I.  Momentum
    A. Definition of momentum
        1.  p = m v
        2. Vector quantity, direction of momentum (p) is the same as the direction of the velocity
    B. A force is required to change the momentum of an object
    C. From Newton's Second Law, Impulse can be defined as F Delta t
        1. Can be used as an alternative to Newton's Second Law in solving problems.
        2. Example

II.  Conservation of Momentum
    A. One of the fundamental Conservation Laws
    B. Statement: When no external forces act on a system, the total momentum of the system remains the same.
    C. Applied to collisions:  The total momentum of the system before the collision will equal the total momentum of the system after the collision.
        1. Remember, momentum is a vector quantity, directions are important!
    D. There are three types of collisions, defined by what happens to the kinetic energy during the collision
        1. Perfectly elastic collisions -- kinetic energy is conserved
        2. Partially inelastic collisions -- some kinetic energy is lost
        3. Perfectly inelastic collisions -- maximum loss of kinetic energy
            a. The objects will also stick together
    E. Restitution
        1. Types of collisions can also be defined by the coefficient of restitution
        2. See table for summary
    F. Solving collision problems
        1. Start with Conservation of Momentum
        2. If two unknowns, use Conservation of KE (only if perfectly elastic) or restitution equation
        3. Examples
            a. Perfectly Inelastic
            b. Partially Inelastic
            c. Perfectly Elastic
        4. You may also use kinetic energy or (more likely) e to determine the type of collision
            a. Example
 
 
 
 
 
 
 
 
 

1. Impulse - Momentum vs. Newton's Second Law

    A car accelerates from 0 to 5.20 m/s in 0.832 s.  What is the average force exerted on a 70.0 kg passenger?

        From Impulse-Momentum:  F DELTA t = m DELTA v so F = m DELTA v / DELTA t = [(70.0 kg)(5.20 m/s - 0)] / 0.832 s = 437.5 N ~ 438 N

        From Newton's Second Law:  F = m a, but a = ? = [v_f - v_o  ] / t = [5.20 m/s -0] / 0.832 s = 6.25 m/s²
                    Then F = m a = (70.0 kg)(6.25 m/s²) = 437.5 N ~ 438 N

2. Summary of collision types -- note, momentum is always conserved
 

Type of Collision	Kinetic Energy	Coefficient of Restitution
Perfectly elastic	conserved	1
Partially inelastic	some loss	0<e<1
Perfectly inelastic	maximum loss	0