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4.2 Newton’s law of universal gravitation • All bodies attract each other. !"#$%#&! !&#$%#"! The Earth attracts the satellite, FS-on-E, and the satellite attracts the Earth, FE-on-S, with the same magnitude but opposite in direction. ! ! FE !on!S = ! FS !on! E • Newton said: The force of attraction between masses is directly proportional to the product of the masses Fg " mA ! mB & '! "#!$!"%! Ex 1: Two masses attract each other with a force of 20 N. What will be the force if the first mass is doubled and the other one tripled? Ex 2: Two masses attract each other with 18 N. What will be the force if one mass is halved? • Newton also said: The force of attraction between masses is inversely proportional to the square of the distance between their centers. !!!!!!!!!!!!!!!!!!!!!!!! ! ! ! ! ! Fg ! 1 r &' ! 2 ! ! (! ! ! ! ! -(! &')*./$!*+!,! ! &')*+!,! ! (! ! ! ! ! &')*.0!$!*+!,! '()( Ex 3:!#1!2!34512678!9:!0;+!""!58<2(2146'!1=9!"25585>!1?8!:9(78!9:! 211(271496!45!*-!,;!@?21!=4AA!B8!1?8!:9(78!4:!"25585!2(8!B(9C'?1! 7A958!19!2!34512678!9:!D;+!""E!!! ! • Now let’s combine what Newton said: ! F" ! g ! mA ! mB r 2 ! ! ! & '! slope = ! ! m A ! mB ! ! ! r rise F g = K9651261)L! = run m A ! mB r 2 2 ! • 69=!=8!"C51!A99F!21!1?8!(8A214965?4<!B81=886! :9(78>!"255!263!34512678! • 4:!G9C!7?26'8!968>!=?21!?2<<865!19!1?8!91?8(5E! ! *+( *,( )( !( H! H! H! *+!,! I-! H! H! E! I-! I-! H! E! I-! I-! I-! E! ID./! I-! I-! E! H! I/! I*.-! E! IJ! I/! I/! E! H! H! I-! E! ! Cavendish Experiment M6!*N0J!K2O86345?!"825C(83! 1?8!O2AC8!9:!L!C546'!2!19(5496! B2A2678;! ! • Formula for universal gravitational force between any two objects ! ! ! ! S64O8(52A!'(2O4121496!79651261! ! )!T;TN!$!*+H**!,•"-.F'-! R255!9:!#!PF'Q! ! L(2O41214962A!:9(78! 9:!211(271496!P,Q! F g = G ! mA ! mB r 2 U4512678!B81=886! -.%/).0!P"Q! R255!9:!%!PF'Q! ! Ex 4: Find the force between two masses of 50 kg and 60 kg separated by a distance of 50 cm ! Ex 5: The force of attraction between two masses of 500 kg is 6.0x10-7 N. Find the distance between them. Ex 6: A person whose mass is 70.0 kg stands on the surface of the Earth. (a) What does the person weigh by using the law of universal gravitation? (b) Use another formula to calculate her weight. Ex 7: The force between two equal masses is 6.5x10-3 N. The distance between the masses is 1.5 m. Find each mass. Ex 8: The force between two masses is 3.5x10-6 N. Find the force between them if the masses are tripled and the distance between them is halved. Ex 9: The gravitational force between two objects is 3.25x10-6 N. The mass of one object is twice the mass of the second object. If the distance between the masses is 2.00 m, find the mass of each object. Ex 10: The gravitational force between two small masses A and B when placed at a short distance apart is 3.24x10-7 N. What is the gravitational force between these objects if the masses of both A and B are doubled and distance between them is tripled? ! ! !
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