1. Chapter 6 Preview Objectives Linear Momentum
Section 1 Momentum and Impulse
Chapter 6
Preview
Objectives
Linear Momentum

2. Chapter 6 Objectives Compare the momentum of different moving objects.
Section 1 Momentum and Impulse
Chapter 6
Objectives
Compare the momentum of different moving objects.
Compare the momentum of the same object moving with different velocities.
Identify examples of change in the momentum of an object.
Describe changes in momentum in terms of force and time.

3. momentum = mass  velocity
Section 1 Momentum and Impulse
Chapter 6
Linear Momentum
Momentum is defined as mass times velocity.
Momentum is represented by the symbol p, and is a vector quantity.
p = mv
momentum = mass  velocity

4. Chapter 6 Momentum Section 1 Momentum and Impulse
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Visual Concept

5. Sample Problem A P199
A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck?
Given:
Asked:
Formula: p = m v

6. Assignment
Page 199: 1,2a,3

7. Linear Momentum, continued
Section 1 Momentum and Impulse
Chapter 6
Linear Momentum, continued
Impulse
The product of the force and the time over which the force acts on an object is called impulse.
The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object’s momentum.
F∆t = ∆p = mvf – mvi
force  time interval = change in momentum

8. Chapter 6 Impulse Section 1 Momentum and Impulse
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Visual Concept

9. Sample Problem B P201
A 1400kg car moving westward with a velocity of 15m/s collides with a utility pole and is brought to rest in 0.30s. Find the force exerted on the car during the collision.
Given:
Asked:
Formula: FΔt = Δp = m vf - mvi

10. Assignment
Page 199: 1,2a,3
Page 201: 1,2,3

11. Linear Momentum, continued
Section 1 Momentum and Impulse
Chapter 6
Linear Momentum, continued
Stopping times and distances depend on the impulse-momentum theorem.
Force is reduced when the time interval of an impact is increased.

12. Impulse-Momentum Theorem
Section 1 Momentum and Impulse
Chapter 6
Impulse-Momentum Theorem

13. Impulse-Momentum Theorem
Section 1 Momentum and Impulse
Chapter 6
Impulse-Momentum Theorem
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Visual Concept

14. Practice Problem C P202
A 2240kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s/ How long does it take the car to decelerate if the force on the car is 8410N to the east? How far does the car travel during the deceleration?
Given:
Asked:
Formula: FΔt = Δp = m vf - mvi

15. Assignments Chapter 6
Page 199: 1,2a,3
Page 201: 1,2,3
Page 203: 1, 2a,b,c

16. Chapter 6 Preview Objectives Momentum is Conserved Sample Problem
Section 2 Conservation of Momentum
Chapter 6
Preview
Objectives
Momentum is Conserved
Sample Problem

17. Section 2 Conservation of Momentum
Chapter 6
Objectives
Describe the interaction between two objects in terms of the change in momentum of each object.
Compare the total momentum of two objects before and after they interact.
State the law of conservation of momentum.
Predict the final velocities of objects after collisions, given the initial velocities, force, and time.

18. total initial momentum = total final momentum
Section 2 Conservation of Momentum
Chapter 6
Momentum is Conserved
The Law of Conservation of Momentum:
The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.
m1v1,i + m2v2,i = m1v1,f + m2v2,f
total initial momentum = total final momentum

19. Conservation of Momentum
Section 2 Conservation of Momentum
Chapter 6
Conservation of Momentum
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Visual Concept

20. Chapter 6 Sample Problem D P208 Conservation of Momentum
Section 2 Conservation of Momentum
Chapter 6
Sample Problem D P208
Conservation of Momentum
A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right,what is the final velocity of the boat?

21. Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6
Sample Problem, continued
Conservation of Momentum
1. Define
Given:
m1 = 76 kg m2 = 45 kg
v1,i = 0 v2,i = 0
v1,f = 2.5 m/s to the right
Unknown:
v2,f = ?

