2. Momentum
Chapter 8

3. Objectives Define momentum.
Define impulse and describe how it affects changes in momentum.
Explain why an impulse is greater when an object bounces than when the same object comes to a sudden stop.
State the law of conservation of momentum.
Describe how conservation of momentum applies to collisions.
Describe how the vector nature of momentum affects the law of conservation of momentum.

4. 8.1 Momentum Momentum is a commonly used term in sports.
A team that has “the momentum" or has “a lot of momentum” is on the move and is going to take some effort to stop.
In Physics, momentum means “inertia in motion” or “mass in motion”. 4

5. p = mv Momentum (p) = mass (m) x velocity (v)
Momentum is a vector quantity with it’s direction matching that of the velocity.
When direction is not important:
Momentum = mass x speed
The units for momentum would be mass units times velocity units.
The standard metric unit of momentum is the kg*m/s.

6. p = mv
The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.
A moving object can have a large momentum if
it has a large mass.
it has a high speed.
it has a large mass and a high speed.

7. Practice What is the momentum of a 1500 kg car traveling at 20 m/s?
What is the momentum of the car if the speed is reduced by ½?
What is the momentum of a 3000 kg truck traveling at 20 m/s?
What is the truck’s momentum if its speed doubles?
Can the car ever have the same or more momentum than the truck? Explain.

8. 8.2 Impulse Changes Momentum
If the momentum of an object changes, either the mass or the velocity, or both, has to change.
The mass usually does not change; therefore, the velocity must change.
What do we call a change in velocity?
An acceleration is a change in velocity.
What produces an acceleration?
A FORCE produces acceleration!

9. 8.2 Impulse Changes Momentum
Since a = F/m, the greater the force, the greater the acceleration.
But recall that a = Δv/t ; so, a greater acceleration means a greater change in velocity.
If p = mv, a greater change in velocity will mean a greater change in momentum!
The greater the force, the greater the change in momentum.

10. 8.2 Impulse Changes Momentum
A change in momentum depends on a force that acts and also the length of time that it acts!
A brief contact by a defensive football player will change the momentum of the offensive player.
However, if the same force is applied over a longer time period, a greater change in momentum will occur.

11. 8.2 Impulse Changes Momentum
The quantity of “force x time interval” is called impulse.
The greater the impulse exerted on something, the greater will be the change in momentum.
Impulse = change in momentum.

12. Increasing Momentum
In order to increase the momentum of the ball, the player needs to apply the greatest force possible for as long as possible – it is necessary to swing hard and follow through.
Since the force applied here (and in situations like this) changes throughout the swing, we really mean the average force.

13. Decreasing
Momentum
In each situation above, the truck experiences a change in momentum to 0. The impulse for each is the same.
In situation 1, by traveling through the haystack, the truck increases the time interval for the change. The force the truck experiences, therefore, is relatively small.
On the other hand, in situation 2, the time interval is very short, so the force the truck experiences is very large.

15. More Examples
If a boxer moves away from a punch, the contact time of the punch is increased and the force is decreased. If he moves towards the punch, the time of contact is reduced and force is increased.
Crumple zones are sections in cars which are designed to crumple up when the car encounters a collision. Crumpling of the car lengthens the time over which the car's momentum is changed; by increasing the time of the collision, the force of the collision is greatly reduced.

16. Practice
When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard floor?
Explain why
a padded dashboard is safer than a rigid one.
airbags save lives.
you should bend your knees when jumping from a height.
bungee cords must be elastic.
If a bungee cord increases contact time by 10 times over a non elastic cord, how much is the force that acts on the jumper reduced?

17. 8.3 Bouncing Bouncing is also known as rebounding.
What affect does bouncing or rebounding have on a change in momentum?
Occasionally when objects collide, they bounce off each other (as opposed to sticking to each other and traveling with the same speed after the collision).
Bouncing off each other is known as rebounding.
Rebounding involves a change in direction of an object; the before- and after-collision direction is different. 17

18. 8.3 Bouncing
Impulses (or changes in momentum) are greater when an object bounces.
An impulse is needed to bring a moving object to a stop.
Another impulse is needed to then “throw” the object back into motion.
For example, your head could provide an impulse to a falling object, reducing its momentum to 0. To then throw the object back up into the air, your head would need to provide another impulse. It takes a greater impulse to catch and throw back an object than to just catch it.

19. 8.3 Bouncing
An object that bounces can yield as much as 2x the impulse to the object it bounces off.
Karate experts strike bricks, for example, in such a way that their hand bounces back. The impulse to the bricks can be up to 2x as much.
See Figures 8.8 & 8.9 in your text, p. 130.

20. 8.4 Conservation of Momentum
According to Newton’s 2nd Law, you accelerate an object by applying a net force to it.
In momentum, to change the momentum of an object, you exert an impulse on it.
In either case, internal forces won’t work.
If you sit in a car and push on the dashboard, the car will not move. The momentum of the car does not change.
Pushing on the outside of the car, though, may cause the car to move. An external force does change momentum.

