MasteringPhysics: HW Ch13-Google Chrome @ https://session.masteringphysics.com/m

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MasteringPhysics: HW Ch13-Google Chrome @ https://session.masteringphysics.com/myct/itemView?offset-next&assignmentProblemID-62357877; Physics 195 8AM Spring 2016 HW Ch13Problem 13.44 Help | Close Resources Y previous | 11 of 12 | next» Problem 13.44 Part A The two stars in a binary star system have masses 2.0x1030 kg and 6.1x1030 kg. They are separated by 1.6x1012 m What is the system's rotation period, in years? Express your answer to two significant figures and include the appropriate units. aal Xb r.1on T-V Units alne Submit My Answers Give Up Incorrect; Iry Again, 3 attempts remaining Part B What is the speed of the lightest star? Express your answer to two significant figures and include the appropriate units. alueUnits 01 alne 7:37 PM 4/23/2016 Search the web and Windows

Explanation / Answer

m1 = 2 * 10^30 kg

m2 = 6.1 * 10^30 kg

d = 1.6 * 10^12 m

centre of mass , x = ( 2 * 10^30 * 0 + 1.6 * 10^12 * 6.1 * 10^30) /( 2 * 10^30 + 6.1 * 10^30)

x = 1.205 * 10^12 m

A)

let the angular speed be w

gravitational force = centripital force

G * m1 * m2 /( d^2) = m1 * x * w^2

6.67 * 10^-11 * 2 * 6.1 * 10^60 /( 1.6 * 10^12)^2 = 2 * 10^30 * 1.205 * 10^12 * w^2

w = 1.148 * 10^-8 rad/s

time period , T = 2 * pi /w

T = 2 * pi /(1.148 * 10^-8)

T = 5.47 * 10^8 s

the system's rotation period is 5.47 * 10^8 s

b)

the speed of the lightest star , v = x * w

v = 1.205 * 10^12 m* 1.148 * 10^-8 rad/s

v = 13833 m/s

the speed of lighter star is 13833 m/s

c)

the speed of the heaviest star , v' = ( d - x) * w

v' = ( 1.6 * 10^12 - 1.205 * 10^12) *1.148 * 10^-8

v' = 4535 m/s

the speed of heavier star is 4535 m/s

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