Momentum, Impulse, Conservation, and Collisions

Syntax

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Overview

Perhaps you have seen two cars collide, each moving at a different speed and each having a different mass. Yet after the collision the cars are stuck together and move in one direction. How does one describe the situation since the mass and velocity is changing? How does one determine the final velocity?

Equations

Momentum (p) is equivalent to mass multiplied by velocity, p=mv.

++If we remember Newton's Second Law Force = mass multiplied by acceleration, and if we remember that acceleration is defined as the change in velocity divided by the change in time. Then we derive the equation Force = The change in momentum divided by the change in time. F = (Pfinal - Pinital)/(Tfinal - Tinital)
++Say an object is traveling at a certain velocity with a particular mass. The object is then slowed down by a force. So the velocity is lower. So momentum has changed. In fact it has decreased. A change in momentum is defined as impulse. So the object had a negative impulse.
++Law of Conservation of Linear Momentum is defined as the total linear momentum will remain constant in a system. This law gives a method for solving collisions. If there is change in the momentum of the system then Pfinal = Pinital. So in the overview question, the momentum of the first car (with mass M1 and velocity V1) can be added to the momentum of the second car (with mass M2 and velocity V2) and is equal to the momentum of the final wreck (mass M1+M2 and velocity V3).
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An asteroid of mass 15 kg going at 5 m/s collides with an astronaut, mass 75 kg and velocity 0 m/s. If the astronaut holds onto the asteroid, what is his final velocity?

If an object, of constant mass 10 kg, changes velocity from 0 m/s to 20 m/s in 10 seconds. What is the impulse and Force needed to cause this change?

Special Cases

Joke - You enter the laboratory and see an experiment.

How will you know which class is it?
If it's green and wiggles, it's biology.
If it stinks, it's chemistry.
If it doesn't work, it's physics.

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