Need help doing 5-1 Assume that a 50-kg runner trips and falls on his extended h

Question

Need help doing 5-1 Assume that a 50-kg runner trips and falls on his extended hand. If the bones of one arm absorb all the kinetic energy (neglecting the energy of the fall), what is the minimum speed of the runner that will cause a fracture of the arm bone? Assume that the length of arm is 1 m and that the area of the bone is 4 cm^2. Repeat the calculations in Exercise 5-1 using impulsive force considerations. Assume that the duration of impact is 10^2 sec and the area of impact is 4 cm^2. Repeat the calculation with area of impact = 1 cm^2. From what height can a 1-kg falling object cause fracture of the skull? Assume that the object is hard, that the area of contact with the skull is 1 cm^2, and that the duration of impact is 10^-3 sec. Calculate the duration of the collision between the passenger and the inflated bag of the collision protection device discussed in this chapter. In a rear-end collision the automobile that is hit is accelerated to a velocity v in 10^-2/sec. What is the minimum velocity at which there is danger of neck fracture from whiplash? Use the data provided in the text, and assume that the area of the cervical vertebra is 1 cm^2 and the mass of the head is 5 kg.

Explanation / Answer

5-1)

m=50 kg=5x104g

v=?

Lo=1 m=100 cm

A=4 cm2

SB=100x107 dyn/cm2

Y=14x1010dyn/cm2

The kinetic energy =The energy required to cause a fracture of the arm

1/2 mv^2 = 1/2 (YA/L0) (SB*L0/Y)^2

5*10^4v^2 = (14*10^10 * 4 /100) (100*10^7*100/14*10^10) ^2

v^2 = (14*10^10*4 / 100*5*10^4) (100*10^7*100/14*10^10) ^2

v^2 = 5.71*10^4 cm^2/sec

v = 239cm/s
= 2.39 m/s

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