# Monday, October 3, 2011

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1 the shuttle blasts off Then comes the tremendous pressure of three G s and the sudden release into weightlessness as the ship leaves the gravitational field behind -from The Arizona Republic 1

2 Quiz #3: Wednesday Chp. 2-4 Next homework (due Wednesday) Chp. 5 Problems: 1, 2 Learning to look: 1, 2 2

3 Chapter 5 Newton, Einstein, and Gravity

4 Outline I. Galileo and Newton A. Galileo and Motion B. Newton and the Laws of Motion C. Mutual Gravitation II. Orbital Motion and Tides A. Orbits B. Orbital Velocity C. Calculating Escape Velocity D. Kepler's Laws Re-examined E. Newton's Version of Kepler's Third Law F. Tides and Tidal Forces G. Astronomy After Newton III. Einstein and Relativity A. Special Relativity B. The General Theory of Relativity C. Confirmation of the Curvature of Space-Time

5 A New Era of Science Mathematics as a tool for understanding physics

6 Isaac Newton ( ) Building on the results of Galileo and Kepler Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: 1. Invented Calculus as a necessary tool to solve mathematical problems related to motion 2. Discovered the three laws of motion 3. Discovered the universal law of mutual gravitation

7 Newton s 1st Law of Motion An object continues in a state of rest or in a state of uniform motion at a constant speed along a straight line unless compelled to change that state by a net force. Why? Because objects have inertia 7

8 Uniform Motion Uniform Motion: same speed, same direction 8

9 Inertia The tendency that Newton observed for objects at rest to stay at rest and objects in motion to stay in uniform motion in a straight line. How do we measure inertia? MASS 9

10 Force 10

11 Force Net force = sum of all forces: Here, we say that the NET force is zero! 10

12 Force Net force = sum of all forces: Here, we say that the NET force is zero! The box stays at rest. There is no change in its state of motion no net force is acting on it. 10

13 The ball moves over my head at a constant speed as shown. Is the ball changing its state of motion? Is there a net force acting on the ball? a. Yes. Yes. b. No. No. c. Yes. No. d. No. Yes e. Yes/Yes if I am moving my hand back and forth. 11

14 Force and Inertia Natural state of motion is at a constant speed, in a straight line. Ball wants to travel in a straight line, but the string continuously pulls it back toward the center of the circle. 12

15 Acceleration A change in velocity (state of motion) Refers to an increase in velocity OR a decrease in velocity OR a change in the direction of velocity. A net force acting on an object will cause that object to accelerate. 13

16 Acceleration Acceleration: can be a change in speed, either increasing or decreasing. 14

17 Acceleration Acceleration: can be a change in direction 15

18 Newton s 2nd Law of Motion The amount of acceleration (a) produced by a force(f) depends on the mass (m) of the object being accelerated. 16

19 Newton s 2nd Law of Motion The amount of acceleration (a) produced by a force(f) depends on the mass (m) of the object being accelerated. Mathematically: Alternatively: F = m a a = F/m 16

20 Newton s 2nd Law of Motion 17

21 Which of the objects are NOT accelerating? a) a car traveling at a constant speed around a bend. b) a ball that has been thrown up into the air just before it begins falling back down. c) a car traveling at 65 mph down a straight highway. d) a car getting off the freeway on a straight off-ramp. e) an electron circling around an atomic nucleus. 18

22 Law of Gravitation 19

23 Law of Gravitation G=

24 Question: A linebacker and a kitten are put into space far from any other object. How do the gravitational forces each feels compare? How do their accelerations compare? a. Linebacker feels larger force, but accelerates less. b. Kitten feels larger force and accelerates more. c. Both feel same force, but kitten accelerates more. 20

25 Example 21

26 Example The linebacker and the kitten on Earth: How do the forces that they feel (due to the Earth s gravity) compare? How do their accelerations compare if they both jump off a table? a. Forces equal, kitten accelerates more. b. Larger force on linebacker, accelerations equal. c. Forces equal, accelerations equal. 21

27 Acceleration of Gravity

28 Acceleration of Gravity Acceleration of gravity is independent of the mass (weight) of the falling object!

29 Acceleration of Gravity Acceleration of gravity is independent of the Iron ball mass (weight) of the falling object!

30 Acceleration of Gravity Acceleration of gravity is independent of the Iron ball Wood ball mass (weight) of the falling object!

