Journal #

1. Journal # • Think about your experience with the CM project so far. What advice would you give Ms. Doyle about making the project directions clearer for next year? • Are there any rules you think should be changed? Why?

2. Chapter 9 Terms Due Wed. 12/1 • Impulse (include formula and unit) • Momentum (include formula and unit) • Impulse-momentum theorem • Law of Conservation of Momentum • Closed System • Isolated System • Elastic Collision (P. 298) • Inelastic Collision (P. 298) • Center of Mass • Law of Universal Gravitation

3. Momentum & Impulse Excerpts from Chapters 9 and 11

4. Newton’s Law of Universal Gravitation • The gravitational force is equal to the universal gravitational constant, times the mass of object 1, times the mass of object 2, divided by the distance (between the centers of the objects) squared.

5. Newton’s Law of Universal Gravitation • Formula:

6. The Universal Gravitational Constant • How large is G? • We know from experience that the attractive force between two normal sized objects is not noticeable. • In 1798, Henry Cavendish created an experiment that finally allowed this number to be measured.

7. Cavendish’s Experiment

8. Cavendish’s Experiment • The main idea was that by using manageable but massive spheres of lead, the gravitational force between the large and small spheres would be enough to cause motion. The force was measured for multiple sets of spheres and the constant was found. • G = 6.67x10-11Nm2/kg2

9. Important!!! • Cavendish’s experiment paved the way for us to know the mass of the Earth, Sun, and other planetary objects. • Numbers for the force of gravity will be small (x10-? N) unless working with REALLY massive objects.

10. Example 1 • What is the gravitational force between two 15-kg packages that are 0.35m apart?

11. Example 1 Answer

12. Homework Problems • P. 191: #53, 55-57

15. Journal # 30 • What do we mean when we ask people to “conserve water”? • What do you think it will mean if we say that momentum is conserved? • Get HW and Vocab out when finished!

16. Answers to HW • 53: F=6.1x10-9 N • 55: F=5.84x10-10 N • 56: F=8.0x10-10 N • 57: F=6.5x10-8 N

17. Journal # 31 • Explain how an airbag protects you by making you come to a stop differently than hitting steering wheel. Try to use the words impulse, force, and time in your answer.

18. Journal # 31 • Impulse is a force applied over an interval of time. In this question, the impulse of hitting the steering wheel and hitting the airbag are the same amount because they both cause you to stop. However, the airbag applies a smaller force to your body over a larger time, therefore keeping you safer.

19. Journal # 32 • Order these objects from the most momentum to the least. • A bullet shot from a rifle • An elephant standing still • A bowling ball rolling • A fly buzzing by your ear

20. Impulse and Momentum • Newton’s 2nd Law of motion can be rewritten by using the definition of acceleration as the change in velocity over the change in time.

21. Impulse and Momentum • If the change in time is multiplied out of the denominator, we are left with the following:

22. The product of force and change in time is called the Impulse (symbol is J). • Impulse is a vector quantity and is measured in Newton-seconds (Ns)

23. Impulse • If a car hits a haystack or the same car hits a wall, momentum is decreased by same impulse – the same products of force and time. • However, impact force is greater into the wall than it is into the haystack as the haystack extends impact time, lessening the impact force. • Impact time is the time during which momentum is brought to zero.

24. Momentum • Can increase with increase in either mass or in velocity or both. • Ex: a rolling bowling ball has greater momentum than a tennis ball rolling at the same speed because its mass is greater • Ex: a racecar going forward at 120 mi/hr has greater momentum than the same size car going 90 mi/hr due to its velocity. • If an object is not moving (no matter how big it is), the momentum = zero

25. The product of the mass and the velocity is called the momentum (symbol  -“rho”) of an object. • Momentum is also a vector quantity and is measured in kg*m/s. • Note that the units for impulse and momentum appear different, but they are actually the same unit when simplified.

26. The impulse-momentum theorem states that the impulse on an object is equal to the object’s final momentum minus the object’s initial momentum. • Can also be written as:

27. Example 1 • Tiger Woods hits a 0.050kg golf ball, giving it a speed of 75m/s. What is the impulse given to the ball?

28. Example 1 Answer

29. Example 2 • Shane hits a stationary 0.12kg hockey puck with a force that lasts for 1.0x10-2s and makes the puck shoot across the ice with a speed of 20.0m/s, scoring a goal for the team. With what force did Shane hit the puck?

30. Example 2 Answer

31. Example 3 • Diana, whose mass is 50.0kg, leaves a ski jump with a velocity of 21.0m/s. What is her momentum as she leaves the ski jump?

32. Homework Attempt as many as you can and set ALL of them up in your notebook with a left-hand lineup! • P. 233 #1-4 Due Thursday • P. 251 #56-64 Even Due Friday • PAY CAREFUL ATTENTION TO THE UNITS GIVEN AND CONVERT THEM WHEN NECESSARY!!!!!!!!

33. Conservation of Momentum • A system is the environment and all of the objects examined in a problem. • A closed system is a system in which no mass is gained or lost. • An isolated system is a system in which the net external force is zero… no forces acting outside of the system have an effect inside of it.

34. Conservation of Momentum • The law of conservation of momentum states that the sum of momentum of any closed, isolated system does not change… or that the sum of the momentum of the objects in that system is constant.

35. Conservation of Momentum • Mathematically, we can view this as a BEFORE and AFTER situation. • For any two objects A and B:

36. Types of Collisions • If two objects bounce apart when they collide, it is called an elastic collision and can be written: • If two objects stick together when they collide, it is called an inelastic collision and can be written:

37. Example 1 • Tubby and his twin brother Chubby have a combined mass of 200.0kg and are zooming along in a 100.0kg amusement park bumper car at 10.0m/s. They bump Melinda’s car, which is sitting still. Melinda has a mass of 25.0kg. After the elastic collision, the twins continue ahead with a speed of 4.12m/s. How fast is Melinda’s car bumped across the floor?

38. Before Collision After Collision T&C Mel T&C Mel Example 1 Picture

39. Example 1 Answer

40. Example 1 Answer

41. Example 2 • If an 800.kg sports car slows to 13.0m/s to check out an accident scene and the 1200.kg pick-up truck behind him continues traveling at 25.0m/s, with what velocity will the two move if they lock bumpers after a rear-end collision?

42. Before Collision After Collision Example 2 Picture

43. Example 2 Answer

44. Example 2 Answer

45. Homework • P. 238 #13-18 • P. 252 #73-77 (All Due Monday)

46. Homework • P. 238 #13-18 13. 1.1 m/s 14. 0.034 m/s 15. 1.2 X m/s 16. 2.8 m/s 17. 6.7 m/s 18. 2.0 m/s • P. 252 #73-77 75. -0.30 m/s 76. -4.94 m/s or 4.94 backward 77.0.35 m/s

47. Homework • P. 251 #56-64 Even 56. 0.013 s 58. 74 kg* m/s; 10. m/s 60. 62. 4.8 N 64. 42 m/s