21. 8.4 Conservation of Momentum
The momentum before firing is 0.
After firing, the force on the cannonball is equal and opposite to the force on the cannon, so the momentum of the cannon-cannonball system does not change. The net momentum is still 0.
Net momentum is neither gained nor lost.

22. 8.4 Conservation of Momentum
In every case, momentum of a system does not change unless the system is acted on by an outside force.
Momentum, therefore, is conserved.
The law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged.
If a system undergoes an internal change, the net momentum of the system before and after the event is the same.
In a collision, for example, the net momentum of the cars before the collision must equal their net momentum after the collision.

23. 8.5 Collisions
A collision is elastic when objects collide without being permanently deformed and without generating heat.
Some heat is generated in most collisions. For our purposes, we will consider it negligible.
At the atomic level, collisions are generally perfectly elastic.
Colliding objects bounce perfectly in elastic collisions.
The sum of the momentum of the objects that collide is the same before and after the collision.
net momentumbefore collsion = net momentumafter collision

24. Elastic Collisions: Sample Problem
A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?
First, determine the momentum before the collision.
net momentumbefore collsion = car mom.before + truck mom.before = mcar beforevcar before + mtruck beforevtruck before
SET UP A MOMENTUM TABLE.

25. Elastic Collisions: Sample Problem
A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?
CAR
TRUCK
TOTAL
Momentum BEFORE
Momentum
AFTER
(1000)(20) =
20000 kg-m/s
(3000)(0) =
0 kg-m/s

26. FILL IN THE TOTAL IN THE AFTER COLUMN
Problem Continued
Next, determine the momentum after the collision.
momentum before = momentum after = kg m/s
FILL IN THE TOTAL IN THE AFTER COLUMN
Then, fill in the information you have about “after”. Use a variable to represent what you don’t know.
momentumafter collision = car mom.after + truck mom.after
= mcar aftervcar after + mtruck aftervtruck after

27. A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest
A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?
CAR
TRUCK
TOTAL
Momentum BEFORE
Momentum
AFTER
(1000)(20) =
20000 kg-m/s
(1000)v
(3000)(0) =
0 kg-m/s
(3000)(10) =
30,000 kg-m/s

28. The car bounced back off the truck in the opposite direction!!
A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?
Finally, solve the algebraic expression that was created in the after column.
1000v = 20000
v = -10 m/s
The car bounced back off the truck in the opposite direction!!

29. Practice
A 3000 kg truck traveling at 20 m/s collides with a 1000 kg car at rest.? If the velocity of the truck after the collision is 10 m/s, what is the velocity of the car?
60000 kg m/s
30 m/s

30. Practice
A 1000 kg car collides head on with a 3000 kg truck. Both vehicles are traveling at 20 m/s. If the truck stops completely upon collision, what is the resulting velocity of the car?
kg m/s
-40 m/s

31. Inelastic Collisions
In an inelastic collision, the colliding objects become distorted and generate heat during the collision.
A totally inelastic collision occurs when the colliding objects become tangled or “stick” together.
Here, as well, the net momentum before is equal to the net momentum after the collision.
net momentumbefore collsion = net momentumafter collision

32. Inelastic Collisions: Sample Problem
A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, what is the velocity of the car and truck after the collision?
Use a momentum table (as before). The only difference is that the velocity of the car AND truck after collision is not known. HOWEVER, you do know it is THE SAME!

33. A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck
A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, what is the velocity of the car and truck after the collision?
CAR
TRUCK
TOTAL
Momentum BEFORE
Momentum
AFTER
(1000)(20) =
20000 kg-m/s
(1000)v
(3000)(0) =
0 kg-m/s
(3000)(v)

34. A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck
A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, what is the velocity of the car and truck after the collision?
As before, use the table to set up an algebraic equation. Then solve it! 1000v v = v = v = 5 m/s

35. Practice
A 3000 kg truck traveling at 20 m/s collides with a 1000 kg car at rest. After collision, the vehicles stick and move off together. At what velocity do the vehicles travel after the collision?

36. Practice
A 1000 kg car traveling at 20 m/s collides head on with a 3000 kg truck, traveling at 20 m/s as well. The collision is not elastic. What is the velocity of the car and truck after collision?

37. 8.5 Collisions
Most collisions usually do involve some external force: friction.
Moving objects will encounter friction with a surface and the air.
Friction provides an impulse to decrease the momentum of moving objects.
External forces, however, are negligible during a collision. Net momentum, therefore, is unaffected.

38. 8.6 Momentum Vectors
Momentum is conserved even when interacting objects don’t move along the same straight line.

39. 8.6 Momentum Vectors
The vector sum of the momenta is the same before and after a collision.
This means we must use vector addition to determine the sum of the momenta of the 2 cars (previous slide) before they collide.
This “net momentum” is the same as the net momentum after the collision.

40. 8.6 Momentum Vectors
Recall that we can use the Pythagorean theorem to find the value of the resultant vector.
(20000)2 + (10000)2 = R2
R = 22,361 kg m/s
NORTHEAST
20000 kg m/s EAST
RESULTANT
10000 kg m/s NORTH

41. Practice
A 1000 kg car traveling east at 15 m/s is struck by a 1000 kg car traveling north at 15 m/s. What is the net momentum after the collision?