How Does Bending Your Knees Reduce the Impact Force When Jumping?

[JaKaL]

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 68.4-kg man just before contact with the ground has a speed of 4.99 m/s. (a) In a stiff-legged landing he comes to a halt in 4.09 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.296 s. Find the magnitude of the average net force now. (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 the forces, find the magnitude of the force applied by the ground on the man in part (b).
2. (EF)= (-m X Vo)/ delta t



I got a) 83451.34 and b)1153.09 but I don't know what to do for c)

 

[RoyalCat]

J ≡ P_f - P_i = F_average*Δt
The formula you used is correct, but remember the original form, where P_f =/= 0 for future problems.

Your answers for (a) and (b) are correct.

For (c), make a free body diagram of the man as he impacts the ground (Remember, he's being decelerated from 4.99 m/s). What forces are acting on him, what is the net force, and what is the source of each of the forces?

 

[nlightner]

I can confirm that the Impulse-Momentum Theorem is a fundamental concept in physics that relates the change in momentum of an object to the impulse applied to it. In this scenario, the impulse is the force applied over a certain amount of time, which leads to a change in the man's momentum.

In part (a), the magnitude of the average net force can be calculated using the formula (EF) = (-m x Vo)/delta t, where m is the mass of the man, Vo is his initial velocity, and delta t is the time taken for him to come to a halt. Plugging in the given values, we get (EF) = (-68.4 kg x 4.99 m/s)/0.00409 s = 83,451.34 N.

In part (b), when the man bends his knees upon landing, the time taken for him to come to a halt increases, leading to a decrease in the average net force. Using the same formula, we get (EF) = (-68.4 kg x 4.99 m/s)/0.296 s = 1,153.09 N.

In part (c), we need to take into account the direction of the forces. The force of the ground on the man is pointing upward, while the force due to gravity is pointing downward. The average net force will be the sum of these forces. To find the magnitude of the force applied by the ground, we can use the Pythagorean theorem. The horizontal component of the force due to gravity is 0, so the magnitude of the force applied by the ground will be the same as the magnitude of the average net force calculated in part (b), which is 1,153.09 N.