Set - 4

1. Set - 4 Explaining Motion

2. What is the difference between speed and velocity? • The two are the same. • Velocity relates to instantaneous speed, but not to average speed. • Velocity is the speed and the direction the object is traveling. • Velocity relates to invisible objects like atoms, while speed relates to visible objects like cars.

3. What is the difference between average speed and instantaneous speed? • Average speed is the speed of an average runner and instantaneous speed is the speed of a very fast runner. • Instantaneous speed is the average speed of a very small portion of the trip. • Average speed is calculated over many trips, but instantaneous speed is calculated during one trip. • They're the same thing.

4. Why do we care about motion? • Because we all move in various ways. Our cars move and they move us. Our friends move. • Music is sound and sound moves through the air. We need these concepts to really understand what music is and how it works.

5. The next slide gives an example of why we need this stuff to understand music.

6. The Ear • Responds to Pressure • A force on the membrane • A movement inside the ear • Translation into the brain • Music !

7. If you drop a piano out of a 20 story building • How long will it take to hit the ground? • How fast will it be moving? • After it hits the ground .. how difficult will it be to play it?

8. This chapter • Mostly physics • Needed for understanding of many concepts in music.

9. Introduction—“Explaining Motion” • In physics, to explain something means to create a model that can predict the outcome of experiments. • Motions appear to be reproducible; that is, if we start out with the same conditions and do the same thing to an object, we get the same resulting motion. The same motion occurs regardless of: • when the experiment is done, and • where the experiment is done. • This reproducibility is a necessary condition for attempting to search for a set of rules that nature obeys. Rules of nature might be difficult to find, but they do not change.

10. Translation • Under identical and repetitive conditions, the same outcome will always occur. • Physical motion is PREDICTABLE based upon certain laws of motion. • There are three of them that are referred to as NEWTON’S LAWS.

11. Do Objects Tend to Rest? • Give your book a brief push across a table. • Although the book starts in a straight line at some particular speed, it quickly slows and stops. • If you epeat this book-pushing experiment on a surface covered with ice. • The book would travel a much greater distance before coming to rest. • The ice is slicker than the desktop. Different surfaces interact with the book with different strengths. • What would happen to the book if the surface were perfectly slick? • The book would not slow down at all; it would continue in a straight line at a constant speed forever.

12. Galileo

13. The man … Galileo of Pisa • Born in Pisa (1564) • Thought the Church had become “sterile” and began to “translate” it nto “modern” music. • His work began the development that culminated in ITALIAN OPERA! • Smart Dude!

14. Galileo • Enrolled in medicine but switched to Mathematics. • At the age of 25, he was appointed Chair of Mathematics at Padula. • In 1610 Developed the telescope • Observed • Mountains on the moon • Moons of Jupiter • Phases of Venus

15. Galileo • From his OBSERVATIONS, he favored the Copernican world view that the Earth orbited around the sun rather than the other way around. • This created big conflicts with the church. Eventually, he was confined to his home where he died in 1642.

16. Galileo’s Thought Experiment • Galileo noted that a ball rolling down a slope speeds up. Conversely, if the ball rolls up the slope, it naturally slows down. • The ball experiences an interaction on the falling slope that speeds it up and an interaction on the rising slope that slows it down. • Now, Galileo asked himself, what would happen to the ball if it were placed on a level surface? Nothing. Because the surface does not slope, the ball would neither speed up nor slow down; the ball would continue its motion forever. FOREVER ???

17. The importance of TIME in Galileo’s Experiments The red dots represent the positions after equal time intervals. What can we say about this motion? Pendulum Acceleration …. WHY??

18. The Tower?? • Aristotle claimed that a heavier object will hit the ground sooner than a light object dropped at the same time. • Galileo did the experiment and proved Aristotle wrong. • There is no evidence to prove that Galileo actually did this experiment. • But he may have!

19. What he would have found had he done the experiment: • The longer the object fell, the faster it went. • The weight (to be more carefully defined shortly) of the object didn’t matter. • The size of the object MAY have mattered.

20. Timing…

21. More importantly • For every second a falling object falls (vertically), its speed increases by about 10 meters per second (or 32 ft/sec). • This only works if air resistance can be neglected. • The object is said to be UNIFORMLY ACCELERATING.

22. The “acceleration” of gravity:g

23. g is a VECTOR!!

