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Lesson Transcript

Instructor:
*Damien Howard*

Damien has a master's degree in physics and has taught physics lab to college students.

People talk about momentum all the time; now you can discover what that word really means. Then learn about the principle of conservation of momentum and what it has to do with objects colliding.

Momentum is a word you're probably very familiar with. Often, you'll hear that something is gaining or gathering momentum. It might be an actual moving object or it might be used more metaphorically like with a sports team. But have you ever taken a moment to think what, exactly, momentum means?

**Momentum** is the quantity of motion of a moving body. In a basic sense, the more momentum a moving object has, the harder it is to stop. This is why you see the term used metaphorically like in the example of the sports team. It means the team is on a roll (generally, a winning streak) and is becoming a stronger team for it. The other teams will have a harder time stopping the team gaining momentum.

We know that momentum is the quantity of motion of a moving body, but what, exactly, does that mean? Let's think about a baseball being thrown in a straight line through the air in order to try and understand this. When you catch a baseball, you feel the momentum of the ball being imparted to you. The ball will probably push your hand back towards you when you catch it. The more momentum the ball has, the more it will push back your hand as it transfers its momentum to you.

Imagine two baseballs are being thrown at you. One is traveling at 50 mph and the other at 150 mph. Even if you somehow catch that 150 mph ball, it might knock you off your feet. It will take more effort on your part to stop the 150 mph ball than the 50 mph one. So it stands to reason that velocity is a very important aspect of momentum. However, that's not all there is to momentum.

Now imagine two balls being thrown at you at 50 mph. One is a baseball and the other is a bowling ball. You probably aren't going to want to try to stop the bowling ball. It's going to keep traveling even after it hits you. Both balls are traveling at the same velocity, so what makes the bowling ball so much harder to stop? It's because it is heavier. It has more mass. So the other important aspect of momentum is mass.

In physics, we define momentum mathematically as the multiplication of mass and velocity as seen in this equation: *p* = *m* * *v*

*p*= momentum*m*= mass*v*= velocity

As far as momentum's units go, we have no special symbol used just for momentum. Instead, it is simply the combination of mass's standard unit of kilograms (kg) and velocity's standard unit of meters per second (m/s). Momentum is measured in standard units of kilograms times meters per second (**kg m/s**).

The **principle of conservation of momentum** states that in an isolated system, two objects that collide have the same combined momentum before and after the collision. That is, momentum is not destroyed in the collision, but transferred between the two objects. In an isolated system, momentum is always conserved in a collision. In the example of you catching a baseball, the momentum from the ball is transferred into your hand.

How momentum is transferred depends on the type of collision. There are three types of collisions: elastic, perfectly inelastic, and partially inelastic.

In an **elastic collision**, two objects collide and bounce off of each other. A good example of this type of collision would be a game of pool. You hit the cue ball with the cue, and it bounces off another ball. Hopefully, that other ball goes in the table pocket, but what's most important for us is that the two balls don't stick together at all. They bounce off of each other.

We can also express the conservation of momentum in an elastic collision mathematically. We know the momentum is conserved, so the total momentum before the collision must equal the total momentum after the collision. We'll call the momentum before the collision the initial momentum (*i*), and the momentum after the collision the final momentum (*f*). Total initial momentum equals total final momentum:

*p*{*i*}total = *p*{*f*}total

Now let's separate the total before and after momentum into the momentum for ball 1 and ball 2.

*p*{1*i*} + *p*{2*i*} = *p*{1*f*} + *p*{2*f*}

Next, we'll add in the equation for linear momentum we learned earlier (*p* = *m* * *v*). This will give us our equation for the conservation of momentum in an elastic collision:

*m*{1} * *v*{1*i*} + *m*{2} * *v*{2*i*} = *m*{1} * *v*{1*f*} + *m*{2} * *v*{2*f*}

You'll notice we didn't specify an initial and final mass like we did with momentum and velocity. This is because the mass of the two objects remains the same before and after the collision. Even though we used two pool balls in our example, you can't always guarantee that the two objects' masses will be the same, so we do keep the masses defined separately as *m*1 and *m*2 in the equation.

Now let's try an example with this equation and unlike the pool balls, we'll use two objects with different masses. Imagine you've gone bowling and a child before you rolled the ball so slowly it stopped mid-lane. No one is around to help you and you don't want to walk out on the lane yourself. You decide to roll your bowling ball into the one stopped on the lane to get it moving.

Your throw your 5.4 kg ball at a velocity of 20 m/s towards the child's ball weighing 2.7 kg. You hit the ball dead on and both balls continue to move in a straight line after the collision. The child's ball is sitting still before the collision so you know it was at an initial velocity of 0 m/s and after the collision, it moves at a velocity of 14 m/s. What velocity is your ball moving at after the collision?

