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10/10/2013 Weight w = mg In orbit, in the space shuttle, an astronaut is Chapter 6 A. B. C. D. 10/11/13 Apparent Weight = normal force • Weight is force of gravity w = mg • Even if you’re falling • Astronauts are not weightless, they are apparently weightless A car is rolling over the top of a hill at a constant speed. At this instant, A. n > w B. n < w C. n = w D. we can’t tell about n without knowing speed. Weightless The same weight as on earth Less than on earth but not weightless More than on earth What is your true weight on the moon? Say you have a mass of 60kg Your weight on the moon is A. 60 kg 9.8 m/s2 = 590 N B. 60 kg 1.6 m/s2 = 98N C. 0 N A car is rolling through the bottom of a valley at a constant speed. At this instant, A. n > w B. n < w C. n = w D. we can’t tell about n without knowing speed. a 1 10/10/2013 Weight w = mg In orbit, in the space shuttle, an astronaut is Gravity and Orbits A. B. C. D. Weightless The same weight as on earth Less than on earth but not weightless More than on earth Newton’s law of gravity Orbits F = Gm1m2/r2 Free fall Newton’s Mountain thought problem G – Gravitational Constant (ALWAYS the same) G = 6.67 x 10-11 N m2/kg2 PhET: Gravity and Orbits Acceleration in Orbit What is the direction of acceleration for the Earth when in orbit around the Sun? A. B. C. D. 2 10/10/2013 PhET: Gravity and Orbits Force Arrows Planet Mass What will happen if the mass of the Planet increases? A. B. C. D. Nothing The planet’s angular velocity will increase The planet’s angular velocity will decrease The planet will crash into the sun! No gravity Star Mass What will happen if the mass of the Star increases? What happens if gravity no longer exists? A. Fall into the sun A. B. C. D. Nothing The planet’s angular velocity will increase The planet’s angular velocity will decrease The planet will crash into the sun! B. Continue in a straight line C. Fly directly away from the sun D. None of the above Moon’s Orbit Which of the following best depicts the path of the moon around the sun? A. C. B. PhET: Gravity and Orbits To Scale D. E. The moon does not orbit the sun. 3 10/10/2013 Ellipses – My Solar System When moving in an ellipse, a satellite's speed is A. Largest when it is closest to the sun B. Largest when it is furthest from the sun C. Equal during the entire orbit Ellipses – My Solar System Does the sun move? Is it attracted to the Earth? A. Sun is stationary in space B. Sun moves as the planets orbit 4-star ballet Slingshot Rotational motion Problems Determine the speed of a satellite of mass m orbiting a body of mass M at a distance r. Approach: Solving Force Equations 1. Givens 2. Draw situation – identify object of interest & forces on it. 3. Draw a Free Body Diagram (FBD) 4. Identify if in equilibrium or dynamic. Does SF = ma or SF = 0? 5. Apply Newton’s 2nd law which means find the net force in the y and find the net force in the x. SFx and Sfy 6. Solve equations you got from 4 and 5 7. Assess 4 10/10/2013 1. Givens M – mass of the planet m – mass of the satellite r – distance from center to center 2. Draw situation and identify forces on the object of interest m Gravity F r v=? M 3. Draw free body diagram F 4. Identify if in equilibrium or dynamic Does SF = ma or SF = 0? F a 5. Apply Newton’s Laws 6. Solve for unknown GmM/r2 = mv2/r F v2 = GM/r a SFx = F = ma SFx = GmM/r2 = ma ma = mv2/r 5 10/10/2013 7. Assess Kepler’s Law v = √GM/r Does not depend on the mass of the planet v = √GM/r = 2pr/T T2 = (4p2/GM)r3 6