When jumping straight down, you can be seriously injured if...

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 2.0 ms. Find the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.10 s. Find 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 force of the ground on the man in parts (a) and (b).

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 2.0 ms. Find the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.10 s. Find 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 force of the ground on the man in parts (a) and (b).

Key Concepts

Impulse-Momentum Theorem

This concept relates the impulse applied to an object to the change in its momentum. It shows that the force applied over a given time interval (impulse) is equal to the change in the object's momentum. Understanding this relationship is key when analyzing collisions or impacts, as it helps in calculating the average force during rapid deceleration.

Newton’s Second Law

Newton’s Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This fundamental principle is used to understand how different forces affect an object’s motion and to calculate forces during changes in velocity, such as during impacts or deceleration events.

Impact Force and Deceleration

This concept involves the relationship between the rate of deceleration and the magnitude of the force experienced during an impact. By spreading the change in momentum over a longer time interval, the force exerted on the object is reduced. This is a critical idea in safety practices, where extending the duration of an impact (e.g., by bending knees) can significantly lower the injurious forces.

Free Fall and External Forces

In free fall situations, both gravitational force and the reaction force from the ground (normal force) act on the object. Analyzing the vector sum of these forces, while considering their directions, is essential to accurately evaluate the net force during landing or collision events. This helps in understanding how external forces combine to produce the resulting motion or deceleration.

Transcript

00:01 Okay, so in number eight, we're looking at the effect that bending your knees when you land a jump has versus not bending your knees.

00:11 So this is all going to be about impulse.

00:13 All right, so let's start at the beginning.

00:14 And i should mention also there are three parts to this question, a, b, and c.

00:18 We'll be doing them all together here in this one video.

00:21 So in part a, we're first looking at what happens if you jump and do not bend your knees.

00:28 So if you land stiff -legged.

00:29 So let's start off with the information that we know.

00:31 We know that the mass of the person is 75 kilograms.

00:38 We know that your initial velocity, the velocity right before you hit the ground, is 6 .4 meters per second.

00:47 And that means your final velocity is when you come to rest, so zero meters per second.

00:56 And this is all happening over a time interval, so delta t of two milliseconds.

01:02 So we're going to write that out of seconds .0 .002 seconds.

01:09 Okay.

01:09 And then here we're looking at what we want to know is the average amount of force that's being exerted on the person.

01:17 Okay.

01:18 So the force is what we're looking for.

01:19 So again, we're going to use our impulse momentum theorem.

01:24 So force times change in time equals our change momentum.

01:29 So our p final minus our p initial.

01:32 Okay.

01:34 As we solve, this we're going to start off we know our momentum final our p final is zero so you're rid of that one and we are going to divide our delta t over to the other side to find our force so we have force equals negative p initial divided by delta t and now we can substitute our numbers in so the average force that's acting on the person at this point is we have a negative and then m times v is our momentum, so 75 kilograms.

02:16 And then our velocity was taking us downwards.

02:19 So we're going to make this a negative 6 .4 meters per second, all divided by the change in time, which was 0 .002 seconds.

02:35 And that gets an average amount of force of 240 ,000 newtons.

02:44 So in this case, this is the amount of net force that's acting on the person who decided to jump and not bend their legs.

02:54 Not a good idea.

02:55 So let's see what happens when we do choose to bend our knees.

02:59 So everything basically stays the same.

03:01 Our mass is still 75 kilograms...