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General Physics

by: Nichole Keebler

General Physics PHYSICS 103

Nichole Keebler
GPA 3.95


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Class Notes
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This 3 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 103 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/205224/physics-103-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.


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Date Created: 09/17/15
Physics 103 Lecture 13 Newtonian Gravity Extended Objects Center of Gravity 0 Today s lecture will cover 3 Newton s Law of Gravitation b Kepler s Laws 3 Center of Gravity 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln Lecture 13 Preflight 1 2 amp 3 0 You are driving a car with constant speed around a horizontal circular track On a piece of paper draw a Free Body diagram for the car How many forces are acting on the car 1 2 3 4 5 gt a gravity b normal force of road m 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln n centripetal force Lecture 13 Preflight 4 amp 5 o The net force on the car is Zero Pointing radially inward toward the center of the circle 4 Pointing radially outward away from the center of the circle To travel in a circle something must supply the centripetal acceleration 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln Lecture 13 Preflight 6 amp 7 0 Suppose you are driving through a valley whose bottom has a circular shape If your car has mass M what is the normal force exerted on you by the car seat as you drive past the bottom of the hill Fquot lt Mg V gt V5 in Fquot gt Mg 4 Normal force must also supply centripetal acceleration 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln A SPECIAL POINT Center of mass or center of gravity If line of force passes thru c m No rotation H 7 m1r1 m2r2m3r3m4r4 cm m1m2 m3m4 Center of mass is the same as the center of the volume Provided uniform density material Symmetry 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln Center of Gravity o The force of gravity acting on an object must be considered in determining equilibrium 0 All of the weight of the object can be considered to be concentrated at one point 1214EI5 Pnysics 1D3 Spring ZEIEIE U Wscunsln Experimentally Determining the er of Gravity I The wrench is hung 39eely 39om two different pivots Question 1 Can a body39s center at gravity be outside its volume I a yes 4 o The intersection of the b no lines Indicates the center Center at gravity 55 is derined es of gravity I A rigid object can be balanced by a single force equal in magnitude to its weight as Ion as the force is acting upward u h the object s center of ravi g ty WM Where m is tne mass at eiernent dt enurdindte xm 2 omnwun mm 55 can be uutside tne vuiume twins thscsm snnnazuus u Wismnsn 7 twins Physicst spiing zuusiu Wscansin a QUEStION 2 A moment later Where is the center at gravity oi a yummy donut it is at tne ongin ot tne circuiar nng nait way trom tne bottom ot tne donut r wnere tnere is no dougn c 5 nos snirted dicing tne iine air symmetry away rrum tne bite twins thscsm snnnazuus u Wismnsn s twins Physicst spiing zuusiu Wscansin tn Newton s Law of Gra ation o Every particie in the universe attracts every other paniCieWitn a torce aiong the iineioiningtnem Tnetorce is directiy proportionai to the product ottneir masses and inverseiy proportionai to the square ot the rn distance between the Nate partieie Ir ein extended abyeet yuu rnust treeit tne vectur air tne center at grayityv 2 Ir d system air extended ubJects yuu rnust stiii cunsider tne eenter air mass i 2n NBS pnysesi uai srnne zuusi u Wismnsn Newton s Law of Gravity mM Magnitude F G 9 2 667x 1041 N m2ltg2 Directiun attractive tpuiis tnern tugether Mm rureeunMduetumidedy rrumMeenterdnd 5707 rareeanrnduetatt iseiweiy rrarnrneenter PEUZMZO Wurk dune tn bring rneiss rn rrarn inrinity tn tne pruximity air rneiss M Oniydirrerenees in patentidi energy rneitter Zeru puint is arbitrary 121 was vnysiestuaiSnnne anusiu Wscansin t2 Close to the Surface of the Earth 0 Consider an object of mass m near the surface of the earth mM FgmaGr 2 mg 19 3 G AIS2 9 8 rns2 E PEZZ GR h APEGMEmLGMEm h a E R41E h 2 h RE 17 Rs APE a m 012 h mgh forsmall i RE RE 121435 Physics 133 Spring ZEUS U WSEDHSW 13 Escaping Gravity 0 Kinetic energy of the rocket must be greater than the gravitational potentia energy 0 De nes minimum velocity to escape from gravitational attraction KE PE constant Consider case when speed is just sufficient to escape to infinity with Vanishing final Velocity At infinity KE PE 0 therefore on Earth imam 5 2 RE 0 112 kms 25000 mph 1214EI5 Pnysics 1D3 Spring 2DEI5U Wscunsin 14 Lecture 13 Preflight 8 amp 9 0 Two satellites A and B of the same mass are going around Earth in concentric orbits the distance of satellite B from Earth s center is twice that of sa ellite A What is the ratio of the centripetal acceleration of B 7 to that DfA39 Since The only force is The 18 gravitational force iT musT cale as The inverse square of Their disTances from The 12 cenTer of The EarT rA g min 2m m m m 1214EI5 Pnysics 1D3 Spring 2DEI5U Wscunsin is Lecture 13 Preflight 10 amp 11 0 Suppose Earth had no atmosphere and a ball were red from the top of Mt Everest in a direction tangent to the ground If the initial speed were high enough to cause the ba 0 travel in a circular trajectory around the earth the balls acceleration would e much less Than 9 because The ball b doesn39T fall To The groun be approximaTely g 4 depends on The velociTy of The ball ESE n tuli Zn39l m mi m 1214EI5 Pnysics 1D3 Spring 2DEI5U Wscunsin 1B Orbits o Acceleration is provided by gravity 1214EI5 Pnysics 1D3 Spring 2DEI5U Wscunsin i7 Kepler s Empirical Laws 0 Based on Tycho Brahe s astronomical measurements 0 Orbit of a planet is an ellipse with the Sun at one focus 0 Equal areas swept out in equal times 0 consTanT E R3 NewTon 2 mV mRa2 0 2 R R 221 T R3 GM T2 4212 Do read Examples 714716if you 1214EI5 Pnysics 1D3 Spring 2DEI5U Wscunsin 1E


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