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Announcements Evening observing Tonight-Thursday. Bring your blue tickets to the roof (elevator to 5th floor, then stairs), wear a jacket, 9-10pm! HW #2 was due last night: if you forgot, finish soon for partial credit! Finish Chapter 4, read Chapter 5.1 for next time. Tuesday, September 21, 2010 Last Time Kepler’s Three laws explain the motion of the planets: Planets move in an ellipse with the sun at one focus Planet–Sun line sweeps out equal areas in equal time (moves faster when closer!) Period and distance (semi-major axis) are related: P2=A3 Tuesday, September 21, 2010 Last Time Speed: rate an object moves Velocity: Speed and direction acceleration: change in the speed and/or direction. Tuesday, September 21, 2010 Gravity, Energy, and Motion Tuesday, September 21, 2010 Momentum and Force momentum = mass x velocity Anything in motion (velocity≠0) has momentum associated with it A net force changes momentum, which means an acceleration (change in velocity) a change in momentum can result from a change in the direction of motion. Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) 1) 2) 3) 4) A car coming to a stop a bus speeding up An elevator moving at a constant speed A car rounding a corner at a constant speed 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) ✓ 1) 2) 3) 4) A car coming to a stop a bus speeding up An elevator moving at a constant speed A car rounding a corner at a constant speed 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) ✓ 1) A car coming to a stop ✓ 2) a bus speeding up 3) An elevator moving at a constant speed 4) A car rounding a corner at a constant speed 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) ✓ 1) A car coming to a stop ✓ 2) a bus speeding up ✕ 3) An elevator moving at a constant speed 4) A car rounding a corner at a constant speed 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) ✓ ✓ ✕ ✓ 1) 2) 3) 4) A car coming to a stop a bus speeding up An elevator moving at a constant speed A car rounding a corner at a constant speed 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Thought Question Is there a net force at work? (✓/✕) ✓ ✓ ✕ ✓ 1) 2) 3) 4) A car coming to a stop a bus speeding up An elevator moving at a constant speed A car rounding a corner at a constant speed ✓ 5) A planet orbiting the Sun at a constant speed Tuesday, September 21, 2010 Force and Momentum We say a force causes a transfer of momentum. Tuesday, September 21, 2010 Describing Motion speed = rate at which an object moves. Distance/Time example: 10 m/s velocity = speed + direction. example: 10 m/s due West Tuesday, September 21, 2010 The Acceleration Due to Gravity All falling objects accelerate at the same rate (not counting air resistance) independent of mass. On Earth, g ≈ 10 m/ s2: speed increases 10 m/s with each falling second 10 m/s per second or 10 m/s2 = 22 mph/s Tuesday, September 21, 2010 Gravity The acceleration due to gravity is the same for any object on the surface of the earth. Hammer and feather fall at the same rate (neglecting air resistance). Tuesday, September 21, 2010 Force and Momentum We say a force causes a transfer of momentum. Tuesday, September 21, 2010 the difference between mass and weight mass - The amount of matter in an object weight - The force that acts upon an object The amount of matter (number of atoms) in you never changes but your weight depends on how strong gravity is at your location. Tuesday, September 21, 2010 What is the difference between mass and weight? A B C D The moon has weaker gravity than the Earth. On the Moon: A) you weigh the same, but your mass is less B) you weigh less, but your mass is the same C) You weigh more, but your mass is the same D) you weigh more, and your mass is more Tuesday, September 21, 2010 What is the difference between mass and weight? A B C D The moon has weaker gravity than the Earth. On the Moon: A) you weigh the same, but your mass is less ✪ B) you weigh less, but your mass is the same C) You weigh more, but your mass is the same D) you weigh more, and your mass is more Tuesday, September 21, 2010 What is the difference between mass and weight? A B C D The moon has weaker gravity than the Earth. On the Moon: A) you weigh the same, but your mass is 29 lbs less ✪ B) you weigh less, but your mass is the same C) You weigh more, but your mass is the same D) you weigh more, and your mass is more Tuesday, September 21, 2010 What is the difference between mass and weight? A B C D The moon has weaker gravity than the