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Spinning Top on a Frictionlesss Surface

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    A particular top can be approximated as a solid cylinder of mass 100 g and radius 2 cm. A string of negligible mass and length 1 m is wound around the top, which is started by pulling horizontally on the string with a constant force of magnitude 0.6 N. The top starts from rest at point O, and the string is pulled off. Ignore all friction between the top and the table on which it moves. (a) What is the final velocity of the center of mass of the top? (b) the final angular velocity of the top about its center of mass?

    2. Relevant equations

    τ = F x R = Iα
    I = 1/2mR^2

    3. The attempt at a solution

    I had originally tried to conserve energy using

    Fd = 1/2mv^2 + 1/2Iω^2, substituting I and solving, but I could not get the right answer.
    According to the answers given (2.4 m/s for (a) and 240 rad/s for (b)), energy is not conserved.

    Thanks ahead of time for the help!
     
  2. jcsd
  3. Oct 29, 2012 #2
    Update: I still can't seem to get an amount of work into the system that matches the amount that the given answer implies. Is there something at work here more than translational (Fd) work or rotational (FΔθ)?
     
  4. Oct 29, 2012 #3

    haruspex

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    What are you plugging in as the distance the force travels? (Think of it from the perspective of the puller.)
     
  5. Oct 29, 2012 #4
    I've been assuming that the distance is 1m. :L Am I mistaken?
     
  6. Oct 29, 2012 #5

    haruspex

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    Imagine you're the one pulling the string. How far did you travel before the string lost contact with the top?
     
  7. Oct 29, 2012 #6
    Would the distance over which the force is applied happen to be 1 m + the distance traveled by the center of mass of the top?

    Then comes the challenge of determining that distance. q.q
     
  8. Oct 29, 2012 #7

    haruspex

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    So try another way. The forces and accelerations are all constant, right? Can you write down some equations for those?
     
  9. Oct 30, 2012 #8
    I tried using the forces and accelerations; however, all I got was that there is a net force of 0.6 N to the left of the top (considering I'm supposed to ignore friction) for some time t. Although, would that time just be the amount of time it takes for the top to make the amount of revolutions necessary (assuming Fr = Iα)?

    Update:

    YES, I just used this method and was able to solve it. Man, this entire thing could have been much easier from the beginning if I had just used forces rather than energy from the very start. Is there even a way to solve this problem using energy?

    Edit: Thanks for the help, guys!
     
  10. Oct 30, 2012 #9

    haruspex

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    Yes. Put an unknown in for the linear distance moved by the top. You can relate this to the total energy put in, the linear acceleration of the top, and its final speed.
     
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