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Circular Motion with Tension and Finding Angle

  1. Sep 17, 2015 #1
    1. The problem statement, all variables and given/known data
    A 0.020-kg mass is attached to a 1.2-m string and moves in a horizontal circle with a constant speed. The tension in the string is measured at 0.200 N. What is the measure of angle θ?

    2. Relevant equations
    ∑F=ma, a=v^2/r

    3. The attempt at a solution
    I broke down the forces at work, being T (tension) and W (weight). I made a free body diagram, then drew a graph. I came up with the x components as -Tsinθ=ma, and y components as Tcosθ-W=0. After plugging in for T and m*g (from W) in the y component equation, I came up with θ=11.2, but this is not correct.

    FullSizeRender(2).jpg
     
  2. jcsd
  3. Sep 17, 2015 #2

    haruspex

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    The question as posted does not indicate whether the angle is to be measured from vertical or from horizontal. I assume there is some diagram which makes it clear it is to the vertical.
    I agree with your answer in degrees. Are you sure the question does not want the answer in radians?
     
  4. Sep 17, 2015 #3
    Haruspex,
    Thank you for your response. Here is the image associated with the problem.
    FullSizeRender(3).jpg
     
  5. Sep 17, 2015 #4

    haruspex

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    Then I see only four possibilities:
    - you were expected to use a slightly different value of g; the answer will be somewhat sensitive to this, .980 giving 11.5 degrees e.g.
    - for the same reason, you should only specify two sig figs.
    - the answer should be in radians
    - the book is wrong (maybe in the question statement)
     
  6. Sep 18, 2015 #5
    Haruspex, thank you. I'll have to do some digging, but it gives the answer as 24.6 degrees. So I'll try to get to the bottom of it. Thanks again!
     
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