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. Starter https://www.youtube.com/watch?v=KeTizNY0zDA A car crash
A truck crash

4. 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

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

6. What do you think?
Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 50 Km/h. Now imagine the same collision with a 2009 model car. In both cases, the car and passengers are stopped abruptly.
List the features in the newer car that are designed to protect the passenger and minimize damage to the car.
How are these features similar?

7. features in the newer car that are designed to protect the passenger
seat belts and air bags
collapsible steering columns
shock absorbing bumpers
car body parts that collapse easily
padded dashboards.
How are these features similar?
The ability to extend the amount of time required for the car and the passenger to stop.

8. 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

9. THINK……….Go wild!!!!
You are an engineer who is working for Chevrolet car company. Your project is to increase the safety of the cars produced by the company?
What might be your innovative ideas to help with the safety of your company cars?

10. Exit Slip
Group A:How can highway safety engineers use the impulse - momentum theorem to determine stopping distances for cars and trucks?
Group B: write the impulse - momentum theorem in your own words

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

12. Momentum and Newton’s 2nd Law
Prove that the two equations shown below are equivalent.
F = ma and F = p/t
Newton actually wrote his 2nd Law as F = p/t.
Force depends on how rapidly the momentum changes.

13. 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.

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

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

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

17. Standard:
HS-PS2-2 Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.

18. 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.

19. 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

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

21. Chapter 6 Sample Problem Conservation of Momentum
Section 2 Conservation of Momentum
Chapter 6
Sample Problem
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?

22. 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 = ?

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. 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.

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

29. Standard:
HS-PS2-2 Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.

30. 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.

31. Watch the videos, then answer the work sheet

32. 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

33. 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

34. What collision is there in the everyday world?
Most collisions are not perfectly inelastic.
Most collisions are not elastic, either.
Most collisions fall in a category between these two extremes
This third category is called inelastic collisions.

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

36. Cross curricular integration
The concept of collisions is very important in chemical reactions.

37. Real life applications
Sports engineering is becoming a popular specialty field of study. Some engineers dedicate their research to understanding collisions between balls and bats; others study the effects of a golf ball colliding with the head of a golf club. Learning how sports equipment interacts with the ball during impact helps engineers design better sports equipment.

38. Real life applications
Mechanical engineers consider momentum and collisions when designing vehicles. Learning how the human body interacts with the inside of a car during a crash, helps engineers design safer vehicles which will affect the whole world.

39. International mindedness

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. 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 = ?

42. 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.

43. 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.

44. 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.

45. 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.

46. 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.

47. Sample Problem, continued
Section 3 Elastic and Inelastic Collisions
Chapter 6
Sample Problem, 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?

48. 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 = ?

49. 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.

50. 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.

51. 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.

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