24. Galileo’s BIG Contribution OBSERVE MODEL Change Something

25. Acceleration • If an object starts with a velocity v0 and ends with a velocity vf after a time t, then the average acceleration is said to be • Units: velocity/time = (m/sec)sec or m/s2

26. Some algebra …

27. An object is thrown into the air with a velocity of 20 m/s. How long will it take to get to the top of the trajectory? How long back to the thrower?

28. No Surprise: Instantaneous Acceleration

29. AGAIN:Acceleration of gravity • ~10 m/s2 • Actually 9.8 m/sec2 • 32 ft/sec2

30. An object is THROWN vertically down from the top of a building with an initial speed of 20 meters per second. 2 seconds later it will have a speed of • 30 m/s • 40 m/s • 50 m/s • 60 m/s

31. A woman throws a ball straight up into the air at a speed of 30 m/s. After how many seconds will the ball return to her hands? • 3 • 4 • 5 • 6 • None of these

32. Look at the graph: Vf v Area = v x Dt = distance traveled V0 Dt Time t Distance = v0t + (1/2) at2

33. Reaction Time Experiment • 2 People • One holds the meter stick • The second has hand at the bottom • When the first person releases the meter stick, the second catches it as fast as possible. • From the distance, we can calculate reaction time.

34. Reaction Time DROP THE RULER Distance = v0t + (1/2) at2 Start from rest so Distance = (1/2) at2 D = (1/2) gt2

35. Let’s do it again!

36. REACTION TIME Minus Signs Are Important

37. The Modern Explanation • Galileo was the first to suggest that constant-speed, straight-line motion was just as natural as at-rest motion. • Natural motion is one in which the speed and direction are constant. • An interaction with an external agent is required to cause an object to change its velocity. • Objects at rest tend to remain at rest. Objects in motion tend to remain in motion. • This property of remaining at rest or continuing to move in a straight line at a constant speed is known as inertia.

38. INERTIA Is Important!

39. Note- • This resistance to changes in motion was later quantified by Sir Isaac Newton • This is the next topic

40. The Modern Explanation • There is more to inertia than getting things moving. If something is already moving, it is difficult to slow it down or speed it up. • An example is drying your wet hands by shaking them. When you stop your hands abruptly, the water continues to move and leaves your hands. • In a similar way, seat belts counteract your body’s inertial tendency to continue forward at a constant speed when the car suddenly stops.

41. The Modern Explanation • All objects do not have the same inertia. • Imagine trying to stop a baseball and a cannonball, each of which is moving at 150 kilometers per hour (about the speed a major-league pitcher throws a baseball). • The cannonball has more inertia and, as you can guess, requires a much larger effort to stop it. • Conversely, if you were the pitcher trying to throw them, you would find it much harder to get the cannonball moving.

42. Fun Trick with Inertia

43. Newton and Galileo’s Legacy • Although Galileo did not fully explain motion, he did take the first important step and, by doing so, radically changed the way we view the motion of objects. • His work profoundly influenced Isaac Newton, the originator of our present-day rules of motion.

44. Sir Isaac Newton • Born in 1642 • One of the GREATS of physics (on a par with Einstein!) • Strange dude … rumor is that he died a virgin.

45. Newton • Born in England and he was supposed to return and look after the family farm. • At age 17 he returned from boarding school he proved to be a total failure at farming. • Went to Trinity College, paying his way by waiting on tables and cleaning rooms for faculty and wealthy students. • Many students do this today as well.

46. Newton • In1667 he published a treatise on infinite series. • Developed a reflecting telescope and was elected membership in the Royal Society. • Decided that Christianity had deviated from the original teachings of Christ and refused to take the college’s holy orders. • He was excused .. The only person ever to have received this allowance.

47. More Newton • In 1686 he published his Principia .. Which established the laws of motion in a mathematical way. • He developed the calculus while Leibnitz developed a different approach. For years they fought over who was the real inventor! • He showed that white light was a mixture of all of the colors of the rainbow. • He developed the math to show that the planets and comets rotated around the sun in elliptical orbits. • He died in 1727.

48. Newton’s First Law • Newton’s first law of motion. It is also referred to as the law of inertia: -The velocity of an object remains constant unless it is acted upon by an external force. • For the velocity of an object to remain constant, its speed and its direction must both remain constant.

49. Newton’s First Law • Remember: • Velocity can be ZERO • Therefore Newton’s first law also says that: an object at REST (not moving) will stay at rest.

50. Newton’s First Law: Force?? • The first law incorporates Galileo’s idea of inertia and introduces a new concept, force. • A book sliding across the table slows down and stops because there is a force (called friction) that opposes the motion. • Similarly, a falling rock speeds up because there is a force (called gravity) acting on it. .