The tibia bone in the lower leg of an adult human will break

The tibia bone in the lower leg of an adult human will break if the compressive force on it exceeds about 4 X 10^5 N (we assume that the ankle is pushing up). Suppose that you step off a chair that is 0.40 m above the floor. If landing stiff-legged on the surface below, what minimum stopping distance do you need to avoid breaking your tibias? Indicate any assumptions you made in your answer to this question.

Solution

Fmax = 4*10^5

Let the minimum stopping distance be d

For h = 0.4 m

the velocity of the leg at the contac point with the surface,

v = sqrt(2*g*h)

and the potential energy lost, PE = mgh

Assuming the compressive force to be contant during the deceleration of the bone,

The work done by the the compressive force

W = -Fmax*d

Now, W + PE = 0 <------- for coming to rest (initital energy = PE. work done = W. SO,final energy = 0 So, PE +W = 0)

So, W = -PE = mgh = Fmax*d

So, d = mgh/Fmax

where m = mass of tibia

g = 9.8 m/s2

h = 0.4

So, d = m*9.8*0.4/(4*10^5) = 9.8*10^-6*m

Just plug in the mass of Tibia in place of m to get the answer