Let's declare your bowling ball to be ball number 1 and the child's to be ball number 2. Note that this is an arbitrary decision since the math works out the same either way it is declared for a 1-dimensional elastic collision. We can now take the values we know and put them into the equation for conservation of momentum in an elastic collision.

*m*{1} * *v*{1*i*} + *m*{2} * *v*{2*i*} = *m*{1} * *v*{1*f*} + *m*{2} * *v*{2*f*}

(5.4 kg) * (20 m/s) + (2.7 kg) * (0 m/s) = (5.4 kg) * *v*{1*f*} + (2.7 kg) * (14 m/s)

(108 kg m/s) + (0 kg m/s) = (5.4 kg) * *v*{1*f*} + (38 kg m/s)

(108 kg m/s) = (5.4 kg) * *v*{1*f*} + (38 kg m/s)

(108 kg m/s) - (38 kg m/s) = (5.4 kg) * *v*{1*f*}

(70 kg m/s) = (5.4 kg) * *v*{1*f*}

(70 kg m/s) / (5.4 kg) = *v*{1*f*}

13 m/s = *v*{1*f*}

So we get the final velocity of your ball to be 13 m/s, which is just a little slower than the lighter ball it hit.

There is one last thing that should be noted. We got an answer that was a positive number. What would it mean if instead, we got our ball's velocity to be -13 m/s? The sign on the velocity of the ball in the collision represents direction. We got all our signs to be positive for this example. So, the heavier ball hit the lighter one, and they both continued rolling in the direction the heavier one was initially traveling. We can assume that was towards the bowling pins.

If we had gotten a negative sign on your ball's velocity after the collision, all it would mean is that the ball was rolling in the opposite direction back towards you. This wouldn't make sense for our example, but you can easily run into problems where it does.

In a **perfectly inelastic collision**, the two objects collide and stick together after the collision. You might try thinking of it like a car crash where the two cars collide and then are stuck together. Before the collision, we have two objects (the cars) and after the collision, we have one object that is the two cars that are stuck together.

Just like the elastic collision, we can express the conservation of momentum for a perfectly inelastic collision mathematically. The good news is the first steps for finding the equation for conservation of momentum for a perfectly inelastic collision are exactly the same for an elastic collision. In fact, we can start with the final equation we found for an elastic collision:

*m*{1} * *v*{1*i*} + *m*{2} * *v*{2*i*} = *m*{1} * *v*{1*f*} + *m*{2} * *v*{2*f*}

The big difference between the two types of collisions is that in a perfectly inelastic collision, both the objects are stuck together at the end. This means that they would be moving at the exact same velocity. There is no *v*{1*f*} and *v*{2*f*}; there is just a single *v*{*f*}. So, we can use that knowledge to get our equation for conservation of momentum in a perfectly inelastic collision.

*m*{1} * *v*{1*i*} + *m*{2} * *v*{2*i*} = *m*{1} * *v*{*f*} + *m*{2} * *v*{*f*}

*m*{1} * *v*{1*i*} + *m*{2} * *v*{2*i*} = (*m*{1} + *m*{2}) * *v*{*f*}

As a final note, let's talk briefly about the third type of collision. In a **partially inelastic collision**, two objects do not stick together, but energy is lost. One way this might happen would be as a combination of a perfectly inelastic collision and an elastic collision.

In our example of the car crash, the two cars stick together permanently at the end. This is not what normally happens in a car crash unless it's a really terrible accident. What happens normally is that the two cars hit and begin to crumple. After a fraction of a second of crumpling, they bounce off one another. During the crumpling stage, the collision is acting like an inelastic collision and during the bouncing stage, is acting like an elastic collision. This is a far more common and complicated type of collision that happens in the real world.

Momentum is the quantity of motion of a moving body. It is expressed mathematically as *p* = *m* * *v* and has units of kg m/s. The principle of conservation of momentum states that in an isolated system, two objects that collide have the same combined momentum before and after the collision.

There are three types of collisions. In an **elastic collision**, two objects bounce off of each other. In a **perfectly inelastic collision**, two objects stick together after the collision. In a **partially inelastic collision**, the two objects stick together momentarily but then bounce off each other, and energy is lost in the collision.

**Momentum**: the measurable quantity of movement in a body or object**Linear Momentum**: the movement measurement of an object traveling in a straight line from point A to point B**Principle of Conservation of Momentum**: momentum does not end in a collision, but is transferred between the two objects**Elastic Collision**: two objects bounce off one another**Perfectly Inelastic Collision**: after collision, two objects are stuck together**Partially Inelastic Collision**: two objects stick together momentarily and then bounce off, losing energy

Your completion of this lesson on momentum could occur simultaneously with your ability to:

- Recite the definition of momentum
- State the principle of conservation of momentum
- Remember the formula for measuring various types of momentum
- Identify the three types of collisions

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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