26lecture2a08

26lecture2a08 - Physics 2A Lecture 26: Mar 10 Vivek Sharma...

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Physics 2A Lecture 26: Mar 10 Vivek Sharma UCSD Physics
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g 12 g 2 Every particle of matter in the universe attracts every other particle with a gravitational force F acting along line joining the two particles F mm r g 2 F G=Universal Gravitational Constant G r =
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Superposition Of Gravitational Forces sat i sat i FF = G G is a t 2 F a t i GM m r = G i
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Superposition Of Gravitational Forces Gravitational forces combine vectorially A satellite is to be sent to position x between earth & moon where there is no NET gravitational force due to these bodies. Find x . 22 EM 0 () ( FF F equilibrium poi )( / ) 0.9d = t n ME Mm M m GG xd x dx x M M x =− + + = = = G G
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Planet Hunting In The Faraway Universe An orbiting planet exerts a small gravitational force on the star causing the star to alternately move towards or away from us: This wobble is measured by analyzing star light Over 140 extrasolar planets discovered !
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Relating Little g and Big G Revised Definition: Weight of a body is the total gravitational force exerted on that body by all other bodies in the universe ! When body is near earth, influence of all other objects is negligible (far far away) Weight = Earth’s grav. attraction g 2 2 Weight force on a body of mass at eart = F h's su w = mg ce m rfa E E E E Mm G g R GM R = =
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Weight Force On A Body Near Earth g 2 w = F r E M m G = As r w 0 →∞ ⇒
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Measuring Weight Force By using Newton’s 1 st law & a known force such as that exerted by stretched spring, one measures other forces such as gravity acting on the block Gravity is not a force that one can sense or measure directly. object appear to weigh whatever the scale reads
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Example: Apparent Weight & Earth’s Rotation spin 2nd Law applied to object of mass m at rest At north pole: mg-w = 0 w g = m Assume you did not know that earth was spinning around N pole 2 2 E E v Appare At equator: nt weight w v mg - w ' = m ( ' g = - m R R ) 2 E 2 2 2 6 E acc. due to gravity (g') v g' = g - (468m/ Appare s) 6.38 10 ; v g = 0.0337m/s m t R n R Δ= = ×
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(Apparent) Weightlessness In Space rad a G
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26lecture2a08 - Physics 2A Lecture 26: Mar 10 Vivek Sharma...

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