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Centripetal Force of swung keys Problem

  1. Apr 9, 2015 #1
    1. The problem statement, all variables and given/known data

    Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

    A) What is the slowest speed the keys can swing and still maintain a circular path?

    B) What is the tension in the string at the bottom of the circle?

    I'm confident with A, however am still a bit shaky with B... Any tips would be greatly appreciated!

    2. Relevant equations

    A)
    Fc = Fg
    m v2 / r = m g

    B)
    Fnet = FT - Fg
    FT = Fnet + Fg


    3. The attempt at a solution

    A)

    Fc = Fg
    m v2 / r = m g
    v = (rg)2
    v = √(0.25) (9.8)2
    v = 1.57 m/s


    B)


    Fnet = FT - Fg
    FT = Fnet + Fg
    FT = m v2 / r + m g
    FT = (0.1) (1.57)2 / 0.25 + (0.1) (9.8)
    FT = 2.0 N
     
  2. jcsd
  3. Apr 9, 2015 #2

    haruspex

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    Is the speed constant?
     
  4. Apr 9, 2015 #3
    The problem is word for word what I've given here. (I wish more info were made available, it seems as if this can be interpreted in more than one way)
     
  5. Apr 9, 2015 #4

    haruspex

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    My question was intended as rhetorical. I would say it is not constant. According to what law would you expect it to vary?
     
  6. Apr 9, 2015 #5
    Conservation of energy.
     
  7. Apr 9, 2015 #6

    haruspex

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    Right.
     
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