22. Assignmments Page 199: 1,2a,3 Page 201: 1,2,3 Page 203: 1, 2a,b,c

23. Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6
Sample Problem, continued
Conservation of Momentum
2. Plan
Choose an equation or situation: Because the total momentum of an isolated system remains constant, the total initial momentum of the boater and the boat will be equal to the total final momentum of the boater and the boat.
m1v1,i + m2v2,i = m1v1,f + m2v2,f

24. Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6
Sample Problem, continued
Conservation of Momentum
2. Plan, continued
Because the boater and the boat are initially at rest, the total initial momentum of the system is equal to zero. Therefore, the final momentum of the system must also be equal to zero.
m1v1,f + m2v2,f = 0
Rearrange the equation to solve for the final velocity of the boat.

25. Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6
Sample Problem, continued
Conservation of Momentum
3. Calculate
Substitute the values into the equation and solve:

26. Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6
Sample Problem, continued
Conservation of Momentum
4. Evaluate
The negative sign for v2,f indicates that the boat is moving to the left, in the direction opposite the motion of the boater. Therefore,
v2,f = 4.2 m/s to the left

27. Assignments Chapter 6 Page 199: 1,2a,3 Page 201: 1,2,3
Page 203: 1, 2a,b,c
Page 209: 1,2,3a,b,4

28. Momentum is Conserved, continued
Section 2 Conservation of Momentum
Chapter 6
Momentum is Conserved, continued
Newton’s third law leads to conservation of momentum
During the collision, the force exerted on each bumper car causes a change in momentum for each car.
The total momentum is the same before and after the collision.

29. Newton’s 3rd Law and Conservation of Momentum
If two objects interact the force on one object by the other is equal and opposite to the force of the other on the first.
F1 = - F2
F1 Δt = m1 v1,f - m1 v1,i
F2 Δt = m2 v2,f – m2 v2,i
Δt = Δt
F1 Δt = - F2 Δt
m1 v1,f - m1 v1,i = -(m2 v2,f – m2 v2,i )
m1 v1,f + m2 v2,f = m1 v1,i + m2 v2,i

30. Assignments Page 199: 1,2a,3 Page 201: 1,2,3 Page 203: 1, 2a,b,c
P211 Section Review 1abcd. 2abc

31. Chapter 6 Preview Objectives Collisions Sample Problem
Section 3 Elastic and Inelastic Collisions
Chapter 6
Preview
Objectives
Collisions
Sample Problem

32. Chapter 6 Objectives Identify different types of collisions.
Section 3 Elastic and Inelastic Collisions
Chapter 6
Objectives
Identify different types of collisions.
Determine the changes in kinetic energy during perfectly inelastic collisions.
Compare conservation of momentum and conserva-tion of kinetic energy in perfectly inelastic and elastic collisions.
Find the final velocity of an object in perfectly inelastic and elastic collisions.

33. total initial momentum = total final momentum
Section 3 Elastic and Inelastic Collisions
Chapter 6
Collisions
Perfectly inelastic collision
A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision.
Conservation of momentum for a perfectly inelastic collision:
m1v1,i + m2v2,i = (m1 + m2)vf
total initial momentum = total final momentum

34. Perfectly Inelastic Collisions
Section 3 Elastic and Inelastic Collisions
Chapter 6
Perfectly Inelastic Collisions
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Visual Concept

35. Sample Problem E P213
A 1850kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?

36. Assignments Chapter 6 Page 199: 1,2a,3 Page 201: 1,2,3
Page 203: 1, 2a,b,c
Page 209: 1,2,3a,b,4
Page 214: 1,2,3

37. Schedule Monday 1/7 P214 Problems/KE in Perfectly Inelastic collisions
Tuesday 1/8 P216 Problems/ Elastic Collisions
Wednesday 1/9 P219 Problems
Thursday 1/10 Demonstration of Collisions
Friday 1/11 Chapter Review (11,13,22,28)
Monday 1/14 Chapter Review (30,31,33,39)
Tuesday 1/15 Chapter 6 Test

38. Elastic and Inelastic Collisions (Page 214)
Inelastic Collision – some of the work done to deform an inelastic material is converted to other forms of energy such as heat or sound.
Kinetic Energy is not conserved in an inelastic collision.
Elastic collision – the work done to deform the material during a collision is equal to the work the material does to return to its original shape.
Kinetic Energy is conserved in an Elastic Collision

39. Inelastic Collision (stick together)
Momentum is conserved:
m1v1,i + m2v2,i = (m1 + m2)vf
total initial momentum = total final momentum
Kinetic Energy is not conserved
∆KE = KEi – KEf

40. Chapter 6 Sample Problem
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem
Kinetic Energy in Perfectly Inelastic Collisions
Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of kg and an initial velocity of 3.00 m/s to the left.What is the decrease in kinetic energy during the collision?

