Linear momentum of jumping straight down

[leezak]

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 73.9-kg man just before contact with the ground has a speed of 5.55 m/s. (a) In a stiff-legged landing he comes to a halt in 3.00 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 0.145 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).

i know how to get (a) and (b) by mv/t, but I'm not sure how to get (c). I found out (b) was 2828.59 N because that's the answer to (73.9*5.55)/0.145. i tried using F=ma for the force of gravity so i did (73.9)(9.8) and subtracted that from the total force received in (b) but that gave me the wrong answer. help?! please! thanks

 

[Doc Al]

To use F=ma, you'd need to know the acceleration. It's not 9.8 m/s^2--that's the acceleration due to gravity for an object in freefall.

But no need for any of that. You found the net force (in part b) which is the vector sum of:

(1) the weight, which acts down
(2) the force that the ground exerts on the man, which acts up​

Write that mathematically and solve for the force that the ground exerts.

 

[quicknote]

!

(c) To find the magnitude of the force applied by the ground on the man in part (b), we can use Newton's second law, F=ma, where F is the net force, m is the mass of the man, and a is the acceleration. In this case, the acceleration is the change in velocity over the change in time, or a= (5.55 m/s - 0 m/s) / 0.145 s = 38.276 m/s^2.

The net force acting on the man is equal to the sum of the force of gravity and the upward force from the ground. The force of gravity can be calculated using F=ma, where m is the mass of the man and a is the acceleration due to gravity, which is approximately 9.8 m/s^2. So, the force of gravity is (73.9 kg)(9.8 m/s^2) = 724.22 N.

To find the magnitude of the upward force from the ground, we can use the net force calculated in part (b) and subtract the force of gravity. So, the upward force from the ground is equal to the net force - force of gravity = 2828.59 N - 724.22 N = 2104.37 N.

Therefore, the magnitude of the force applied by the ground on the man in part (b) is 2104.37 N.