1. Momentum
Dr. Walker

2. Momentum
Momentum is the reaction of an object to a force exerted upon it
Refers to inertia in motion
Inertia is the tendency of an Object to Resist a Change in Movement
Mass is a Measurement of Inertia
It is harder to stop a large truck than a smaller vehicle
In football, a 220 lb running back that is moving forward can run through a stationary (or moving) 190 lb defensive back

3. Momentum Momentum = mass x velocity
Momentum is a vector quantity similar to force

4. Momentum Different objects can have the same momentum
The 220 lb (100 kg) running back with a velocity of 8.5 m/s has the same momentum as a 198 lb (90 kg) defensive back with a velocity of 9.44m/s.
Running back momentum = 100 kg x 8.5 m/s = 850 kg.m/s
Defensive back momentum = 90 kg x 9.4 4m/s = 850 kg.m/s

5. Changes In Momentum
If the mass (unlikely) or velocity (more likely) of an object changes, the momentum (p) changes
If a force acts on a moving object
The object will accelerate (F = ma)
The velocity changes (v = at)
The momentum will change (p = mv)
p is the symbol for momentum

6. Changing Momentum
If the change in momentum occurs over a long time, the force of impact is small.

7. Changing Momentum
If the change in momentum occurs over a short time, the force of impact is large.

8. Impulse Impulse is a change in momentum Impulse = FDt
When you work out the units for impulse, you have kg.m/s2 x s, which equals kg.m/s
This is the same unit as momentum, which is mass x velocity
The relationship between force, acceleration, velocity, and time can be rearranged in a number of different ways

9. Changes In Momentum a. The boxer moves away from the punch.
The impulse provided by a boxer’s jaw counteracts the momentum of the punch.
a. The boxer moves away from the punch.
b. The boxer moves toward the punch. Ouch!

10. Impulse and Momentum Impulse – Momentum Theorem
The Impulse Produced by a Net Force is Equal to the Change in the Object’s Momentum

11. Example 1
Give the momentum of a 1000 kg truck driving at a velocity of 30 m/s.
p = mv
p = (1000 kg)(30 m/s) = kg m/s

12. Example 1
Give the momentum of a 1000 kg truck driving at a velocity of 30 m/s.

13. Example 2
Hilary strikes a 0.058kg golf ball with a force of 272N and gives it a velocity of 62.0m/s. How long was Hilary’s club in contact with the ball?

14. Example 2
Hilary strikes a 0.058kg golf ball with a force of 272N and gives it a velocity of 62.0m/s. How long was Hilary’s club in contact with the ball?
(272 N)(Dt) = (0.058 kg)(62.0 m/s) – (0.058 kg)(0 m/s)
Dt = s

15. Example 3
A 6.0g bullet is fired at a velocity of 350 m/s into a container of ballistic gelatin that stops the bullet in 1.8ms. What is the average force that stops the bullet?

16. Example 3
A 6.0g bullet is fired at a velocity of 350 m/s into a container of ballistic gelatin that stops the bullet in 1.8ms. What is the average force that stops the bullet?
F ( s) = (0.006 kg)(0 m/s m/s)
F = -1.2 x 103 N
Notice the force is negative because it is acting in the opposite direction that the bullet was initially moving
Vector quantities!!

17. Example 4
A hockey puck has a mass of 0.115kg and is at rest. A hockey player makes a shot, exerting a constant force of 30.0N on the puck for 0.16s. With what speed does it head toward the goal?

18. Example 4
A hockey puck has a mass of 0.115kg and is at rest. A hockey player makes a shot, exerting a constant force of 30.0N on the puck for 0.16s. With what speed does it head toward the goal?
(30.0 N)(0.16s) = (0.115 kg)(vf) – (0.115 kg)(0 m/s)
v = 42 m/s

19. Conservation of Momentum
In a given system, the momentum can not change unless it is acted on by an external force
We talked about this previously
In science, when a quantity doesn’t change, it is conserved
In chemistry, we talked about the Law of Conservation of Mass

20. Conservation of Momentum
The momentum before firing is zero. After firing, the net momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.
Cannon has no momentum
Before firing
Cannonball has forward
Momentum. The cannon
Has rearward momentum
Net momentum = 0

