The total cross-sectional area of the load-bearing calcified portion of the two

Question

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.20 cm2 . During a car crash, the passenger attempts to brace himself with his hand such that his forearm is perpendicular to the dashboard. His forearm is slammed against the dashboard, hand first. The arm comes to rest from an initial speed of 80.0 km/h in 4.90 ms. If the arm has an effective mass of 3.00 kg, what is the compressional stress that the arm withstands during the crash?

Explanation / Answer

stress is force/area
you alread have an area, so lets work on a force
force is mass x acceleration
you have a mass, so lets find an acceleration
Acceleration is the change in speed with respect to time
dv/dt or delta V/delta t
your delta V is 80km/hour and your delta t is 5.2 ms

lets put these in the proper units and solve:
80km/hr*(1000m/km)*(1hr/3600sec)=22.22...
time = 4.9ms(1s/1000ms)=.0049sec
acceleration=4534.69 m/s2
back to mass
F=ma=3.0kg*4534.69 m/s2= 13604.07 Newtons

back to area
2.2cm2*(1m2/10000cm2)=0.00022m2

Stress then equals 13604.07 /0.00022
618366818.2 Pascals or 61.836 GPa

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.