31 Weight Weight: Weight is NOT the same as mass. Weight is equivalent to the gravitational force the Earth exerts on your body. 23

32 Are you weightless on the Moon? a) yes b) no c) depends 24

33 Are you weightless on the Moon? a) yes b) no c) depends Is there gravity on the Moon? 24

34 Weight on other planets Weight on Earth, Mars, and Saturn: M mars = 0.1 M earth R mars = 0.5 R earth 25

35 Weight on other planets Weight on Earth, Mars, and Saturn: M mars = 0.1 M earth R mars = 0.5 R earth M saturn = 95 M earth R saturn = 9.4 R earth 25

36 Are the astronauts orbiting the Earth weightless? a) yes b) no c) depends 26

37 Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons: Example: Earth and moon attract each other through gravitation. Since Earth is much more massive than the moon, the moon s effect on Earth is small. Earth s gravitational force constantly accelerates the moon towards Earth. This acceleration is constantly changing the moon s direction of motion, holding it on its almost circular orbit. v v Moon F Earth

38 Orbital Motion (2) In order to stay on a closed orbit, an object has to be within a certain range of velocities: Too slow => Object falls back down to Earth Too fast => Object escapes Earth s gravity

39 Geosynchronous Orbits

40 What s wrong with this. the shuttle blasts off Then comes the tremendous pressure of three G s and the sudden release into weightlessness as the ship leaves the gravitational field behind -from The Arizona Republic 30

41 Kepler s Third Law Explained by Newton

42 Kepler s Third Law Explained by Newton Balancing the force (called centripetal force ) necessary to keep an object in circular motion with the gravitational force expression equivalent to Kepler s third law

43 Kepler s Third Law Explained by Newton Balancing the force (called centripetal force ) necessary to keep an object in circular motion with the gravitational force expression equivalent to Kepler s third law P y 2 = a AU 3

44 The following questions are offered for additional practice. They are not meant to represent the exact content or type of questions that will be on the quiz. They are also not meant to represent the totality of the information that will be on the quiz. The lecture notes and their embedded class participation questions should give you a good idea of the content covered in class. 32

45 1. The period of Jupiter's orbit around the sun is approximately 12 years. What is the approximate distance from the sun to Jupiter? a. 144 AU b AU c. 42 AU d. 5.2 AU e

46 2. In pre-copernican astronomy, it was almost universally believed that a. the planets traveled in elliptical orbits about the Earth. b. the center of the universe was the Sun with the Milky Way representing other distant planets. c. the Sun was at the center of the universe. d. the Earth was at the center of the universe. e. None of the above was believed. 34

47 3. An apparent westward motion of a planet in the sky compared to the background stars (as viewed from the Earth) when observed on successive nights is referred to as a. epicycle b. retrograde motion c. prograde motion d. heliocentric motion e. deferent 35

48 4. The purpose of using epicycles and deferents to explain the motion of the planets in the night sky was to account for a. prograde motion. b. Mercury and Venus' limited angular distance from the Sun. c. retrograde motion. d. non-uniform speed of the planets in their orbits. e. precession of the equinoxes. 36

49 5. The greatest inaccuracy in Copernicus' model of the solar system was that the planets a. travel in circular orbits with uniform motion. b. traveled on epicycles whose centers followed orbits around the Sun. c. traveled in elliptical orbits. d. were allowed to travel backwards in their orbits. e. the planets orbited the Sun. 37

50 6. The orbit of the planet Jupiter is ellipse with the Sun at one focus. What is located at the other focus? a. The asteroid belt b. Earth c. Saturn d. Jupiter e. Nothing 38

51 7. Which of the following statements best describes Kelper's 3 rd law of planetary motion? a. The smaller the diameter of a planet, the faster its rotational period. b. The orbital period of a planet is directly proportional to the diameter of the planet. c. The smaller the orbit, the longer its orbital period. d. The larger the orbit, the longer its orbital period. 39

52 8. Why did Galileo's observations of moons orbiting Jupiter disagree with the geocentric model of the universe of his time? a. The moons moved in non-circular orbits about Jupiter. b. The moons did not appear to orbit the Sun. c. The moons did not appear to orbit the Earth. d. The moons appeared to be too small, and therefore too far away, to be considered part of the solar system. 40

53 1.d 2.d 3.b 4.c 5.a 6.e 7.d 8.c 41

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