When jumping straight down, you can be seriously injured if you land stiff-legge

Question

When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 75-kg man just before contact with the ground has a speed of 4.6 m/s.

(a) In a stiff-legged landing he comes to a halt in 2.1 ms. Find the average net force that acts on him during this time.
  N

(b) When he bends his knees, he comes to a halt in 0.13 s. Find the average force now.
  N

(c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of these forces, find the force of the ground on the man in parts (a) and (b).

Explanation / Answer

Using Newton's second law of motion, force F acting on a body is equal to time rate of change in momentum in the body.

So F = dp/dt

a) in first case of stiffed legs, dp = 0 - mu = - 75 × 4.6 kg.m/s

= - 345 N

dt = 2.1 ms = 2.1 × 10-3s

Hence Force acting on person F = -345÷(2.1 × 10-3)

F = -164.28 × 103N

-ve sign shows that direction of this force is upwards.

Now force acting on the person by gravity = mg = 75 × 9.8N = 735N

This force is due to gravity which acts downward but according to Newton's third law, same force will be applied on man by the ground so they will cancel each other, hence net average force acting on the man is F = 164.28 × 103N

b) when dt = 0.13s, than force upwards is F = -345/0.13 = -2.65 × 103N

Hence net average force F = 2.65 × 103N

c) If we consider only the force of ground on the man, ignoring the force of gravity, than in first case, F = 164.28 × 103 + 735

F = (164 .28 + 0.74) × 103 = 165.02 × 103N

In second case F = 2.65 × 103 + 735 = (2.65 + 0.74) × 103N

= 3.39 × 103N

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