Momentum (p)
Equations
- Definition - Product of an object's mass and velocity.
- Momentum is conserved when no external forces act on a system
- Momentum is a vector
- SI units - kg*m/s
Equations
How momentum and net force are related?
A bigger net force over the same time period means a larger change in momentum. For example, a heavy truck coming to a stop will have a much larger change in momentum than a light car in the same amount of time. A larger change in momentum means a larger external force is needed to slow it down, so the truck brakes have to work much harder.
Is net force the same as the average force?
For a constant force over time, the net external force is the same as the average external force over the time period.
Helpful Video:
A bigger net force over the same time period means a larger change in momentum. For example, a heavy truck coming to a stop will have a much larger change in momentum than a light car in the same amount of time. A larger change in momentum means a larger external force is needed to slow it down, so the truck brakes have to work much harder.
Is net force the same as the average force?
For a constant force over time, the net external force is the same as the average external force over the time period.
Helpful Video:
Impulse (J)
Equations
- Definition - product of the average force exerted on an object and the time interval during which the force is exerted
- Impulse is equal to the change in momentum (∆p) and it sometimes represented with the symbol J
- Impulse is a vector
- SI units - N*s or kg*m/s
Equations
How force changes momentum?
If we take impulse equation and solve for force, another relationship of the equation presents itself:
F∆t = ∆p --> F = ∆p/∆t
When a net force is exerted on an object, it changes that object's momentum over the time f the force exertion. Force is the rate at which momentum changes. If an object experiences a large momentum change over a short time duration, the there must have been a large net force applied to it. On the contrary, if an object experiences a small momentum change over a long time duration, then there must have been a small net force applied to it.
If we take impulse equation and solve for force, another relationship of the equation presents itself:
F∆t = ∆p --> F = ∆p/∆t
When a net force is exerted on an object, it changes that object's momentum over the time f the force exertion. Force is the rate at which momentum changes. If an object experiences a large momentum change over a short time duration, the there must have been a large net force applied to it. On the contrary, if an object experiences a small momentum change over a long time duration, then there must have been a small net force applied to it.
Force V.S. Time Graph Impulse is the area under the curve of the Force V.S. Time graph. Areas above the time axis are positive ∆p and areas below the axis are negative ∆p. If the force is not constant, we can divide the graphs into sections and add up the impulse in each section. |
Conservation of Momentum
Key Term: Center of Mass
- Definition - average position of all parts of the system, weighted by mass. The velocity of a system's center of mass does not change if the system is closed (meaning not external force)
Types of Collisions
Elastic Collisions
Inelastic Collisions
If objects stick together, then a collision is a completely inelastic. When objects don't stick together, we can figure out the type of collision by finding the initial kinetic energy and comparing it with the final kinetic energy. If the kinetic energy is the same, then the collision is elastic. If the kinetic energy changes, then the collision is inelastic regardless of whether the objects stick together or not. In either case, collisions with no external forces, momentum is conserved.
(*Don't believe it? Check out the Momentum Lab that proves the conservation of momentum in all situations.
Helpful Video:
Elastic Collisions
- Collisions where both momentum and kinetic energy are conserved. There is no change in kinetic energy in the system as a result of the collision.
- p initial = p final
Inelastic Collisions
- Collisions which conserves momentum but not kinetic energy.
- Completely inelastic collision
- Collisions where the objects stick together and have the same final velocity
- Explosion
- Reverse inelastic collision where momentum is conserved and kinetic energy increases
If objects stick together, then a collision is a completely inelastic. When objects don't stick together, we can figure out the type of collision by finding the initial kinetic energy and comparing it with the final kinetic energy. If the kinetic energy is the same, then the collision is elastic. If the kinetic energy changes, then the collision is inelastic regardless of whether the objects stick together or not. In either case, collisions with no external forces, momentum is conserved.
(*Don't believe it? Check out the Momentum Lab that proves the conservation of momentum in all situations.
Helpful Video:
Momentum Bar Charts (LIL Charts)
One tool which can be utilized to express an understanding of the momentum-impulse model is to draw a bar chart.
Example Problem:
One tool which can be utilized to express an understanding of the momentum-impulse model is to draw a bar chart.
Example Problem:
A person moving on Rollerblades throws a medicine ball in the direction opposite to her motion. Choose the correct impulse-momentum bar chart for this process. The person is the system. Choices on the left.
The correct answer is A, because the person's initial momentum is positive, the medicine ball gives a positive impulse to the person, so there's about one bar of impulse added to the system. Thus, at the end, there are 3 bars of momentum in total for the person (system). Other Examples: |
Connect Them All!!!
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