of the area of the leg's cross-section. The correct area formula involves using the radius squared, leading to a revised force calculation of 7.1E4 N. The clarification on using the correct area formula resolves the confusion.
maxd23
Messages
6
Reaction score
0

Homework Statement



While unrealistic, we will examine the forces on a leg when one falls from a height by approximating the leg as a uniform cylinder of bone with a diameter of 2.3 cm and ignoring any shear forces. Human bone can be compressed with approximately 1.7 × 10^8 N/m2 before breaking. A man with a mass of 80 kg falls from a height of 5 m. Assume his acceleration once he hits the ground is constant. For these calculations, g = 10 m/s2.

With how much force can the "leg" be compressed before breaking?

Homework Equations

The Attempt at a Solution


The correct answer:
I’m confused about how the answer is 7.1E4 N , can you explain how to get this answer from the data given?

wouldn’t it be F = (1.7 × 10^8 N/m2)*(2.3cm(1m/100cm)^2 = 3.9E4 N ?
 
Physics news on Phys.org
Looks like you are using the square of the diameter of the cylinder for the area. What is the formula for the area of a circle?
 
A=pi(r^2)
Ahhh I see! lifesaver over here.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Force Problem: Calculating Ground Force on Jumping Boy with Stiff-Legged Landing
Replies
2
Views
1K
How Much Force Can a Human Femur Withstand Before Breaking?
Replies
2
Views
9K
Drag, terminal velocity, and force.
Replies
9
Views
5K
Calculation of the weight of an insect floating by surface tension
Replies
1
Views
3K
Finding out distance before breaking leg using Hooke's Law
Replies
1
Views
4K
Calculating Initial Height of a Falling Safe on a Spring
Replies
5
Views
2K
Compression of a spring by an object in free fall
Replies
8
Views
3K
Stress and strain, maximum applied force before permanent deformation/breakage
Replies
3
Views
3K
The minimum applied force before an object slips off wall
Replies
4
Views
3K
Femur Compression/Young's Modulus
Replies
7
Views
16K

Hot Threads

Recent Insights

Back
Top