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Another Tension problem

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    A child’s indoor swing consists of a rope of length L anchored to the ceiling, with a seat at the lower end. The total mass of child and seat is m. They swing in a horizontal circle with constant speed v, as shown in Fig. 6-2; as they swing around, the rope makes a constant angle 0 with the vertical. Assuming the time τ for one revolution (i.e., the period) is known, find the tension T in the rope and the angle θ.


    2. Relevant equations
    ƩF=mac=m(v2/r)
    ƩF=mg

    3. The attempt at a solution
    I decided the force from the child on the swing would be Ftotal=( ƩF=mg and ƩF=mac=m(v2/r)).
    And the tension of the line is Ty= Ftotal cosθ and Tx= Ftotal sinθ

    Therefore T=Ftotal(cosθ+sinθ)
    where Ftotal=m(v2/r+g)
    Rewritten: T=(m(v2/r+g))(cosθ+sinθ)

    And, rearranging this equation would give me θ if I so desired.

    Am I doing this right??

    Thanks for help
     
  2. jcsd
  3. Apr 22, 2012 #2
    Draw a simple FBD.
    In any istant, the (rope tension) x (cos θ) must equal the gravity force.
    Do you agree ?
    Then you easily have the rope tension.
     
  4. Apr 22, 2012 #3
    Since, Tycosθ=mg then Ty=mg/cosθ. Then Tx =m(v2/r)sinθ

    Is this correct?
     
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