1. PHYSICS 103: Lecture 13 Review of HW Momentum Agenda for Today:
Impulse
Conservation of Momentum
Collisions

2. Momentum
Momentum is the product of mass times velocity of an object P = m v
Momentum is a vector quantity (same direction as v)
Units = kg m/s

3. NEWTON’S LAWS OF MOTION
Second LAW:
The force on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force.
F = m . a
a = Dv/Dt
F = m . Dv/Dt
F . Dt = m . Dv
Impulse =F . Dt
Dp = m . Dv
Change in “momentum”

4. NEWTON’S LAWS OF MOTION
Third LAW:
For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object.
(For every action there is an equal but opposite reaction)
F . Dt = m . Dv
If the external force acting on a system of objects is zero, the total momentum is conserved.

5. CONSERVATION OF MOMENTUM
During a collision, there are no external forces, so momentum is conserved.
This means: total momentum before collision = total momentum after collision

6. Types of Collisions
- no kinetic energy is lost during collisions (things bounce off each other)
Elastic
Partially Inelastic
- some kinetic energy is lost during collisions
Perfectly Inelastic
- objects stick together

7. Example Collision: Before: After:
Total momentum before collison = Total momentum after collision
v = 10 m/s
v = 0 m/s
Before:
V’ = 5 m/s
After:
(m  10 m/s)before = (2m  V’)after
This is an example of an inelastic collision

8. Test your understanding:
A 1-kg cart and a 2-kg cart roll toward the center of a straight track from opposite ends of the track, each with a speed of 1 m/s. They collide and stick. The combined mass moves at a speed of
(A) 0 m/s.
(B) 1/2 m/s.
(C) 1/3 m/s.
(D) 1/6 m/s.
(E) 1.5 m/s.
1 m/s
1 m/s

9. Before: After: 1 m/s 1 m/s V=?
(2 kg  1 m/s - 1 kg  1 m/s)before = (3 kg  V)after
V = 1/3 m/s

10. Main Points from Today’s Lecture
Momentum
You should understand impulse, momentum, conservation of momentum in different kinds of collisions. You should review the example problems in this lecture.