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 6.4 m/s. (a) In a stiff-legged landing he comes to a halt in 2.5 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 0.12 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

We know that, Impulse is given by:

Impulse = Change in momentum = Average force*Impact time

I = dP = Favg*dt

dP = m*dV = m*(Vf - Vi)

So, Favg*dt = m*(Vf - Vi)

Favg = m*(Vf - Vi)/dt

Part A.

given that when he lands with stiff-legged, then

m = mass of man = 75 kg

Vf = final speed of man = 0 m/sec

Vi = speed of man just before contact with ground = 6.4 m/sec

dt = impact time = 2.5 ms = 2.5*10^-3 sec

So, Magnitude of avg force will be:

|Favg| = |75*(0 - 6.4)/(2.5*10^-3)| = |-192000|

|Favg| = 1.92*10^5 N

Part B.

when man lands after bending the knees,

dt = 0.12 sec

then in this case

Magnitude of avg force will be:

|Favg| = |75*(0 - 6.4)/0.12| = |-4000|

|Favg| = 4000 N

Part C.

Given that Force of ground on the man is pointing upward

Force due to gravity is pointing downward

Now average net force acting on the man will be pointing upward, So

Using Force balance:

Favg = F_ground - F_gravity

F_ground = Favg + F_gravity

F_gravity = Weight of man = m*g

F_ground = Favg + m*g

for case (A)

F_ground = 192000 + 75*9.81 = 192735.75 N

F_ground = 192735.75 N (for case A when stiff legged landing)

In case (b)

F_ground = F_avg_b + m*g

F_ground = 4000 + 75*9.81 = 4735.75 N

F_ground = 4735.75 N (for case B when bent legged landing)

Let me know if you've any query.