- Introduction
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Momentum
Watch the video Momentum (3:32) for an introduction to momentum. Login information.
Momentum is the product of an object's mass multiplied by its velocity. We represent momentum by the following equation:
p = mv
The unit of measurement for momentum is kg•m/s. It is a vector, therefore, it must be written with:
- a magnitude,
- a unit, and
- a direction of motion.
The momentum of an object is always in the same direction as its velocity.
Example Calculation
Let's try using this equation to find momentum in the scenario below.
A runner with a mass of 77 kg has a velocity of 9 m/s east. What is the runner's momentum?
- First, let's identify the known and unknown values.
m = 77 kg
v = 9 m/s E
p = ?
- Next, enter the values into the problem and solve.
p = mv
p = (77 kg) (9 m/s)
p = 693 kg•m/s
- Answer: The momentum of a runner with a mass of 77 kg and a velocity of 9 m/s east is 693 kg•m/s.
More About Momentum
To learn more, read the following 3 pages from Physics Classroom and complete any interactive questions you find.
Collisions and Momentum
Since the mass and velocity are equally weighted in momentum, it is possible for a smaller object to have greater momentum than a larger object. From a scientific perspective, momentum takes into consideration the size and velocity of objects.
For instance, a massive football player running fast will have much more momentum than a smaller player running slowly. If the two players were to run into each other, the smaller player would not fare very well. Since the mass and speed are of equal proportions, a smaller yet faster player could knock down a larger slower player.
To learn more about collisions, watch the video Collisions (9:10). Login information.
Elastic Collisions
The hardest collision occurs when both players are the same mass and are running about the same speed and run head on into one another. Their combined motion will cause a great collision and both players could bounce off each other and end up on the ground. This is called an elastic collision that occurs in a closed system.
- An elastic collision is an encounter between two objects in which the total kinetic energy of the two objects after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms. You know an elastic collision has occurred when the objects “bounce apart.”
- A closed system means that the objects involved in the collision are the only objects that remain in the system. There are no objects lost or gained. In the case of the football players, there were two players running toward each other and there were two players after the collision. This system does not lose or gain mass.
Inelastic Collisions
In some collisions on the football field, players will collide but, instead of bouncing apart, they stick together and travel in the same direction. This is an inelastic collision.
- An inelastic collision is an encounter between two objects where some kinetic energy is lost in the encounter. The final kinetic energy is different than the initial kinetic energy. While the kinetic energy is not conserved in the collision, the momentum is conserved. In an inelastic collision, objects end up “sticking together” and they begin traveling in the same direction after the collision.
Conservation of Momentum
The Law of Conservation of Momentum states that if there is no external force acting on a system the total momentum does not change.
Watch the video Collisions and the Conservation of Momentum (12:05) to learn more. Login information.
- You'll notice the video references to inelastic collisions as “hit and stick collisions” and calls elastic collisions “hit and rebound collisions.”
- Those are easy ways to remember what occurs in each type of collision, but for this course you should refer to collisions using the terms “elastic collistions” and “inelastic.”
Compare and Contrast Collisions
Check out the interactive Collisions on an Air Track. Login information.
In the interactive, change the mass of the right-hand cart and the type of collision to compare and contrast the different scenarios.
Can you confirm conservation of momentum in this activity? What happens in the elastic collisions? What happens in the inelastic collisions?
