The compressive force per area necessary to break the tibia in the lower leg, is about F/A =1.6 ×10 N m^2. The smallest cross sectional area of the tibia, about 3.2 cm^2, is slightly above the ankle. Suppose a person of mass m =6.0 ×10 kg jumps to the ground from a height h0 =2.0 m and absorbs the shock of hitting the ground by bending the knees. Assume that there is constant deceleration during the collision. During the collision, the person lowers his center of mass by an amount d=1 cm.
a) What is the collision time, t?
b) Find the average force of the ground on the person during the collision.
c) What is the average impulse of the ground on the person?
d) Will the person break his ankle? How much would you need to lower your center of mass so you do not break your ankle?
p = mv
F = p/t
J = pf - pi
The Attempt at a Solution
a) I first started by finding the final velocity.
vf = sqrt(2ad) = sqrt(2(9.8)(2)) = 6.26 m/s
I then divided the distance he lowers his mass by this amount.
t = d/v = 0.01/6.26 = 1.6 x 10^-3 s
b) The average is force is simply the change in position over the time.
F = m(vf-vi)/t = 60(0-6.26)/(1.6 x 10^-3) = -234750 N
c) The impulse is the change in momentum.
J = pf - pi = 0 - 60(6.26) = -375.6
d) P = F/A = -234750/(3.2x10^-4) = 7.3 x 10^8
This pressure is greater, therefore, he will break his ankle.
I'm not sure if I did anything correctly. Can someone show me what I'm supposed to do?