Lecture 35 - Gravitation.pptx

7/21/2019 Lecture 35 - Gravitation.pptx

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Chapter 13

Gravitation



Law of Gravitation

“Every particle of matter in theuniverse attracts every otherparticle with a force proportional

to the product of the masses ofthe particles and inverselyproportional to the square of thedistance between them.”

$11 & &



,ome important notes on)ravity

• Gravitational forces always act along

the line joining the two particles• -hese forces form an action-

reaction pair.

• Even when the masses of theparticles are dierent the twointeraction forces have equal

magnitude.



• /hen the bodies aresphericallysymmetrical the

gravitational forces between them is thesame if weconcentrated the

mass of each sphere atthe sphere’s center.



Conceptual E"ample

/hy do hu)e bodies tend to bespherical *stars planets+ whilesmaller bodies *asteroids+ do not0



E"ample

,uppose two spheres with masses m1

= 0.010 kg and m2 = 0.00 kg are

placed with their centers 0.00 m apart in outer space. /hat is thema)nitude of the acceleration ofeach relative to some inertial frame0

a1 = 1.33 " 1#$ m's&

a& = &. " 1#$1#

m's&



E"ample

Consider the three$star system shown.2f at an instant they form a !0 right triangle nd the total

gravitational force e"erted on thesmall star.

4 = 1.! " 1#& %

5 = 16.#



,tricter 7enition of /ei)ht

• /ei)ht is the total )ravitational forcee"erted on the body by all other"odies in the universe.

• %ear the surface of the earth thecontribution is appro"imately due tothe Earth alone and is )iven by

mE = 8.9 " 1#&6 ()

RE = .3 " 1# m



-he denition of )

%ote that ) is dependent on RE. :t

distances r ; RE we have



E"ample

:n ob<ect on #arth wei)hs $%&20 '.4ind its wei)ht on (ars *(( = ).!2

* 102$ kg +(

= $.!0 * 10) m+. :lso

nd the acceleration due to )ravity*)+ there.

/ = 18## %

) = 3.! m's&



-he determination of G

7urin) the time of >enry Cavendish?

%ewton@s Law of Gravitation

:cceleration 7ue to )ravity gAadius of the earth *rst done

by the )reat #ratosthenes+

, ass of the EarthBpon (nowin) G



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Lecture 35 - Gravitation.pptx

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