Chapter 07, Problem 08 When jumping straight down, you can be seriously injured

Question

Chapter 07, Problem 08 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 78.8-kg man just before contact with the ground has a speed of 4.80 m/s. (a) In a stiff-legged landing he comes to a halt in 3.28 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 0.254 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) (a) Number (b) Number (c) Number Click if you would like to Show Work for this question: Open Show Work Units Units

Explanation / Answer

(a) The expression for Newton's Second Law of motion is -  

F = m * a

where F is the (average) force the ground exerts on the man and m is the mass of the man,
and a is the average acceleration the man undergoes.

You still need to find the average acceleration, which is given by the formula
a = (Vf - Vi) / t
where Vf is the final velocity, in this case, zero,
Now, the initial velocity Vi is given as, - 4.80 m/s (negative because it is downward)
and t is the time it takes to stop the man.

So, from the above expression -  

F = m * (-Vi) / t

=> F = 78.8 kg * -(-4.8 m/sec) / (0.00328 sec) = 115.32 kN

(b) In this case -

F = 78.8 kg * -(-4.8 m/sec) / (0.254 sec) = 1.489 kN

(c) Magnitude of forces applied by the ground in part (b) is -

1.489 kN + mg = 1.489 kN + 78.8*9.81 N = 1.489 kN + 773 N = 1.489 kN + 0.773 kN = 2.262 kN

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