ࡱ> #%"@ *bjbjFF .2,, BBBB$f4  $ R[ ]u8F `0lBj<, A  "BBTAP 401-2: Newtons gravitational law These questions are intended to give you practice in using the gravitational law. They will give you a feeling for typical forces with a range of masses and also how sensitive force is to distance. Useful data G = 6.67 10 11 N m2 kg 2 Earth s mass = 5.97 1024 kg Moon s mass = 7.34 1022 kg Sun s mass is 2.0 1030 kg Radius of the Moon = 1.64 106m Radius of the Earth = 6.37 106 m Earth Moon distance = 3.8 105 km Earth Sun distance = 1.5 108 km 1. You may sometimes find it difficult to get up from the sofa after watching a TV programme. Assuming the force of gravity acts between the centre of your body and the centre of the sofa, estimate the attraction between you and your sofa. 2. Calculate the size of the gravitational pull of a sphere of mass 10 kg on a mass 2.0 kg when their centres are 200 mm apart. What is the force of the 2.0 kg mass on the 10 kg mass? 3. At what distance apart would two equal masses of 150 kg need to be placed for the force between them to be 2.0 10 5 N? 4. Calculate the gravitational pull of the Earth on each of the following bodies: the Moon; satellite A with mass 100 kg at a distance from the Earth s centre 4.2 107 m; and satellite B mass 80 kg at a distance from the Earth s centre 8.0 106 m. 5. Show that the unit for G, the universal gravitational constant, can be expressed as m3 s 2 kg 1. 6. Calculate the weight of an astronaut whose mass (including spacesuit) is 72 kg on the Moon? What is the astronaut's weight on Earth? Comment on the difference. 7. Show that pull of the Sun on the Moon is about 2.2 times larger than the pull of the Earth on the Moon. 8. Why then does the Moon orbit the Earth? The American space agency, NASA, plans to send a manned mission to Mars later this century. Mars has a mass 6.42 x 1023 kg and a radius 3.38 x 106 m. G = 6.67 x 1011 N m2 kg-2 9. (a) The mass of a typical astronaut plus spacesuit is 80 kg. What would be the gravitational force acting on such an astronaut standing on the surface of Mars? (b) State whether an astronaut on Mars would feel lighter or heavier than on Earth. Practical advice This resource could be used for either class work or homework. Answers and worked solutions 1. For the values estimated in the answers: EMBED Equation.3 2. Pull on the 2.0 kg mass EMBED Equation.3 The pull on the 10 kg mass will be equal but opposite in direction. 3. EMBED Equation.3 4.         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FMicrosoft Equation 3.0 DS Equation Equation.39q  F=GMObjInfo Equation Native _1189062629F`0l`0lOle mr 2 =(6.6710 "11 Nkg "2 m 2 )10kg2.0kg0.200m() 2 =3.310 "9 N. FMicrosoft Equation 3.0 DS EqCompObjfObjInfoEquation Native _1189062628F`0l`0luation Equation.39q+ r= Gm 2 F  =m GF  =150kg 6.6710 "11 Nkg "2 m 2 2.010 "5 N  =0.27m. FMicrosoft Equation 3.0 DS Equation Equation.39qH= F=GMmr 2 =(6.6710 "11 NkgOle !CompObj"fObjInfo$Equation Native %8 "2 m 2 )(5.9710 24 kg)(7.3410 22 kg)3.810 8 m() 2 =2.010 20 N. FMicrosoft Equation 3.0 DS Eq_1189062626F`0l`0lOle .CompObj/fObjInfo1uation Equation.39qH F=GMmr 2 =(6.6710 "11 Nkg "2 m 2 )(5.9710 24 kg)100kg4.2Equation Native 2_11890626251F`0l`0lOle :CompObj ;f10 7 m() 2 =23N. FMicrosoft Equation 3.0 DS Equation Equation.39q8= F=GMmr 2 =(6.67ObjInfo!=Equation Native >_1203838465 ,$F`0l`0lOle F10 "11 Nkg "2 m 2 )(5.9710 24 kg)80kg8.010 6 m() 2 =5.010 2 N. FMicrosoft Equation 3.0 DS EqCompObj#%GfObjInfo&IEquation Native J!_1189062623)F`0l`0luation Equation.39q 4 Nkg "2 m 2 =kgms "2 kg "2 m 2 =m 3 s "2 kg "1 .Ole OCompObj(*PfObjInfo+REquation Native S FMicrosoft Equation 3.0 DS Equation Equation.39q@= F=GMmr 2 =(6.6710 "11 Nkg "2 m 2 )72kg(7.3410 22 kg)1.6410 6 m() 2 =1.310 2 N. FMicrosoft Equation 3.0 DS Equation Equation.39q_12038387806.F`0l`0lOle \CompObj-/]fObjInfo0_Equation Native `_1189062621;'3F`0l`0lOle iCompObj24jfl F=GMmr 2 =(6.6710 "11 Nkg "2 m 2 )72kg(5.9710 24 kg)6.3710 6 m() 2 =7.110 2 N. FMicrosoft Equation 3.0 DS Equation Equation.39qH= F=GMmr 2 =(6.6710 "11 NkgObjInfo5lEquation Native m8_12038388298F`0l`0lOle v "2 m 2 )(2.010 30 kg)(7.3410 22 kg)1.510 11 m() 2 =4.410 20 N. FMicrosoft Equation 3.0 DS EqCompObj79wfObjInfo:yEquation Native z<_1189062619=F`0l`0luation Equation.39q xD F=GMmr 2 =(6.6710 "11 Nkg "2 m 2 )(5.9710 24 kg)(7.3410 22 kg)3.810 8 m() 2 =2.010 20 N. 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