1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two spheres hanging, find charge.

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Two identical, small spheres of mass 2.0g are fastened to the ends of a 0.6m long light, flexible, insulating fishline. The fishline is suspended by a hook in the ceiling at it's exact center. The spheres are each given the same electric charge. They are in static equilibrium, creating an angle of 30° between the halves of the string. Calculate the magnitude of the charge on each sphere.

    Here's a sketch of the picture given on the worksheet:
    Owokl.gif
    Red lines are what I drew over the diagram to make a right triangle.

    This being a bonus type question, I was given three possible answers and had to find out which one was the real one:

    q =
    3.7 x 10^-7 C or
    1.2 x 10^3 C or
    1.2 x 10^-3 C.

    2. Relevant equations

    Coulombs Law: [tex]F = k \ \frac{q_1 q_2}{r^2}[/tex]

    3. The attempt at a solution

    First I converted the mass into kilograms: m = 0.002kg

    Then I split the angle into two right triangles to get the distance between the spheres.

    r/2 = Sin15 x 0.3 m
    r = approx. 0.16m

    Then I figured since the spheres are at rest, then a = 0 and Fg = Fe...so I tried coulombs law to solve for q:

    [tex]F_{g} = F_{e}[/tex]
    [tex]mg = k \ \frac{q_1 q_2}{r^2}[/tex]
    [tex]\frac{mgr^2}{k} = q_1 q_2[/tex]

    I ended up with 2.6 x 10^-11...obviously way off any of the true answers.

    Thanks for taking the time to read over all this. =D

    Cheers - Krunklehorn
     
  2. jcsd
  3. Jan 30, 2012 #2
    You need to look at the forces acting on the balls.
    There is a vertical force = weight of a ball = 2x10^-3x9.81 = 0.0196N
    There is a sideways force, F, due to the repulsion.
    Can you see that F/0.0196 = Tan15
    This will give you F to use in the repulsion equation.
    I got Q = 1.2x10^-7C, on your list there is 1.2x10^-3C
    I use k = 8.98x10^9 in the repulsion equation
     
  4. Jan 30, 2012 #3
    Oh I see! Fe pushes the spheres to the side while Fg pushes them down to the ground.

    Tan = Opp / Adj so my equation should be:

    [tex]Tan15 Fg = Fe[/tex]

    [tex]\frac{Tan15mgr^2}{2k} = q[/tex]

    Awww too bad it's actually wrong. I am getting 7.03x10^-15 as an answer.
     
  5. Jan 30, 2012 #4
    Agree with technician. The force on one of the spheres is equal to the x-component of the fishline force(S):

    Sx=S*sin15

    and

    S=Sy/cos15

    Therefore

    q=1.19*10-7

    since

    Fe=m*g*tan15
     
    Last edited: Jan 30, 2012
  6. Jan 30, 2012 #5
    Oh I completely agree with him and appreciate the help immensely....I just don't see why I'm getting such a mangled answer.

    Did I rearrange the equation wrong?
     
  7. Jan 30, 2012 #6
    The equation

    Fe=(k*q2)/(r2)

    can(as you know) be rewritten as

    q=r*Sqrt[Fe/k]

    Sum of forces in x-direction equals zero:

    Fe-Sx=0

    therefore

    Fe=Sx

    Similarly in the y-direction:

    Sy-w=0

    therefore

    Sy=w=m*g

    Now, from simple trigonometry you see that

    Sy=S*cos15

    and

    Sx=S*sin15

    This means that you can write Sx as

    Sx=(Sy/cos15)*sin15=m*g*tan15

    And from the equilibrium equation in the x-direction you see that

    Fe=m*g*tan15

    Now you have Fe. You then need the distance r between the spheres:

    r=2*0.3*sin15

    Filling all this information into the expression for q then gives you

    q=1.187*10-7 C
     
    Last edited: Jan 30, 2012
  8. Jan 30, 2012 #7
    Thanks for the help! I understand completely now.
     
  9. Jan 30, 2012 #8
    Great.....well done.....don't always believe published answers
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Two spheres hanging, find charge.
  1. Two Hanging Spheres (Replies: 1)

Loading...