ACCELERATION & NEWTON'S LAW A BODY MASS 2...

KnowledgeMath

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ACCELERATION & NEWTON'S LAW A BODY MASS 2 KILOGRAMS MOVES ON A CIRCLE OF RADIUS 3 METERS,MAKING ONE REVOLUTION EVERY 5 SECONDS. FIND THE CENTRIPETAL FORCEACTING ON BODY the answer is -24Pi2(cos(2Pit/5),sin(2Pit/5))/25 *** this is the solution in back of book,can someone show me how they derived to this answer? thanks

 

Answer No.1

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From problem data, we have: {Object Mass} = m = 2 kg {Circle Radius} = R = 3 m {Time For 1 Revolution} = T = 5 sec {Frequency Of Revolution} = f = 1/T = (1/5)rev/sec {Object Speed} = v = {Circle Circumference}/T= {2*π*R}/T = 6*π/5 m/sec Let object be moving around Radius "R" circle centered at Origin {=(0,0)}. Then, vector Centripetal Force "F"acting on mass "m" moving in circle of Radius "R" with constant magnitude speed "v" is given by (fromPhysics 101): F = {Magnitude{F}}*{Unit_Direction{F}} (<--- Eq#1) Magnitude{F} = m*v2/R = (2)*(6*π/5)2/(3) = 24*π2/25 Unit_Direction{F} = {INWARD TowardCircle Center} = = {OPPOSITETo Unit Position Vector P} where Unit Position Vector "P" is the unit vectorpointing from the Origin to the current object position (and will change in time while objectmoves around circle). The "X-component" and "Y-component" of UnitPosition Vector "P" can be parameterized in Time "t": {X-component ofP} = Cos{2*π*f*t} = Cos{2*π*t/5} {Y-component of P} = Sin{2*π*f*t} = Sin{2*π*t/5} ----> {UnitPosition Vector P} = <Cos{2*π*t/5}, Sin{2*π*t/5}> ----> {Opposite To P} = - <Cos{2*π*t/5}, Sin{2*π*t/5}> Thus, from Equation #1 and others above, we get: F = -24*π2*(<Cos{2*π*t/5}, Sin{2*π*t/5}>)/25 .

Answer No.2

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ACCELERATION & NEWTON'S LAW A BODY MASS 2 KILOGRAMS MOVES ON A CIRCLE OF RADIUS 3 METERS,MAKING ONE REVOLUTION EVERY 5 SECONDS. FIND THE CENTRIPETAL FORCEACTING ON BODY RPS =N = 1/5 R = RADIUS = 3 M SPEED = V= 2PI*R*N=6PI/5 M/SEC M= 2 KG CENTRIPETAL FORCE =MV^2/R = 2*36(PI^2)/(25*3)=24PI^2/25 IS THE ANSWER. the answer is -24π2(cos(2πt/5),sin(2πt/5))/25 *** this is the solution in back of book,can someone show me how they derived to this answer? thanks

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