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Power Question Need Help

  1. Sep 20, 2008 #1
    Power Question !!Need Help

    1. The problem statement, all variables and given/known data
    A particle of mass 'm' is moving in a Circular path of constant radius 'r' such that it's centripetal acceleration is given by ac= k2rt2 where k is constant. The power delivered to the particle by the force acting on it is :-

    A) 2(pi)mk2r2t
    B) mk2r2t
    C) (mk4r2t5)/3
    D) zero

    2. Relevant equations



    3. The attempt at a solution
    Centripetal force will be f=mac so f=mk2rt2.

    Now, Centripetal acceleration = v2/r.
    so v= krt
    now,
    power = force*distance/time for which work is done
    (mk2rt2*vt)/t

    from this i am getting power as mk3r2t3.
     
    Last edited: Sep 20, 2008
  2. jcsd
  3. Sep 20, 2008 #2

    Doc Al

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    Staff: Mentor

    Re: Power Question !!Need Help

    What direction does the force act? What direction is the displacement of the particle?
     
  4. Sep 20, 2008 #3
    Re: Power Question !!Need Help

    Force is centripetal so i think it is acting towards centre. And it is moving in circular track.
    Do i have to take the component of force acting along displacement.
     
  5. Sep 20, 2008 #4
    Re: Power Question !!Need Help

    sorry i think force is acting away from centre
     
  6. Sep 20, 2008 #5

    Doc Al

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    Re: Power Question !!Need Help

    Good!
    Absolutely, in order to find the work done on the particle by that force.
    No, you were right the first time.
     
  7. Sep 20, 2008 #6

    Redbelly98

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    Re: Power Question !!Need Help

    Yes.

    As Doc Al said, you need to use the force component along the particle's displacement.

    Is there another equation for power that you are familiar with?
     
  8. Sep 21, 2008 #7
    Re: Power Question !!Need Help

    F.scosX/t ??
     
  9. Sep 21, 2008 #8
    Re: Power Question !!Need Help

    ohk , I got the answer.
    Here is how i got it :

    Let us assume that the particle moves a quarter. so its displacement will be
    21/2r.
    Now since the force acts in the direction towards centre.
    so taking the component of displacement along force :
    21/2rcos45.
    now using the same formula:
    Power = Force*displacement /time

    (mk2r2t2*21/2rcos45)/t
    =mk2r2t2*r/t
    =mk2r2t

    so, (B) is correct option.

    Thank you guys.
    PF rocks!!
     
  10. Sep 21, 2008 #9

    Doc Al

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    Re: Power Question !!Need Help

    I just realized that I misread the question. :redface:
    I was thinking that it said "Find the power delivered by the centripetal force", which is an entirely different question. The force acting on this particle is not simply centripetal.

    Nonetheless, as already stated: Find the component of the force in the direction of the particle's velocity. Or find the energy of the particle as a function of time.
     
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