# Collisions and impulse momentum relationship

### Real-World Applications

The impulse-momentum theorem states that the change in momentum of an The impulse-momentum theorem is logically equivalent to Newton's second law of. Learn what momentum and impulse are, as well as how they are related to force. This equivalence is known as the impulse-momentum theorem. Because of the impulse-momentum . What are two dimensional collisions? Force vs. time. If an impact stops a moving object, then the change in momentum is a fixed quantity, and extending the time of the collision will decrease the time average of the.

We can't use force because we don't know it yet, but I can figure out the change in momentum 'cause I know the velocities. So, we know that the change in momentum is gonna be P final, the final momentum, minus the initial momentum. What's my final momentum? My final momentum is M times V, so it's gonna be mass times V final, minus mass times V initial, and my mass is. My final velocity is five, because the ball recoiled to the right with positive five.

Positive five 'cause it's moving to the right. I'm gonna assume rightward is positive. Then minus, the mass is. My initial velocity is not This is 10 meters per second to the left, and momentum is a vector, it has direction, so you have to be careful with negative signs here. This is the most common mistake. People just plug in positive 10, then get the wrong answer. But this ball changed directions, so the two velocities here have to have two different sides, so this has to be a negative 10 meters per second, if I'm assuming rightward is positive.

This leftward velocity, and this leftward initial velocity, has to be negative And, if you didn't plug that in, you'd get a different answer, so you gotta be careful. So, what do I get here if I multiply this all out? I'm gonna get zero, no, sorry, I'm gonna get one kilogram meters per second, minus a negative two kilogram meters per second, and that's gonna give me positive three kilogram meters per second is the impulse, and that should make sense.

The impulse was positive. The direction of the impulse, which is a vector, is the same direction as the direction of the force. So, which way did our face exert a force on the ball?

### Impulse of Force

Our face exerted a force on the ball to the right. That's why the impulse on the ball is to the right. The impulse on this person's face is to the left, but the impulse on the ball is to the right, because the ball was initially going left and it had a force on it to the right that made it recoil and bounce back to the right.

That's why this impulse has a positive direction to it. Now, if you've been paying attention, you might be like, wait a minute, hold on. What we really did was we found the change in momentum of the ball, and when we do that, what we're finding is the net impulse on the ball.

In other words, the impulse from all forces on the ball. But what this question was asking for was the impulse from a single force. The impulse from just the person's face. Now, aren't there other forces on this ball? Isn't there a force of gravity? And if there is, doesn't that mean what we really found here wasn't the impulse from just our face, but the impulse from the person's face and the force of gravity during this time period?

And the answer is no, not really, for a few reasons. Most important reason being that, what I gave you up here was the initial horizontal velocity. This 10 meters per second was in the X direction, and this five meters per second, I'm assuming is also in the X direction.

When I do that, I'm finding the net impulse in the X direction, and there was only one X directed force during this time and that was our face on the ball, pushing it to the right. There was a force of gravity.

That force of gravity was downward. But what that force of gravity does, it doesn't add or subtract any impulse in the X direction. It tries to add impulse in the downward direction, in the Y direction, so it tries to add vertical component of velocity downward, and so we're not even considering that over here.

We're just gonna consider that we're lookin' at the horizontal components of velocity. How much velocity does it add vertically, gravity? Typically, not much during the situation, because the time period during which this collision acted is very small and the weight of this ball, compared to the force that our face is acting on the ball with, the weight is typically much smaller than this collision force.

So that's why, in these collision problems, we typically ignore the force of gravity. So, we don't have to worry about that here. That's not actually posing much of a problem. We did find the net impulse in the X direction since our face was the only X directed force, this had to be the impulse our face exerted on the ball.

Now, let's solve one more problem.

## Momentum and Impulse Connection

Let's say we wanted to know: What was the average force on this person's face from the ball? Well, we know the net impulse on the ball, that means we can figure out the net force on the ball, because I can use this relationship now. The concepts in the above paragraph should not seem like abstract information to you. You have observed this a number of times if you have watched the sport of football.

### Impulse & Momentum - Summary – The Physics Hypertextbook

In football, the defensive players apply a force for a given amount of time to stop the momentum of the offensive player who has the ball. You have also experienced this a multitude of times while driving.

As you bring your car to a halt when approaching a stop sign or stoplight, the brakes serve to apply a force to the car for a given amount of time to change the car's momentum. An object with momentum can be stopped if a force is applied against it for a given amount of time. A force acting for a given amount of time will change an object's momentum.

Put another way, an unbalanced force always accelerates an object - either speeding it up or slowing it down. If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed.

Impulse These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit. To truly understand the equation, it is important to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity.

The physics of collisions are governed by the laws of momentum; and the first law that we discuss in this unit is expressed in the above equation. The equation is known as the impulse-momentum change equation. The law can be expressed this way: In a collision, an object experiences a force for a specific amount of time that results in a change in momentum. The result of the force acting for the given amount of time is that the object's mass either speeds up or slows down or changes direction.

The impulse experienced by the object equals the change in momentum of the object.