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 5.4 m/s.

(a) In a stiff-legged landing he comes to a halt in 2.2 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 0.14 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).

stiff legged landing _______N

bent legged landing _______ N

Answer 1

This is a Newton's Second Law problem. The problem asks for the average force, which can be gotten from

F = m * a

where F is the (average) force the ground exerts on the man,
m is the mass of the man,
and a is the average acceleration the man undergoes.

You still need to find the average acceleration, which is given by the formula
a = (Vf - Vi) / t
where Vf is the final velocity, in this case, zero,
Vi is the initial velocity, in this case -5.4 m/s (negative because it is downward)
and t is the time it takes to stop the man.

Substituting this second experession in for a into the equation for force gives

F = m * (-Vi) / t

The answer for part (a) is therefore

F = 75 kg * -(-5.4 m/sec) / (0.0022 sec) = 184kN

and for part (b) is

F = 75 kg * -(-5.4m/sec) / (0.14 sec) = 2.892 kN

Because of the much larger forces acting on the man when landing stiff-legged, he stands a much greater chance of being injured if he lands this way. If he lands bent-legged, he is likely to escape injury altogether. (The velocity on impact implies that he jumped from a height of about 2 meters.)

The calculations in parts (a) and (b) do not include the extra force the ground exerts on the man to counteract the gravitational acceleration when he makes contact with the ground. To get the answer to part (c), you must add an m * g term to the final answer, g being the acceleration of gravity. Depending on your class, you may be using the rounded approximate value of 10 m/sec or the more precise 9.8 m/sec for g.