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A ball is swung in a circular path

  1. Mar 21, 2016 #1
    1. The problem statement, all variables and given/known data
    A 0.5 kg ball is swung in a circular path from a 80 cm long rope, attached to a vertical pole.
    A. What is the speed of the ball theta (between the pole and rope) is 40 deg?
    B. What is the KE of the ball at theta = 40 deg?
    C. The ball slows down and the KE drops to 50% of the value in (B). What is the new value of theta?

    2. Relevant equations
    F = ma
    centripetal acceleration = V^2/r

    3. The attempt at a solution

    A.
    Fy = 0
    Tcos(theta) = mg
    Fx = mv^2/r
    Tsin(theta) = mv^2/r - > V = sqrt(g*r*tan(theta)) = 2.056 m/s
    B. KE = 0.5 *m*v^2 = 1.057151179
    C. I get all the have to new velocity but i don't know how to get the angle... I need some pointers.

    Also, i am not sure if this is the right approach.

    Thanks
     
  2. jcsd
  3. Mar 21, 2016 #2

    BvU

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    Hello jazzy, :welcome:

    Looks like the right approach. A few remarks: KE = 1.06 J (don't forget the units and don't give many more digits than the given variables have -- but if the first digit is a one, then give one more).

    For C, you have the same equilibrium equation (##\ v^2 = g\, r \tan\theta\ ##), only now v is given and ##\theta## has to be determined. Your problem is then the goniometric equation when you put in ##r = L \sin\theta## (L is the length of the rope).

    If you have no way to solve this, perhaps you are supposed to find the answer with trial and error ?
     
  4. Mar 21, 2016 #3
    Yea, i get suck at the trig. And, it's definitely not trial and error. Trying different reference frame to see if I can get rid of a trig.
     
  5. Mar 21, 2016 #4

    haruspex

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    What trig equation do you get? Something like sin(θ)tan(θ)=value? There is an analytic way to solve that.
     
    Last edited: Mar 22, 2016
  6. Mar 22, 2016 #5
    (Sin^2(theta))/( cos(theta)) = some number. I tried using some trig identities but nothing seemed to work. As I write this, I think I could've solved it, cuz that also equals (1 - cos^ 2(theta))/ cos(theta) = something and set x = cos(theta) and sove the quadratic. But that will give two answers... I'll solve it later. But if you have any othersuggestions, please let me know.
     
  7. Mar 22, 2016 #6

    haruspex

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    That is the method I had in mind.
     
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