1. Momentum…. just another way to talk about motion and changes in motion
What Newton was really talking about in his famous paper…

2. Momentum
The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity
SI Units are kg m / s
Vector quantity, the direction of the momentum is the same as the velocity’s

3. Momentum…or not?
paper clip on desk? no Ant crawling on ground? yes

4. More…or…less? Godzilla on rampage or rolling tank?
Shuffling zombie or speeding bullet?
Moving defensive lineman or offensive guard?

5. How can we change the motion of these objects?
Yes…you remembered…APPLY A FORCE

6. Impulse causes change in momentum…
In order to change the momentum of an object, a force must be applied
The rate of change of momentum of an object is equal to the net force acting on it
Gives an alternative statement of Newton’s second law

7. Impulse cont.
When a single, constant force acts on the object, there is an impulse delivered to the object
is defined as the impulse
Vector quantity, the direction is the same as the direction of the force

8. Impulse-Momentum Theorem
The theorem states that the impulse acting on the object is equal to the change in momentum of the object
If the force is not constant, use the average force applied

9. Case 1: impulse causes a decrease in momentum
Car crash
Getting hit by a punch
Person doing parcour and landing on her feet

10. Impulse Applied to Auto Collisions
The most important factor is the collision time or the time it takes the person to come to a rest
This will reduce the chance of dying in a car crash
Ways to increase the time
Seat belts
Air bags

11. Air Bags The air bag increases the time of the collision
It will also absorb some of the energy from the body
It will spread out the area of contact
decreases the pressure
helps prevent penetration wounds

12. How long does an accident take?
At ~.080sec, F maximizes at 800,000 N
By sec, it’s all over!

13. Other situations in which longer Δ t results in less force on body
Tuck and roll
Bending knees when landing from a jump
Roll with the punches
MINIMIZE FORCE BY MAXIMIZING Δ t !!

14. Case 2: impulse causes an increase in momentum
Bat and ball
Foot and ball
Starting from rest on a rollercoaster

15. What about maximizing Δ p ?
When do you want to get something going ASAP?
Roller coaster, or catapult launch on aircraft carrier: max F in short time
Kicking, hitting a ball: max F but try to also maximize contact time!!
Follow through!!
Longer barrel on a gun maximizes time that expanding gas acts on potato, bullet, etc.

17. Case 3: impulse causes a change in direction…bouncing
Physics you can use to win valuable prizes…
Should I choose a bouncy ball or a non-bouncy ball to knock over the bottles at the Six Flags boardwalk game?

18. Let’s investigate change in momentum…
Calculate momentum at different points in time
Compare and calculate change in momentum
Which experienced bigger change in momentum?

19. So far discussions have been about one object at a time…
What if we consider all the objects that are interacting or are about to interact…
Through extensive observations and data collection we would conclude that
The total momentum of objects about to interact is the same as the total momentum of the objects right after they interact!!

20. CONSERVATION OF MOMENTUM!
One of the great principles of physics!
This explains the transfer of momentum in any collision, explosion, interaction of objects moving through space and time!

21. Σ p (before, initial) = Σ p (after, final)
Add up the momenta of all objects before the interaction
Add up the momenta of all objects after the interaction
Before = after

22. Examples?
Can you use the equipment available to design a demo of conservation of momentum?
AIR TRACK Demos

23. Examples of calculations

24. Conservation of Momentum, cont.
Mathematically:
Momentum is conserved for the system of objects
The system includes all the objects interacting with each other
Assumes only internal forces are acting during the collision
Can be generalized to any number of objects

25. Notes About A System
Remember conservation of momentum applies to the system
You must define the isolated system

26. Collisions! Momentum is conserved in any collision
Inelastic collisions
Kinetic energy is not conserved
Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object
Perfectly inelastic collisions occur when the objects stick together
Not all of the KE is necessarily lost

27. More Types of Collisions
Elastic collision
both momentum and kinetic energy are conserved
Actual collisions
Most collisions fall between elastic and perfectly inelastic collisions

28. More About Perfectly Inelastic Collisions
When two objects stick together after the collision, they have undergone a perfectly inelastic collision
Conservation of momentum becomes

29. Some General Notes About Collisions
Momentum is a vector quantity
Direction is important
Be sure to have the correct signs

30. Summary of Types of Collisions
In an elastic collision, both momentum and kinetic energy are conserved
In an inelastic collision, momentum is conserved but kinetic energy is not
In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

31. Problem Solving for One -Dimensional Collisions
Coordinates: Set up a coordinate axis and define the velocities with respect to this axis
It is convenient to make your axis coincide with one of the initial velocities
Diagram: In your sketch, draw all the velocity vectors and label the velocities and the masses

32. Problem Solving for One -Dimensional Collisions, 2
Conservation of Momentum: Write a general expression for the total momentum of the system before and after the collision
Equate the two total momentum expressions
Fill in the known values

33. Sketches for Collision Problems
Draw “before” and “after” sketches
Label each object
include the direction of velocity
keep track of subscripts

34. Sketches for Perfectly Inelastic Collisions
The objects stick together
Include all the velocity directions
The “after” collision combines the masses