I have figured out everything except the last part of this problem. No clue how to figure that can someone help me...
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 6.9 m/s.
(a) In a stiff-legged landing he comes to a halt in 2.0 ms. Find the average net force that acts on him during this time.
258750 N
(b) When he bends his knees, he comes to a halt in 0.10 s. Find the average force now.
5175 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
-258750 N
bent legged landing ??????
N
(a) and (b) are OK.
(c) For the average NET force on the man, subtract the weight M g from the average forcw applied by the ground.
I need a better answer
To solve this problem, we need to use the equation for average net force:
Average Net Force = Change in Momentum / Change in Time
We can find the change in momentum using the equation:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
Let's solve each part of the problem step by step:
(a) In a stiff-legged landing, the man comes to a halt in 2.0 ms. We are given the mass of the man (m = 75 kg) and the initial velocity before contact with the ground (v_i = 6.9 m/s).
To find the average net force, we need to first calculate the change in momentum. Using the equation:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
Change in Momentum = 75 kg * (0 m/s - 6.9 m/s)
Change in Momentum = -517.5 Ns
Now we can calculate the average net force by dividing the change in momentum by the time interval:
Average Net Force = Change in Momentum / Change in Time
Average Net Force = -517.5 Ns / (2.0 ms x 10^-3)
Average Net Force = -258750 N
Therefore, the average net force in a stiff-legged landing is -258750 N (pointing downward).
(b) When the man bends his knees, he comes to a halt in 0.10 s. We are given the same mass (m = 75 kg) and the same initial velocity (v_i = 6.9 m/s).
Again, we need to calculate the change in momentum:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
Change in Momentum = 75 kg * (0 m/s - 6.9 m/s)
Change in Momentum = -517.5 Ns
Now we can calculate the average net force using the time interval:
Average Net Force = Change in Momentum / Change in Time
Average Net Force = -517.5 Ns / 0.10 s
Average Net Force = -5175 N
Therefore, the average net force when bending his knees is -5175 N (pointing downward).
(c) The force of the ground on the man points upward, while the force due to gravity points downward. The average net force accounts for both of these forces.
In part (a), the force of the ground on the man is equal to the average net force, since the force due to gravity cancels out with the upward force of the ground:
Force of Ground on Man (stiff-legged) = -258750 N (pointing upward)
In part (b), the force of the ground on the man, now that he bends his knees, can be found by subtracting the force due to gravity from the average net force:
Force of Ground on Man (bent-legged) = Average Net Force - Force due to Gravity
Force of Ground on Man (bent-legged) = -5175 N - (75 kg * 9.8 m/s^2)
Force of Ground on Man (bent-legged) = -5175 N - 735 N
Force of Ground on Man (bent-legged) = -5910 N (pointing upward)
Therefore, the force of the ground on the man is -5910 N (pointing upward) when he bends his knees.