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Simple accelerometer proof (a=tan(theta)) help

  1. Nov 6, 2011 #1
    The situation is there is a ball attached to a string in a car, and the angle that the string makes is measured when the car is accelerating. I'm having a bit of trouble with the proof that a=tan(theta)

    so far I've gotten that
    weight=mg=Tcos(theta)
    a=ma=Tsin(theta)

    But what I don't understand is why you need to find the ratio between them and how that shows acceleration.
    a/g=sin(theta)/cos(theta)
    a=gtan(theta)

    another one of my questions is what happens to the g in the equation?

    Help is much appreciated thanks!
     
  2. jcsd
  3. Nov 6, 2011 #2
    It's normal to have trouble. This is not correct. Look at the units. Tan(theta) is dimensionless. How can be equal to the acceleration?

    You have two equations with two unknowns (T and a). As you are interested in a, you can isolate T from the first equation, replace in the other one and solve for a.
    a = g tan(theta) makes sense.

    PS. It may be that you found the a=tan(theta) in a text where they measure acceleration in units of "g"?
    Then what you have there is actually a/g=Tan(theta).
     
  4. Nov 6, 2011 #3
    AH, ok that makes sense. Thanks for the clarification!
     
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