41. Assignments Chapter 6 Page 199: 1,2a,3 Page 201: 1,2,3
Page 203: 1, 2a,b,c
Page 209: 1,2,3a,b,4
Page 214: 1,2,3
Page 216: 1,2,3

42. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
1. Define
Given: m1= kg m2 = kg
v1,i = 4.00 m/s to the right, v1,i = m/s
v2,i = 3.00 m/s to the left, v2,i = –3.00 m/s
Unknown: ∆KE = ?

43. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
2. Plan
Choose an equation or situation: The change in kinetic energy is simply the initial kinetic energy subtracted from the final kinetic energy.
∆KE = KEi – KEf
Determine both the initial and final kinetic energy.

44. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
2. Plan, continued
Use the equation for a perfectly inelastic collision to calculate the final velocity.

45. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
3. Calculate
Substitute the values into the equation and solve: First, calculate the final velocity, which will be used in the final kinetic energy equation.

46. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
3. Calculate, continued
Next calculate the initial and final kinetic energy.

47. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Kinetic Energy in Perfectly Inelastic Collisions
3. Calculate, continued
Finally, calculate the change in kinetic energy.
4. Evaluate The negative sign indicates that kinetic energy is lost.

48. Elastic and Inelastic Collisions (Page 214)
Inelastic Collision – some of the work done to deform an inelastic material is converted to other forms of energy such as heat or sound.
Kinetic Energy is not conserved in an inelastic collision.
Elastic collision – the work done to deform the material during a collision is equal to the work the material does to return to its original shape.
Kinetic Energy is conserved in an Elastic Collision

49. Chapter 6 Elastic Collisions Elastic Collision
Section 3 Elastic and Inelastic Collisions
Chapter 6
Elastic Collisions
Elastic Collision
A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision.
Momentum and Kinetic Energy Are Conserved in an Elastic Collision

50. Two Extremes- Reality is in Between P217
Elastic and perfectly inelastic collisions are limiting cases, most collisions actually fall into a category between these two extremes.
In this third category, called inelastic collisions, the colliding objects bounce and move separately after the collision, but the total kinetic energy decreases.
For problems in this book we consider all collisions in which the objects do not stick together to be elastic.
Therefore we will assume that the total momentum and the total KE will each stay the same before and after a collision that is not perfectly inelastic.

51. Chapter 6 Types of Collisions
Section 3 Elastic and Inelastic Collisions
Chapter 6
Types of Collisions
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Visual Concept

52. Sample Problem G P218, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem G P218, continued
Elastic Collisions
A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface.What is the velocity of the kg marble after the collision?

53. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Elastic Collisions
1. Define
Given: m1 = kg m2 = kg
v1,i = m/s to the right, v1,i = m/s
v2,i = m/s to the left, v2,i = –0.180 m/s
v1,f = m/s to the left, v1,i = –0.315 m/s
Unknown:
v2,f = ?

54. Assignments Chapter 6 Page 199: 1,2a,3 Page 201: 1,2,3
Page 203: 1, 2a,b,c
Page 209: 1,2,3a,b,4
Page 214: 1,2,3
Page 216: 1,2,3
Page 219: 1a,b,2a,b, 3a,b
Chapter Review Page
11a,b, 13, 22a,b, 28, 30a,b, 31a,b, 33, 39
5 Points Extra Credit Problem 43 Page 226

55. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Elastic Collisions
2. Plan
Choose an equation or situation: Use the equation for the conservation of momentum to find the final velocity of m2, the kg marble.
m1v1,i + m2v2,i = m1v1,f + m2v2,f
Rearrange the equation to isolate the final velocity of m2.

56. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Elastic Collisions
3. Calculate
Substitute the values into the equation and solve: The rearranged conservation-of-momentum equation will allow you to isolate and solve for the final velocity.

57. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, continued
Elastic Collisions
4. Evaluate Confirm your answer by making sure kinetic energy is also conserved using these values.