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Transcript
Advanced Physics Chapter 5 Circular Motion: Gravitation Chapter 5: Circular Motion: Gravitation 5-1 Kinematics of Uniform Circular Motion 5-2 Dynamics of Uniform Circular Motion 5-3 Highway Curves, Banked and Unbanked 5-4 Nonuniform Circular Motion 5-6 Newton’s Law of Universal Gravitation 5-7 Gravity near the Earth's Surface 5-8 Satellites and “Weightlessness” 5-10 Types of Forces in Nature 5-1 Kinematics of Uniform Circular Motion Uniform Circular Motion object that moves in a circle with constant speed magnitude of velocity is constant but direction is changing 5-1 Kinematics of Uniform Circular Motion Centripetal (radial) acceleration (ar or ac) center-seeking acceleration acceleration directed toward the center of the circle velocity and acceleration vectors are perpendicular to each other 5-1 Kinematics of Uniform Circular Motion Velocity v = d/t d = 2r so v = 2r/T where T = period of revolution (sec) and f = frequency (sec-1) T = 1/f 5-1 Kinematics of Uniform Circular Motion Centripetal acceleration aR = v2/r aR = 42r/T2 5-2 Dynamics of Uniform Circular Motion According to Newton’s Second Law: Fnet = ma FR = maR = mv2/r net centripetal force (FR) must be directed toward center (why?) centripetal force vs. centrifugal force 5-3 Highway Curves, Banked and Unbanked When a car goes around a curve in the road what keeps it on the road? When is the friction between the tires and the road greater, when they are rolling or sliding? So to keep a car on the road on a curve we must…… 5-3 Highway Curves, Banked and Unbanked Banking a curve reduces skidding why? Fn is at an angle toward the center of the curve so a portion of the Fn goes into FR so the tires need to supply less frictional force to make up for the remaining FR needed 5-3 Highway Curves, Banked and Unbanked Banking angle of road Fnsin = mv2/r since Fncos = mg then Fn = mg/cos mg(sin /cos) = mv2/r g(tan ) = v2/r tan = v2/rg so banking angle of road doesn’t depend on m, just v,r and g 5-4 Nonuniform Circular Motion For an object in UCM; the only acceleration is due to radial (centripetal) acceleration aR is caused by what? Equation? But if the object in circular motion is speeding up or slowing down there is another type of acceleration, tangential acceleration 5-4 Nonuniform Circular Motion Tangential acceleration (atan) Acceleration caused by the change in the magnitude of the velocity of an object moving in a circular path atan = v/t 5-4 Nonuniform Circular Motion Total vector acceleration (a) Acceleration caused by the change in the magnitude and direction of the velocity of an object moving in a circular path It is the sum of both the tangential and radial acceleration of an object a = atan + aR 5-4 Nonuniform Circular Motion Total vector acceleration (a) a = atan + aR The magnitude of a at any moment is: a = 2 (a tan + 2 1/2 a R) 5-6 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation every particle in the Universe attracts every other particle with a force that is proportional to their masses and inversely proportional to the distance between them 5-6 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation the force of gravity acts along a line joining the two particles. F = Gm1m2/d2 G = 6.67 x10 Nm2/kg2 –11 5-6 Newton’s Law of Universal Gravitation Find the force of gravity between two electrons that are 2.3x10-2 nm apart Answer: 1.05 x 10-49 N 5-7 Gravity near the Earth's Surface Since the force of gravity is equal to the weight of an object… Gmome/r2 = mog so…. g = Gme/r2 so..gravity (g) doesn’t depend on the mass of the object, just G, me and r! 5-8 Satellites and “Weightlessness” Why do satellites orbit the Earth? How can a person orbiting the Earth experience “weightlessness”? Many nasty effects of weightlessness on the body 5-8 Satellites and “Weightlessness” What is the relationship between Fn, Fa, and Fg in the following situations? stationary accelerating up accelerating down in free-fall 5-10 Types of Forces in Nature Four different fundamental forces: gravitational force force between any two objects electromagnet force force between any two charged objects strong nuclear force force that holds the nucleus together weak nuclear force force involved in certain types of nuclear decay 5-10 Types of Forces in Nature What is GUT?