Module 5: Impulse and Momentum
You’ve seen how concepts of impulse and momentum, tied together with Newton’s Third Law, are powerful tools for analyzing interactions.
Momentum is the product of an object’s mass and its velocity. Any object in motion has momentum. With either more mass or more velocity, an object will have a greater magnitude of momentum. Momentum is also a vector quantity, so the direction matters. Momentum vectors can be added and may add to zero.
In order to change the momentum of an object, you apply an impulse. Impulse is the product of force and the amount of time that the force is applied. The units for impulse and momentum are equivalent, with impulse being in Newtons seconds, while momentum is kilograms times meters per second. The amount of the impulse will precisely equal the change in momentum.
When two objects interact, according to Newton’s Third Law, the forces between them are identical in magnitude, type and duration, but act in opposite directions. Forces come in pairs that act on different objects. Therefore, when two objects interact, they will always receive the same impulse, but in opposite direction. This means that when two objects interact, they will experience equal and opposite changes in momentum.
There are several different ways in which objects interact. Explosions occur when objects begin at rest with one another and a pair of forces between them sends them apart from one another. Collisions involve two objects that are initially not touching. Collisions may be elastic when objects bounce off of one another. If no energy is converted to other forms, such as heat, sound or light, or is used to deform an object, kinetic energy is conserved. Most collisions are inelastic because energy is not conserved. When the two objects stick together after a collision, the collision is considered perfectly inelastic.
In all interactions, momentum is conserved, so we can always write that the sum of the momentum of the two objects before the collision equals the sum of the momentum of the two objects after the collision, or m1 v1 plus m2 v2 before equals m1 v1 plus m2 v2 after.
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