Momentum (p) is the product of an object's mass and it's velocity, sometimes considered an object's tendency to stay in motion. To change an object's velocity, and therefore it's momentum, an an object must receive an impulse (J), which is a force over a period of time. This means that impulse can be represented by the area under a force time graph.
https://www.youtube.com/watch?v=9PA0MyxjsyQ
Because impulse is a change in momentum, the relationship between the two is J=∆p. This relationship comes from Newton's 2nd Law:
J=∆p
F•t=m•∆v
F=m• (∆v/t)
F=m•a
F•t=m•∆v
F=m• (∆v/t)
F=m•a
The concepts of momentum and impulse help explain the motion of objects in collisions. These collisions can be classified into four types:
- Completely elastic collisions have no loss in kinetic energy or momentum. Objects simply bounce off of each other. In this scenario, the kinetic energy of the system remains constant as well as its momentum.
- Completely inelastic collisions result in a loss in kinetic energy but the momentum of the system remains constant. In these collisions objects stick together.
- Inelastic collisions are those that fall between completely inelastic and elastic. Momentum as always conserved, but some kinetic energy is lost.
- Explosions are the opposite of inelastic collisions, as kinetic energy is gained by some force between two objects, making them move in opposite directions. While kinetic energy increases, the net momentum of the system remains constant.
https://www.youtube.com/watch?v=Y-QOfc2XqOk
In all of these collisions the total momentum of each object in the system is conserved. Because the only way to change the momentum is through an impulse, momentum will always be conserved in an isolated system.
https://www.youtube.com/watch?v=2E9fY8H6O1g
The momentum of a system can also be represented by bar charts which show the amount the momentum of each object in the system
Credit: Zach Pabis
For example, in the above chart, two carts roll into each other and bounce off. While the momentum of each cart changes, the total momentum of the system before and after the collision is zero. This is because there is no impulse (J) acting on the system.
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