Imagine a person you are walking with slips and falls backwards. They are unable
ID: 2030229 • Letter: I
Question
Imagine a person you are walking with slips and falls backwards. They are unable to catch themselves and end up hitting their head on the floor. The person's head is 5 kg and is moving at 3 m/s second when it first hits the floor. The floor gives .005 m from the impact of the head. The change in gravitation potential energy and strain energy during the impact are going to be very small in this case so ignore them.
a) How much kinetic energy does the head have the instant before it contacts the floor?
b) How much work does the floor do to stop the motion of the head?
c) What average impact force does the floor exert on the head during the impact? Estimate a peak impact force.
d) What is the peak acceleration of the head?
e) What is the peak acceleration of the head in g's?
f) Describe briefly the likely results of the head hitting the floor.
Explanation / Answer
a] KE = 0.5mv^2 = 0.5*5*3^2 = 22.5 J
b] work done = - 22.5 J
c] impact force F = Work/distance = 22.5/0.005 = 4500 N
d] accleration a = F/m = -4500/5 = -900 m/s^2 downward or 900 m/s^2 upward
e] a = -900/9.8 = -92 g, taking absoulte value, it is 92 g
f] this is huge acceleration, so skull fracture can happen.