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Conservation of Momentum

Teacher/Instructor Matt Jones
Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

The law of conservation of momentum says that if two objects collide, the force lost by one object is equal to the force gained by the other object. The total momentum of the system is the same after the collision as before it as shown by the equation initial momentum = final momentum (where final momentum is the sum of all momentums present in the system). This principle is similar to the law of conservation of energy.

Conservation of momentum, conservation of momentum simply states that the momentum of a system remains the same despite any collisions or interactions that occur within that system, the overall momentum will continue to remain the same. Okay so let's just review what momentum is, momentum is again a mass times a velocity alright so a mass typically is in kilograms, velocity meters per second. Alright so you've all observed this if you've ever watched balls on a pool table. Right if I've got a ball and it's moving into a certain momentum and it strikes another ball, this ball will continue at the same momentum since the balls have the same mass they'll also continue at the same velocity.

Okay if I have a ball moving at a certain momentum in this direction and it strikes a ball moving at the, with an opposite momentum together those 2 balls are going to collide and they're going to balance off each other right so our this ball is now moving this way, this ball is now moving this way but again the momentum of this ball is continuing it's just now being observed in this ball, the momentum of this ball is continuing it's now being observed in this ball. So again these are both examples of conservation of momentum. Let's look at some examples, that you might be asked to solve and demonstrating conservation of momentum. Let's say I've got a cannon and I'm firing a cannon ball at 25 meters per second and my cannon ball has a mass of 5 kilograms okay.

If I solve this problem what I need to figure out is my initial momentum must equal my final momentum but my final momentum is going to now have 2 different momentums. It's going to have the momentum of the ball which we'll call momentum b and the momentum of the cannon which we'll call momentum c. Alright but what we want to figure out here is what after this ball is fired, what is going to be the velocity of that cannon in that direction? So when start our initial momentum is going to be essentially 0 kilograms per meters squared because we have 0 velocity. Okay that's going to equal the momentum of the ball which is 25 kilograms times I'm sorry 5 kilograms times 25 I got my units mixed up meters per second.

And that is also again conservation means I also have to add the cannon which is 100 kilograms times v because what we're trying to solve for is what is the velocity of the cannon. Alright so v is our unknown here and if we simply this we have 5 times 25 is 125 kilograms meters squared plus 100 kilograms times v okay and we divide by 100 kilograms and when I do that my units cancel and I'm going to get v is going to equal negative 125 meters per second. Okay because if I have a positive velocity here I have 7 negative velocity to equal that. So in this case this velocity is going to be negative 1.25 meters per second. Okay let's look at second example, this time we're going to look at what's called an inelastic collision. In this case I've got a Velcro ball of 1 kilogram it's going to go 4 meters per second and it's going to collide with a big Velcro ball of 5 kilograms.

Now when they collide I have no initial velocity here or no 0 momentum here but when they collide the new system is going to have a certain velocity and oops, what is that new velocity going to be? Alright well let's look at that alright so what we have here is the initial momentum and it has to equal the final momentum. Alright so my initial momentum is made up of 2 components this ball and this ball and the momentum of each. So let's calculate that, I've got 1 kilogram times 4 meters per second for that one and I'm going to add that to 5 kilograms and my velocity here is 0 meters per second okay so this unit is 0. We can forget about it, so our initial momentum is just 4 kilograms meters per second alright and that's going to equal our final velocity, now these 2 are 1. So our unit is now, has a mass of 1+5 which is 6 kilograms and we need to figure out what the velocity is, we're solving for v there.

Okay, so how do we solve that? Well we've got to divide 4 by 6 kilograms to get rid of our unit there and when we do that, that cancels and we get v equals 0.66 meters per second okay. So in this case we've used the conservation of momentum to figure out what the velocity of our new system is after smaller system with a smaller momentum has collided with larger object and we've calculated the new velocity. So these are 2 of the types of problems you'll be asked to solve using the conservation of momentum.