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Gravitational/electrostatic Equilibrium on a ramp

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data
    A ball is at a known height on a certain ramp with an unknown angle theta. The ball has a known charge and a known mass. There is also a known charge at the bottom of the ramp. I am supposed to find the angle theta.


    2. Relevant equations
    F=(8.988x10^9)q1q2/d^2 F=mgsin(theta)


    3. The attempt at a solution

    How do I incorporate theta into the electric force equation? Do I just multiply d^2 by theta? Then I would set the two equations equal and solve for theta: Is that correct? It does not seem to be working for me. Thanks/
     
  2. jcsd
  3. Sep 13, 2011 #2

    Doc Al

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    Staff: Mentor

    Not quite right. Hint: How would you express the distance d in terms of h (height) and theta?
     
  4. Sep 13, 2011 #3
    Distance in terms of height and theta => Normally I would use the sine function. That is
    sin(theta)=height/hypotenuse.

    In this instance I know what the hypotenuse is; however, I am not given height and the problem is to find theta. i.e. I know that the ball is 13 cm up the ramp. Since I do not know two of the three variables I do not know how to proceed.
     
  5. Sep 13, 2011 #4

    Doc Al

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    So you are given the distance d and not the height? Great. That makes it even easier.

    Seems to me that the only unknown is theta, which is what you are solving for.
     
  6. Sep 13, 2011 #5
    Well, I do not know theta, the length of the ramp nor the height of the ramp. However, you are correct in that theta is the only unknown I need to solve for. I have been trying mgsin(theta)=(8.98*10^9)(q1)(q2)/[(d^2)(sin(theta))]; however, I have been obtaining the wrong answer. I know m, g, q1, q2, and d so clearly I either have a computational error or a formula error. I cannot find any computational errors so I assume it is something with the formula.
     
  7. Sep 13, 2011 #6

    Doc Al

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    That's what you're asked to find.
    You have d, which is the only distance you need.
    I don't understand why you have a sin(theta) factor on the right hand side. The direction of the electric force is parallel to the ramp (if I understand the set up correctly), so no need for any sine or cosine. (Assuming that's what you were trying to do.)
    Yes, you'll need to correct your formula, as pointed out above.
     
  8. Sep 13, 2011 #7
    Do you mean I should have the equation: mgsin(theta)=(8.98*10^9)(q1)(q2)/(d^2) instead? I also tried that and have also been unsuccessful. Or is my mistake somewhere else? Thank you for all your help so far.
     
  9. Sep 13, 2011 #8

    Doc Al

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    Yes.
    Give it another try.

    If it doesn't work, show the details of your calculation. Or perhaps copy the exact problem statement, word for word. Perhaps we're misinterpreting something.
     
  10. Sep 13, 2011 #9
    q1 = 1.05 × 10 -7 C is fixed at the base of
    a plane that makes an angle  with the horizontal direction.
    A ball of mass m = 1.15 g and a charge q2 =3.10 ×
    10-8 C is placed into a frictionless groove in the plane
    that extends directly to the fixed charge. It is allowed to move up and down until it finds a
    stable position l=10.2 cm from the fixed charge. What is the
    value of ?

    Should my formula work?
     
  11. Sep 13, 2011 #10

    Doc Al

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    Sure. (The corrected version.)

    Be careful with units.
     
  12. Sep 13, 2011 #11
    I now got it correct - thank you for your help. I actually tried to use that formula earlier with no success - this time I found that I had been forgetting to square my distance in my calculations. Thank you again for your assistance.
     
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