Earth. On the Moon: A) you weigh the same, but your mass is less ✪ B) you weigh less, but your mass is the same C) You weigh more, but your mass is the same D) you weigh more, and your mass is more Tuesday, September 21, 2010 Units of Mass/Force Tuesday, September 21, 2010 English Metric Force Pounds Newtons Mass Slugs Kilogram back to... Sir Isaac Newton English scientist, 1642–1727 Greatest scientist ever? Light, motion, gravity Newtonian physics dominated until Einstein. Invented calculus to help solve a different problem. Tuesday, September 21, 2010 How did Newton change our view of the Universe? Realized that the same physical laws that operate on Earth also operate in the heavens. We can therefore use the laws of physics to understand the universe! Tuesday, September 21, 2010 Newton’s Three Laws of Motion I. An object remains at rest or moves at a constant velocity unless a net force acts to change its direction or speed. The Apollo command module keeps moving even without firing its engines Tuesday, September 21, 2010 Newton’s Three Laws of Motion II. If an object is acted on by a net force, then this force changes the momentum of the object, accelerating it in the direction of the force. Force = mass x acceleration F = ma Give me F, and I will tell you how an object moves (a). Tuesday, September 21, 2010 Newton’s Three Laws of Motion III. For every force, there is always and equal and opposite reaction force The Space Shuttle is propelled upward with a force equal and opposite to the force with which the gas is expelled out the rockets Tuesday, September 21, 2010 A B C D Why does a rocket accelerate? A) The exhaust pushes on the air, causing it to move forward. B) It is propelled forward as its exhaust is sent backwards. C) Force of will Tuesday, September 21, 2010 A B C D Why does a rocket accelerate? A) The exhaust pushes on the air, causing it to move forward. ✪ B) It is propelled forward as its exhaust is sent backwards. C) Force of will Tuesday, September 21, 2010 Weightlessness Sense of weight comes from Newton’s 3rd law. Earth’s gravity pulls you down, but the floor pushes back with the same force: we feel weight! You are “weightless” anytime you are freely falling. Tuesday, September 21, 2010 Weightless Astronauts A B C D An astronaut is weightless because: A) B) C) D) Tuesday, September 21, 2010 The ship’s rockets holds them up There is no gravity in space They are constantly in free fall They are not attracted to the Earth Weightless Astronauts A B C D An astronaut is weightless because: A) B) C) D) Tuesday, September 21, 2010 The ship’s rockets holds them up There is no gravity in space They are constantly in free fall They are not attracted to the Earth Weightless Astronauts A B C D An astronaut is weightless because: A) B) ✪ C) D) Tuesday, September 21, 2010 The ship’s rockets holds them up There is no gravity in space They are constantly in free fall They are not attracted to the Earth Weightless Astronauts A B C D An astronaut is weightless because: A) B) ✪ C) D) The ship’s rockets holds them up There is no gravity in space They are constantly in free fall They are not attracted to the Earth See Interactive Fig. 4.4 Tuesday, September 21, 2010 Aboard an Airforce Training Airplane Tuesday, September 21, 2010 Law’s of Conservation Newton’s laws are really deeper statement about nature: “conservation laws”. Conservation of Momentum. Conservation of Angular Momentum. Conservation of Energy. Tuesday, September 21, 2010 Conservation of Angular Momentum Angular momentum is a special kind of “circling or rotating momentum”. Law: The total angular momentum of a system cannot change unless it interacts with something (i.e., gives up or receives angular momentum) Tuesday, September 21, 2010 Tuesday, September 21, 2010 Angular Momentum Since angular momentum is conserved... Angular momentum in an orbiting planet does not change. Conservation of angular momentum Explains Kepler’s 2nd law!!! Tuesday, September 21, 2010 Angular Momentum Since angular momentum is conserved... Angular momentum in an orbiting planet does not change. Conservation of angular momentum Explains Kepler’s 2nd law!!! Tuesday, September 21, 2010 Angular Momentum Since angular momentum is conserved... Angular momentum in an orbiting planet does not change. Tuesday, September 21, 2010 Angular Momentum Since angular momentum is conserved... Angular momentum in an orbiting planet does not change. Conservation of angular momentum Explains Kepler’s 2nd law!!! Tuesday, September 21, 2010 Newton’s laws of