Chapter 6: Momentum and Collisions!

1. Chapter 6: Momentum and Collisions!

2. The Solar System(not to scale!) A Question for you to ponder… Why do the Sun and all of the planets (except Venus) rotate In the same direction?

3. The Answer lies in the Formation of the Solar System

4. That’s us  4 billion miles away…do you see what I see?

5. So What? • What does this have to do with Chapter 6? • Planet formation is directly tied to the law of conservation of momentum! • Yay for more laws 

6. Linear Momentum • Momentum describes how the motions of objects are changed • Newton’s Laws explain why • The Linear Momentum equation • p=mv • Momentum = mass x velocity MOMENTUM IS A VECTOR!!

7. Sample Problem • A 3000kg elephant is chasing a 1 kg squirrel across the road at a velocity of 5 m/s to the west. What is the momentum of the elephant? If the squirrel is running at 7 m/s west what is its momentum?

8. Solve the Problem • Momentum of the elephant • p = mv = (3000 kg)(5m/s)= 15000 kgm/s West • Momentum of the squirrel • p=mv= (1kg)(7m/s)= 7 kgm/s West

9. Change in Momentum • A change in momentum takes force and time • It takes a lot of force to stop an object that has a lot of momentum

10. Impulse Momentum Theorem • A net external force, F, applied to an object for a time interval, Δt, will cause a change in the object’s momentum equal to the product of the Force and the time interval. • In other words…

11. What does that mean? • A small force acting for a long time can produce the same change in momentum as a large force acting for a short time. • In sports like baseball, this is why follow through is important. The longer the bat is in contact with the ball, the greater the change in momentum will be.

12. Sample Problem p. 211 #3 • A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?

13. What do we know? • M = 0.40 kg • Vi= +18 m/s • Vf= -22 m/s • What does impulse mean? • Impulse is equal to FΔt • Impulse is also equal to the object’s change in momentum

14. Solve the problem

15. Stopping Distance • The stopping distance is the distance it requires an object to come to rest • The greater the momentum, the more distance it takes to stop

16. Sample Problem p.213 #2 • A 2500 kg car traveling to the north is slowed down uniformly from an initial velocity of 20.0 m/s by a 6250 N braking force acting opposite the car’s motion. Use the impulse momentum theorem to answer the following questions: • A. What is the car’s velocity after 2.50 s? • B. How far does the car move during 2.50 s? • C. How long does it take the car to come to a complete stop.

17. Answer part a. Why is F negative? Because it is acting opposite the car’s motion! • m= 2500 kg • Vi= 20 m/s North • F= -6250 N • t= 2.50 s • Vf= ?

18. Use the impulse-momentum theorem!!

19. Solve Part B • How far does the car move in 2.5 s? • Which kinematic equation should we use?

20. Solve Part c • How long does it take for the car to come to a complete stop? • Use impulse momentum theorem!

21. Summary of 6.1 • Momentum is a vector quantity that is equal to the product of an object’s mass and its velocity (p=mv) • Impulse = FΔt= Δp • A small force applied over a long period of time produces the same change in momentum as a large force applied over a short period of time

22. Section 6.2: Conservation of Momentum • Remember...we talked about the formation of the solar system and conservation of momentum.

23. Let’s Talk about the Moon

24. We are the only inner planet with a large moon…why? • Our moon didn’t form with us in the nebula • We acquired it later through a collision with another planetoid • http://vimeo.com/2015273

25. The Moon is trying to leave us • Every year, the moon moves about 4 cm away from the Earth and thus it’s velocity increases • Conservation of Momentum says that velocity has to come from somewhere. So…the moon steals it from us • So every year, our rotation slows down… adding about 0.0002 seconds to our day.

26. Momentum is Conserved • The Law of Conservation of Momentum says: • The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

27. In mathematical form Be very careful with your signs when using this equation!!

28. Collisions • There are many different ways to describe collisions between objects • In any collision, the total amount of momentum is conserved but generally the total kinetic energy is not conserved

29. Perfectly Inelastic Collisions • When two objects collide and move together as one mass, the collision is perfectly inelastic • Since the two objects stick together and move as one, they have the same final velocity. • Kinetic Energy IS NOT CONSERVED in PERFECTLY INELASTIC COLLISIONS

30. Sample Problem p. 219 #2 • An 85.0 kg fisherman jumps from a dock into a 135 kg rowboat at rest on the west side of the dock. If the velocity of the fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity of the fisherman and the boat?

31. What do we know • M1= 85 kg • M2= 135 kg • V2,i=0 • V1,i= -4.30 m/s • What type of collision is this? • PERFECTLY INELASTIC because they stick together and move as one mass

32. Rearrange the equation and solve for Vf • Vf= 1.66 m/s West

33. What is the change in Kinetic Energy for this problem? • Initial Kinetic Energy of the boat= 0 J • Initial Kinetic Energy of the fisherman • KE= 0.5mv^2= 0.5(85kg)(4.3m/s)^2=785.3 J • Total Initial KE= 0+ 785.3 J= 785.3 J Final KE= 0.5(85+135)(-1.66)^2=303.1 J ΔKE=KEf – Kei = 482.2 J

34. Elastic Collisions • In an elastic collision, two objects collide and return to their original shapes with no change in total energy. • After the collision, the two objects move separately. • Momentum is conserved • Kinetic Energy is Conserved

35. Sample Problem p.229 #2 • A 16.0 kg canoe moving to the left at 12 m/s makes an elastic head-on collision with a 4.0 kg raft moving to the right at 6.0 m/s. After the collision, the raft moves to the left at 22.7 m/s. Disregard any effects of the water. • a. Find the velocity of the canoe after the collision.

36. What do we know? • V1,i= -12 m/s • V2,i = 6 m/s • V1,f = ? • V 2,f = -22.7 m/s • M1= 16 kg • M2= 4 kg

37. Conservation of Momentum says… • This is an elastic collision, so we should use the following equation:

38. Rearrange and solve • We need to solve for V1,f so we should rearrange the conservation of momentum equation So The final velocity of the canoe is 4.8 m/s Left.

39. Impulse In Collisions Think about Newton’s 3rd Law: Every action force has an equal and opposite reaction force Since Impulse = FΔt then in a collision between objects, the impulse imparted to each mass is the same!!!!

40. Comparison of Collisions

41. Summary of Section 6.2 and 6.3 • In all interactions between isolated objects, momentum is conserved • Few collisions are elastic or perfectly inelastic • Impulse imparted is the same for all objects in a collision