Elastic Deformation through compression (stress)

Click For Summary
SUMMARY

The discussion centers on calculating the compressional stress on the forearm bones (radius and ulna) during a car crash scenario. The total cross-sectional area of the load-bearing portion is 2.16 cm², and the effective mass of the arm is 1.88 kg. Using the formula for stress (σ = F/A), the calculated force (F) is derived from the mass and acceleration, resulting in a stress value of approximately 25.65 MPa. The participant raised concerns about the interpretation of the cross-sectional area and significant digits, but the consensus is that the total area is appropriate for the calculation.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of stress calculation (σ = F/A)
  • Familiarity with unit conversions (cm² to m²)
  • Basic principles of kinematics (Vf = Vo + at)
NEXT STEPS
  • Review the concept of significant figures in scientific calculations
  • Study the effects of compressive stress on biological tissues
  • Learn about the biomechanics of bone structure and load distribution
  • Explore real-world applications of stress calculations in automotive safety engineering
USEFUL FOR

Students in physics or engineering, biomechanics researchers, automotive safety engineers, and anyone interested in the effects of stress on biological materials.

fanie1031
Messages
12
Reaction score
0
1. The total cross-sectional area of the load-bearing calcified portion of the two forearms bones (radius and ulna) is approximately 2.16cm^2. During a car crash, the forearm is slammed against the dashboard. Tha arm comes to rest from an initial speed of 81.9km/h in 7.72 s. If the arm has an effective mass of 1.88kg what is the compressional stress on the arm? Answer in units of Pa.
2. Stress=F/A ,
additional
F=ma
Vf=Vo+at
3.
Conversions
A=2.16cm^2*1m^2/10^4cm
=2.16e-4m^2
Vo=81.9km/h*(1hr/60mins)(1min/60s)(1000m/1km)
=22.75m/s

F=ma
a=(Vf-Vo)t=-2.94689.

I assumed I could make it positive since the problem's context is in forward motion not retardation.

F=1.88kg*2.94689
=5.540kg*m/s^2

P=F/A
P=5.540kg*m/s^2/2.16e-4
=25.648.8677N/m^2= same in Pa.I feel like I put in the appropriate conversions and formulas but when I plug in the answer, I'm told I am wrong. Does it have to do with the fact that it mentions "two forearm bones" in the beginning? If it is, where do I half the cross sectional area?

I hope I'm not too far off.
 
Physics news on Phys.org
Your method looks fine. Units are OK.

Check the significant digits is about all I can suggest.

Your concern about 2 cross sections should be allayed by the statement of total cross section.
 

Similar threads

  • · Replies 17 ·
Replies
17
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
16K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
7K
  • · Replies 9 ·
Replies
9
Views
12K
  • · Replies 3 ·
Replies
3
Views
2K