Lesson 1: Momentum
Objectives: |
When you have completed this lesson and the homework, you will be able to:
- define the term momentum
- understand that momentum is a vector quantity
- be able to calculate the momentum for an object.
In this lesson we will address the following standard from the Indiana Academic Standards for Physics I:
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P.1.15 |
Distinguish between the concepts of momentum (using the formula p = mv) and energy. |
The Lesson |
Introduction
The word momentum is a common part of our speech. We use it often, especially in the context of sports. Here are a few examples:
- Current debates include such statements as "the Patriots will win the superbowl: they have all the momentum on their side".
- a fullback in college football is hard to stop because he weights 280 lbs and once he gets going he has a lot of momentum
What exactly is this idea of momentum, and why is it important? That's the question for this lesson.
Defining momentum
As is usually the case, the common usage of a scientific work helps us understand its meaning, but we have to be much more precise in our definition. In physics, momentum is a very specific quantity:
momentum is defined as the product of an objects mass and velocity.
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where
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Conceptually, it might be helpful to think of momentum as "inertia in motion". Because both the mass and the velocity are involved in momentum, both are important when determining the momentum of an object. Consider the following three football players.
| Player | Mass | Velocity | Momentum |
| James | 200 kg | 2 m/s | 400 kg m/s |
| Thomas | 160 kg. | 2.5 m/s | 400 kg m/s |
| LaMarcus | 100 kg | 4 m/s | 400 kg m/s |
In all three cases, they have the same momentum. But it is easy to see that James does not have to move as fast as LaMarcus in order to have the same momentum.
Units for momentum
Since momentum is the product of mass and velocity, it will have units that are a product of the units of mass and the units of velocity. In the metric system, our standard units are kilograms for mass and m/s for velocity.
The metric unit for momentum is the kg m/s.
Momentum is a vector
From earlier in the course, we learned that vectors are quantities that have both magnitude (size) and direction. Since velocity is a vector, then any quantity that is multiplied by the velocity will also be a vector. From this, we must conclude that
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momentum is a vector quantity. |
It's direction will always be the direction of the velocity. If the velocity is southwest, then the momentum will be southwest also.
To keep things simple, in this chapter we will only study systems that are moving in one dimension. (Remember Harry the incarcerated ant?). In this case, direction can always be defined with a sign: + means one direction (usually to the right or upwards) and - means the opposite direction (usually to the left or downwards). So in this unit we can always state the direction of our momentum with a sign in front of our number:
Example Problem:
| Problem: | What is the momentum of a car that has a mass of 1200 kg and is speeding to the left at 30 m/s? |
| Solution: | To find the momentum, we will use our equation
but we must know what the mass and the velocity are. The problem states the mass to be 1200 kg, but the velocity is the speed and the direction. Since the car is moving to the left, we use the normal sign convention from cartesian coordinate systems and make that the negative direction. So we must use -30 m/s as the velocity.
So the car has -36,000 kg m/s of momentum. |
| Try this: What is the momentum of a 7 kg. bowling ball that is rolling
to the right at 3 m/s? Express your answer in kg m/s |
Changes in momentum.
We will later (lesson 2) be very interested in any changes in the momentum of an object, like when a ball is hit by a bat. So we will quickly review how to calculate the change in momentum.
Remember that the symbol D (pronounced "delta") means "the change of". You might also remember that to find the change, we always take the final quantity and subtract from it the initial quantity. Example: If I have $15 in my pocket now, and an hour later I have $5, then the change in my net worth would be expressed as $5 - $15 = -$10. The negative is important: it means that my net worth has decreased.
For momentum, we can express this as a relationship:
If the change in momentum ( Dp ) is negative, then the object must have lost some momentum. If it is positive, then it must have gained some momentum.
Example Problem
| Problem: | A 0.25 kg. tennis ball is moving to the right at 10 m/s when it is hit by a tennis raquet. After the collision with the raquet, it is moving to the left at 20 m/s. What is the change in the momentum for this ball? |
| Solution: |
First, we make a list of our variables:
Notice that the velocities have been given a sign. Since they are vectors, then need a direction. We will use the relationship
to solve this problem. But in order to use this relationship, we must first find the initial and final momentum. We will use the subscripts f for final and i for initial. We can then use our definition for momentum to write
From this we can see that the momentum of the ball underwent a change of -7.5 units of momentum. Another way to think of it is that the momentum when from +2.5 to -5, so it decreased 7.5 units. It is very important to worry about the signs of the velocity when doing momentum calculations. |
Summary
Momentum is the product of the mass and the velocity. It is represented by the variable p, and can be expressed as
The change in the momentum tells us how much the momentum of an object increased or decreased. It can be expressed as
Links for further study
Need an alternate explanation? Try this site:http://www.physicsclassroom.com/Class/momentum/U4L1a.html
This is the end of the lesson. You can return to the unit main page or start the homework assignment