21. Conservation of Momentum
Note that no outside force acted on the system. The ignition of the gunpowder provided energy to send the cannonball forward. To conserve momentum, the cannon reacted in the opposite direction.
Cannon has no momentum
Before firing
Cannonball has forward
Momentum. The cannon
Has rearward momentum
Net momentum = 0

22. Collisions An example of a collision with conserved momentum

23. Collision Examples

24. Conservation Of Momentum
If a system undergoes changes wherein all forces are internal, the net momentum of the system before and after the event is the same. Examples are:
Atomic nuclei undergoing radioactive decay
Cars colliding
Stars exploding

25. Conservation of Momentum
In mathematics terms…
pa = - pb
mava = - mbvb

26. Example
Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?

27. Example
Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?
pbefore lunch = pafter lunch
pbig fish + plittle fish = pbig fish (after)

28. Example
Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?
pbefore lunch = pafter lunch
pbig fish + plittle fish = pbig fish (after)
(6 kg)(1m/s) + (2 kg)(0 m/s) = (8 kg)(vafter)
Vafter = 0.75 m/s

29. Example 2
Consider a 6-kg fish that swims at 1.0 m/s toward and swallows a 2-kg fish that is swimming 2.0 m/s in the opposite direction. What is the velocity of the larger fish after his meal?

30. Example 2
Consider a 6-kg fish that swims at 1.0 m/s toward and swallows a 2-kg fish that is swimming 2.0 m/s in the opposite direction. What is the velocity of the larger fish after his meal?
pbefore lunch = pafter lunch
pbig fish + plittle fish = pbig fish (after)
(6 kg)(1.0 m/s) + (2 kg)(- 2.0 m/s) = (8 kg)(vafter)
Vafter = 0.25 m/s
Notice the velocity is
negative because the little
fish is swimming in the
opposite direction!!

31. Example 3
Ben and Erika are at an ice skating rink they stand at rest and Ben pushes Erika. Ben is sent in one direction at a velocity of 0.90m/s while Erika is sent the other direction at 1.2m/s. If Ben’s mass is 96 kg, what is Erika’s mass?

32. Example 3
Ben and Erika are at an ice skating rink they stand at rest and Ben pushes Erika. Ben is sent in one direction at a velocity of 0.90m/s while Erika is sent the other direction at 1.2m/s. If Ben’s mass is 96 kg, what is Erika’s mass?
pBen = pErika
(96 kg)(0.90 m/s) = mErika(1.2 m/s)
mErika = 72 kg

33. Example 4
Erika (72 kg) is standing still on ice skates, when Ben (96 kg) is skating at 1.5 m/s and grabs Erika. After grabbing Erika, what is the new velocity of the pair assuming momentum is conserved?

34. Example 4
Erika (72 kg) is standing still on ice skates, when Ben (96 kg) is skating at 1.5 m/s and grabs Erika. After grabbing Erika, what is the new velocity of the pair assuming momentum is conserved?
pBen + pErika = pboth
(96 kg)(1.5 m/s) + (72 kg)(0 m/s) = (168 kg)(vboth)
vboth = 0.86 m/s

35. Example 5
A 2575kg van runs into the back of an 825kg compact car at rest. They move off together at 8.5m/s. Assuming that the friction with the road is negligible, calculate the initial speed of the van.

36. Example 5
A 2575kg van runs into the back of an 825kg compact car at rest. They move off together at 8.5m/s. Assuming that the friction with the road is negligible, calculate the initial speed of the van.
Pvan + pcar = pcombined
(2575 kg)vvan + (825 kg)(0 m/s)= (2575 kg kg)(8.5 m/s)
(2575 kg)vvan = kgm/s
Vvan = 11.2 m/s

37. Momentum Vectors Since momentum is a vector, is has a direction
Not all collisions are head on
If collisions occur at an angle, the combined momentum will have a resultant, just like any other 2-dimensional process

38. Momentum Vectors
If an object breaks apart, the pieces will have the same total momentum as the original
This is observed when firecrackers explode