Physics HWK: Avoid Injury w/Stiff-Legged vs. Bent-Legged Landings

[shawonna23]

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 5.6 m/s.

(a) In a stiff-legged landing he comes to a halt in 2.3 ms. Find the average net force that acts on him during this time.
1.8E5 N
(b) When he bends his knees, he comes to a halt in 0.14 s. Find the average force now.
3000 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
1.8E5N
bent legged landing
? N

I got the right answer for part a and b, but I can't seem to get the answer to the last question of part c. The answer I got was -3000, but it was wrong. what am I doing wrong?

 

[BlackMamba]

Again, I had this same exact problem for homework some time ago. The last part of (c) was tricky for me as well.

If you draw a free body diagram of the forces acting on the man when he lands bended knee. It will help.

This equation will come in handy: W = ma

 

[wais]

It seems like you may have forgotten to take into account the direction of the force of gravity in your calculation for part c. Remember, in a stiff-legged landing, the net force is equal to the average force acting on the man, which is in the opposite direction of the force of gravity. So the force of the ground on the man would be equal to the average force (1.8E5 N) plus the force of gravity (-735 N, calculated using F=mg where m=75 kg and g=9.8 m/s^2). This would give you a final answer of 1.8E5-735=1.8E5 N for the force of the ground on the man in a stiff-legged landing. Similarly, for a bent-legged landing, the force of the ground on the man would be equal to the average force (3000 N) plus the force of gravity (-735 N), giving a final answer of 3000-735=2265 N for the force of the ground on the man. Remember to always consider the direction of the forces when calculating net force.