Question

The maximum energy a bone can absorb without breaking is surprisingly small. For a healthy human of mass 60 kg60 kg, experimental data show that the leg bones can absorb about 200 J.

Required:
a. From what maximum height could a person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed in the leg bones in a rigid landing.
b. People jump from much greater heights than this; explain how this is possible.

Answer 1

the maximum height a man can jump from and land rigidly upright on both feet without breaking his legs is 0.34 m

Step-by-step explanation:

Mass of a healthy man = 60 kg

energy the bone can take without breaking = 200 J

If a healthy man jumps from a height 'h', he falls with an energy equal to the potential energy due to his initial height above the ground.

initial potential energy of the healthy man = mgh

where m = mass of the man

g = acceleration due to gravity = 9.81 m/s^2

h = the height above ground

==> PE = 60 x 9.81 x h = 588.6h

If we assume that all energy is absorbed in the leg bones in a rigid landing, then we can safely say that this calculated PE for a healthy man is equal to the energy his bone can absorb in the jump without breaking.

equating, we have

200 = 588.6h

the maximum height a man can jump from without breaking his legs = 200/588.6 = 0.34 m

When people jump from a height, the sudden deceleration to zero can impact a big force on the leg bones, shattering them. If the time spent in decelerating to zero is increased, the overall force on the leg bones is reduced greatly.

Bending the knees gradually on landing from a jump from a height, and then rolling increases the time spent decelerating, and reduces the impact force on the legs due to the landing. If you observe carefully you will see that this is what professional stunts men and acrobats do when they jump from a height.