Gravity Every mass attracts every other mass. Strength of attraction is directly proportional to the product of their masses The strength of that attraction is inversely proportional to the square of the distance between them. Tuesday, September 21, 2010 Examples M1 M2 FG = G d2 Double Mass #2: new FG M1 (2M2 ) =G = 2F G 2 d 2 Tuesday, September 21, 2010 Examples M1 M2 FG = G d2 Double the distance: Fnew G =G 2 Tuesday, September 21, 2010 M1 M2 (2d) 2 M1 M2 1 =G = F G 2 4d 4 Examples The force of gravity between the Earth and an apple is given by, MEarth Mapple FG = G 2 REarth Newton’s Second Law: F = ma FG = mapple aapple Give me F, and I will tell you how an object moves (a). Gravity causes an apple to fall (accelerate) from a tree Tuesday, September 21, 2010 Explaining Kepler’s Laws Newton’s laws of motion and gravity together explain Kepler’s laws of planetary motion. Newton’s laws work everywhere: not just for planets orbiting the sun, but satellites orbiting planets, etc. Newton’s version of Kepler’s third law is an improvement: you can calculate the mass of the object being orbited! Tuesday, September 21, 2010 How does Newton’s Law of Gravity Extend Kepler’s Laws? Newton also showed that Kepler’s Laws apply to all orbiting objects, including moons, stars, galaxies. Ellipses are not the only orbit possible bound: ellipses unbound: parabola hyperbola Tuesday, September 21, 2010 How does Newton’s Law of Gravity Extend Kepler’s Laws? The same thing that causes apples to fall to the Earth keeps the planets in orbit around the Sun Newton was the first to show that the laws of physics work in the heavens. Tuesday, September 21, 2010 Newton’s Version of Kepler’s Third Law If a small object orbits a large object, and you can measure the smaller objects orbital period and average distance from the larger object, then you can measure the mass of the larger object. Measure the mass of the Sun using the Earth Measure the mass of the Earth from observations of satellites Measure the mass of Jupiter from its moons Tuesday, September 21, 2010 Thought Question: The gravity of the Earth pulls on you and your gravity pulls on the Earth Is the force you exert on the Earth, larger, smaller, or the same as the force the Earth exerts on you? Tuesday, September 21, 2010 Thought Question: The gravity of the Earth pulls on you and your gravity pulls on the Earth Is the force you exert on the Earth, larger, smaller, or the same as the force the Earth exerts on you? The same! Tuesday, September 21, 2010 Myou MEarth FG = G d2 How does gravity cause tides? Tuesday, September 21, 2010 Newton gives the answer! M1 M2 FG = G d2 Tuesday, September 21, 2010 Tides vary with the phase of the moon. “Spring” tides are the most extreme because the gravity of the Sun and moon combine. Tuesday, September 21, 2010 Conservation of Energy A fundamental law of physics is that energy must be conserved. Energy can: 1) Transfer from one object to another 2) Change forms Total amount stays the same! Tuesday, September 21, 2010 Basic Types of Energy Basic types: Kinetic(motion) Radiative(light) Potential (stored) Energy can change types, but not be destroyed. Tuesday, September 21, 2010 Units of Energy In the U.S., we are used to the Calorie. (a typical adult needs 2,500 Calories) Scientists use the joule. 1 Calorie = 4,184 joules ( a typical adult needs to eat 10 million joules of energy a day) Tuesday, September 21, 2010 Kinetic Energy Kinetic Energy is energy due to motion. Tuesday, September 21, 2010 Gravitational Potential Energy Potential Energy On Earth it depends on: 1) mass of the object 2) strength of gravity 3) how far an object can fall Tuesday, September 21, 2010 Potential vs. Kinetic The total energy of the ball is conserved (kinetic +potential) but the ball’s energy can shift between kinetic and potential Tuesday, September 21, 2010 Mass-Energy 2 E=mc Einstein found that mass itself is a form of energy A small amount of matter can be converted into a large amount of energy Tuesday, September 21, 2010 Examples of 2 E=mc Hiroshima and Nagasaki bombs fueled by an ounce of matter New York City could be run for a month with a newspaper A baseball’s worth could keep a car going at 65 m.p.h for 5,000 years As Electricity, the energy in an ounce of matter is worth $70 million! Tuesday, September 21, 2010 Reminders Evening observing at brooks observatory Tonight through Thursday night. Come to the roof of this building at 9-10pm. Weather permitting. HW #3 available on MasteringAstronomy Tuesday, September 21, 2010