   # The Principle of Conservation of Momentum

Contributor: Jay Gregorio. Lesson ID: 13191

Which has a higher momentum - a slow-moving truck or a fast-moving car? Interestingly, they can carry the same amount of momentum! Explore this "mass in motion" and discover how momentum is conserved.

categories

## Physical Science, Physics

subject
Science
learning style
Visual
personality style
Beaver
Middle School (6-8), High School (9-12)
Lesson Type
Dig Deeper

## Lesson Plan - Get It! • Have you ever played eight-ball before?

Eight-ball, also known as billiards, pool, and snooker, is a game played with a cue stick, a cue ball, and 15 object balls numbered 1 through 15. Popular around the world, it is a game of skill where a cue stick is used to strike a set of balls, causing them to move around a cloth-covered table.

For billiards fans, it is the best sport in the world! For science enthusiasts, it is more than that. In fact, there is so much physics in this game. The combination of forces and exchange of energy involved in every motion could be overwhelming yet interesting.

• What are these forces?
• How do they affect the motion of the balls? Take a look at the photo above.

The force needed to strike the cue ball with the cue stick must be enough to allow the cue ball to move across the table and hit the eight-ball. While the cue ball is moving, it experiences friction, which slows it down to a certain degree. You may think that the table's surface is smooth, but when you look closer, it is not. The bumpy and rugged surface creates the friction force that will slow the ball down and eventually stop it.

Once the cue ball hits the eight-ball in a process called collision, the cue ball is expected to stop and the eight ball moves – evidence of energy transfer.

Whoa! Does that sound like a lot of science? Keep reading to discover how the simple situation above demonstrates the concept of momentum and its conservation.

What is Momentum?

When a sports commentator says that a player is "gaining momentum," what does that really mean? In the language of sports, the word momentum describes something that is moving and hard to stop. It could be a fast-moving cue ball, a sprinter on the track field, or a sports team that is on a winning streak.

• Any object that is in motion has momentum in the language of sports.

The language of physics, however, defines momentum in more specific terms. It is dependent upon two variables: the mass of an object and its velocity. In the case of the cue ball, the word mass describes the amount of matter the cue ball has. Likewise, velocity describes how fast the cue ball is moving after being hit by a cue stick.

It is acceptable to define momentum as a mass in motion. However, expressing this definition mathematically indicates how much momentum the cue ball carries.

• Momentum (p) is expressed as a product of mass (m) and velocity (v).
• In an equation, it is written as p = mv.

Since the standard unit of mass is kilograms (kg), and velocity is meters per second (m/s), the unit of momentum is kg m/s.

In the game of billiards, the 0.17-kg cue ball can travel at about 10 m/s after being hit by a cue stick. What would be its momentum? Use the equation and perform simple substitution:

• p = mv
• p = (0.17 kg)(10 m/s)
• p = 1.7 kg m/s

Looking at this calculation, we know that an increase in the mass of the cue ball will increase its momentum. Conversely, an increase in its velocity will also increase its momentum.

In summary, we conclude that the momentum of the object is directly proportional to the mass and the velocity. If the cue ball stops moving at some point, the velocity becomes zero, and therefore, momentum is also zero. Objects that are not in motion have zero momentum.

Collisions and Momentum Conservation

The example above explains how an object like a cue ball gains momentum by increasing its mass or moving faster.

• When this cue ball collides with an eight-ball, what happens to their individual momentum?
• Do they lose it during their collision?

The answer is no. The law of conservation states that nothing is created nor destroyed. When the cue ball collides with the eight-ball, momentum is conserved. We see this momentum conservation in the balls movement before, during, and after the collision, and it can be proven mathematically.

Before we dig deeper, watch this video created using the Collision Lab Flash interactive from Physics Education Technology (phET) Interactive Simulations:

• What did you notice about the momentum of each ball before and after collision?

Before the collision, the cue ball has a momentum of 0.17 kg m/s while the stationary eight-ball has 0 kg m/s. After the collision, the cue ball has 0 kg m/s while the eight-ball has 0.17 kg m/s. In this simulation, you have seen how the momentum of an object is transferred to another object in a seemingly perfect fashion.

• The total momentum of the two balls before collision is 0.17 kg m/s, and the total momentum after collision is also 0.17 kg m/s.

This is the principle of conservation of momentum. Within the collision system that you analyzed, the total momentum before collision is equal to the total momentum after the collision.

In expression:

• Before Collision = After Collision
• pbefore = pafter
• m1v1 + m2v2 = m1v1 + m2v2

Where:

• the total momentum before collision is pbefore
• the total momentum after collision is pafter
• the mass of the cue ball (ball 1) is m1
• the mass of the eight ball (ball 2) is m2
• the velocity of the cue ball (ball 1) is v1
• the velocity of the eight ball (ball 2) is v2

It should be pointed out that the momentum of an object could be a negative number.

• What does that mean?

In our momentum equation p = mv, the velocity (v) of the object in motion can be a negative number if it is moving in the opposite direction or if it is moving to the left. It is important to note that the negative sign does not mean a very small amount of momentum.

We must also understand that this mathematical expression for momentum does not consider other factors that may affect the balls' motion. You know that there is friction on the surfaces and air resistance as well. It would be very complicated to consider these in our calculations. So, we kept it simple by ignoring those forces. In physics terms, we say that our system is isolated.

Head over to the Got It? section, to demonstrate your understanding of the conservation of momentum!

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