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Rotational Plus Translational Motion for Sphere of Yarn

  1. Mar 22, 2012 #1
    A massless string is wrapped around the equator of a solid sphere (mass M = 76.2 kg, radius R = 0.211 m). A girl holds the free end of the string, and the sphere is released from rest, Assume:
    - the sphere is always parallel to the floor
    - the string is always perpendicular to the radius of the sphere
    - the string does not slip over the sphere

    What is the length of the string that has been unwound when the sphere reaches an angular speed ω = 28.6 rad/s?

    Can someone please help? Here is what I did but answer is wrong:

    v = ωr = 6.0346 m/s

    vf^2 = v0^2 + 2as
    s = 1.86 m

    1.86 = 1/2at^2
    t= .615s

    .615s * 28.6 = 17.59

    17.59 * .211 = 3.7....but this wrong....please help?
     
  2. jcsd
  3. Mar 22, 2012 #2

    tiny-tim

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    hi sweetpete28! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)
    you're assuming that a = g

    what about the tension? :wink:
     
  4. Mar 22, 2012 #3
    Ohhh

    You're right! Tension would = mg since it does not fall...right? So there is 0 acceleration.

    I know θ(t) multiplied by radius r will give me length string has been unwound...but how do I get what t equals? I'm still stuck...
     
  5. Mar 22, 2012 #4
    If mg is tension = 748 N and work done on sphere is 555J once it reaches 28.6 rad/s angular velocity....can I divide 555J by 748N to get length unwound since F times d = Work??

    Which would give answer of 555/748 = .742 m???
     
  6. Mar 22, 2012 #5

    tiny-tim

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    hi sweetpete28! :smile:
    nooo, of course it accelerates, but at less than g

    either call the tension T, and consider forces and torques,

    or (probably easier) use conservation of energy :wink:
     
  7. Mar 22, 2012 #6
    If mg is tension = 748 N and work done on sphere is 555J once it reaches 28.6 rad/s angular velocity....can I divide 555J by 748N to get length unwound since F times d = Work?? (I used KE = 1/2MIω^2 to get work done on sphere = 555J).

    Which would give answer of 555/748 = .742 m???
     
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