Conservation of Momentum/Energy…is hypnotizing

1. Conservation of Momentum/Energy…is hypnotizing Linear Momentum is conserved in the collisions between the balls. The collisions are elastic in that the balls compress like springs then push on their neighbor in the direction of the momentum. Mechanical energy is conserved in the balls that swing upward in the gravitation field of the earth…Their direction however is reversed when they swing back down… "Newtons cradle animation book 2" by DemonDeLuxe (Dominique Toussaint) - Image:Newtons cradle animation book.gif. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Newtons_cradle_animation_book_2.gif#/media/File:Newtons_cradle_animation_book_2.gif http://science.howstuffworks.com/newtons-cradle.htmhttp://demonstrations.wolfram.com/PhenomenologicalApproximationToNewtonsCradle/

2. Homework Unit 10 Average 81.5% See me if you need help…

3. Classical MechanicsUnit 11 examples Unit 11 Examples: Conservation of Momentum Inelastic Collisions Center of mass frame

4. Bullet Galaxy Cluster-Evidence for Dark Matter Astronomy Picture of the Day 2006 August 24 X-rayHot Gas OpticalGalaxies Gravitational lensingDark Matter http://apod.nasa.gov/apod/ap060824.html http://arxiv.org/pdf/astro-ph/0608407v1.pdf

5. Conservation of Momentum matters….. Modified Newtonian Dynamics http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Galaxy Rotation Curves – unexplained by Newton alone Momentum is not Conserved …or Dark matter Physicists prefer momentum conservation and Dark matter conservation of momentum matters…. To physicists at least

6. Conservation laws/Symmetry/Invariance Emmy Noether “If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time” http://en.wikipedia.org/wiki/Symmetry_%28physics%29 http://en.wikipedia.org/wiki/Noether%27s_theorem

7. Main Points http://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle

8. Main Points

9. Momentum (Prelecture 11) Energy (Prelecture 8) What is the different between conservation of Momentum and conservation of energy? How do I know if the Momentum is conserved or energy is conserve?

10. Clicker Question A wood block rests at rest on a table. A bullet shot into the block stops inside, and the bullet plus block start sliding on the frictionless surface. The momentum of the bullet plus block remains constant Before After A) Before the collision. B) During the collision C) After the collision D) All of the above E) Only A and C above As long as there are no external forces acting on the system

11. Recap

12. CheckPoint A) Yes, and it moves to the right. B) Yes, and it moves to the left. C) No, it remains in place. Suppose you are on a cart initially at rest that rides on a frictionless track. If you throw a ball off the cart towards the left, will the cart be put into motion? Left Right Conservation of momentum means the cart must move to the right since the ball moves to the left.

13. CheckPoint Suppose you are on a cart which is initially at rest that rides on a frictionless track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball bounces straight back as shown in the picture, will the cart be put into motion after the ball bounces back from the surface? Left Right A) Yes, and it moves to the right. B) Yes, and it moves to the left. C) No, it remains in place.

14. Clicker Question Suppose you are on a cart that is moving at a constant speed v toward the left on a frictionless track. If you throw a massive ball straight up (relative to the cart), how will the speed of the cart change? Left Right v A) Increase B) Decrease C) Will not change As long as there are no external forces acting on the system,Ptotalis conserved Mechanics Lecture 11, Slide 14

15. Checkpoint Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck. Which box ends up moving faster? A) Box 1 B) Box 2 C) same 1 2

16. CheckPoint Which box ends up moving faster? A) Box 1 B) Box 2 C) same 1 2 A) As the ball bounces to the left, cart 1 moves faster to the right to conserve momentum. Think of a 2-step “bounce”

17. Clicker Question Two equal-mass balls swing down and hit identical bricks while traveling at identical speeds. Ball A bounces back, but ball B just stops when it hits the brick. Which ball is more likely to knock the brick over? B A A) A B) B C) They both have the same chance.

18. B A DPB DPA > DPB DPA The change in the momentum of the ball is bigger in A

19. Ballistic Pendulum http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html

20. Ballistic Pendulum m v M H A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m+Mrise to a height of H. Given H, what is the initial speed v of the projectile?

21. Breaking it down into steps M before during after V m v H splat Which quantities are conserved before the collision? A) momentum B) mechanical energyC) both momentum and mechanical energy

22. Breaking it down into steps M before during after V m v H splat Which quantities are conserved during the collision? A) momentum B) mechanical energyC) both momentum and mechanical energy

23. Breaking it down into steps M before during after V m v H splat Which quantities are conserved after the collision A) momentum B) mechanical energyC) both momentum and mechanical energy

24. Ballistic Pendulum m v M H

25. Car-Truck Collision

26. Car-Truck Collision

27. Car-Truck Collision

28. Car-Truck Collision 2

29. Car-truck Collision 2

30. Car Truck Collision 2

31. What else can be learned from collisions?... The structure of matter. What does an atom look like? or Nuclear model: with positive charge concentrated in a nucleus of diameter about 7 x10-15m across with a swarm of electrons out to about about 10-10 m . “plum-pudding” model: Uniform positive charged sphere about 10-10 m in diameter with embedded electrons…. http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html http://socratic.org/questions/how-did-rutherford-s-gold-foil-experiment-disprove-the-plum-pudding-model

32. What can be learned from collisions?... How do we find out? Let’s collide some atoms! He nuclei (a-particles) vs Au From head-on collision (180 degree scatter) Rutherford saw b ~ 2.7x10-14m ~ 7 x 10-15m not enough energy to reach to center.. http://chemistry.tutorvista.com/nuclear-chemistry/rutherford-scattering.html http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html http://socratic.org/questions/how-did-rutherford-s-gold-foil-experiment-disprove-the-plum-pudding-model http://en.wikipedia.org/wiki/Rutherford_scattering

33. SLAC Fixed target collisions https://www6.slac.stanford.edu/ http://en.wikipedia.org/wiki/SLAC_National_Accelerator_Laboratory http://fermi.gsfc.nasa.gov/

34. LHC Proton-Proton Collisions http://www.atlas.ch/multimedia/proton-event.html Collider detectors are in the center of mass frame… http://www.atlas.ch/multimedia/proton-event.html

35. Center of Mass Frame

36. Before LHC…LEP collider 10m tall – 10 m long cylinder packed with particle detectors…about 1 million channels 27 km (17 miles) circumference 50-150m underground

37. Standard Model of Particle Physics http://en.wikipedia.org/wiki/Standard_Model

38. Standard Model of Particle Physics Expressed Mathematically! http://www.math.fsu.edu/~marcolli/SMtalkVU.pdf

39. Two Train Cars

40. Two train cars

42. Two Train Cars 2

43. Two Train Cars 2