Momentum and Impulse
Momentum (p) is defined as the quantity of motion that an object has. It can sometimes be considered an object's tendency to stay in motion (how hard it is to stop an object). Momentum is a product of mass and velocity, so to find momentum you multiply an object's mass by its momentum. Any changes in mass or velocity therefore change an object's momentum. A change in momentum is called impulse (J). Impulse is a force over a period of time, and can be measured with the area under a force vs. time graph.
Units are N * s or kg * m/s
Units are N * s or kg * m/s
https://www.youtube.com/watch?v=qMc6KOkmjTU&frags=pl%2Cwn
Because impulse is a change in momentum, the relationship between the impulse and momentum 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
Collisions
Momentum is conserved in all collisions.
Elastic Collisions
Inelastic Collisions
Perfectly inelastic (stick together)
Explosions
Elastic Collisions
- Hard collisions = no deformation occurs
- Conservations of momentum and conservation of energy
- Example: Billiards (pool balls)
Inelastic Collisions
- Deformation occurs
- Momentum is conserved but kinetic energy is lost
- Most collisions are inelastic (bounce off and energy is lost)
- Objects move with different final velocities (don't stick together)
- Example: Car crash
Perfectly inelastic (stick together)
- Objects stick together and travel as one object and deformation occurs
- Momentum is conserved but kinetic energy is lost
- After the collision there is one velocity
- Example: Bullet and wood block
Explosions
- Reverse of perfectly inelastic collisions (kinetic energy is gained)
- Momentum of the center of mass remains unchanged
https://www.youtube.com/watch?v=8ko3qy9vgLQ
The only way to change the momentum is through an impulse, so momentum will always be conserved in an isolated system. pi = pf. This is the conservation of momentum. For non-isolated systems, pi + J = pf. It is important to remember that the center of mass of the system will always maintain the same momentum.
https://www.youtube.com/watch?v=2E9fY8H6O1g
LIL Charts
Similar to LOL Charts for energy, LIL Charts are qualitative drawings to show momentum and impulse. This bar chart shows the amount of each object in the system, initial and final.
An example is below. In this situation, 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, as shown by the empty center column.
An example is below. In this situation, 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, as shown by the empty center column.
Credit: Dylan Torrey - From Momentum Lab
Relating Momentum Energy, Forces, and Kinematics
This is the end of my Unit 5 - Momentum & Impulse Content Page. Thanks for reading.
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