Help with deriving an equation (coloumb's law, pith ball charges)

[rad5brandon]

Homework Statement

A lab we were recently given in AP Physics class contained an equation already derived. This lab was about determining the charge on a pith ball, using the static charge of a fur to charge the balls negatively, so they repel. Finding the angle and distance between the two balls, the electric charge can be determined.

This is the final equation

q = 2Lsinθ√((mgtanθ)/k)

theta is the measured angle in the experiment (in this case 17 degrees)
m is average mass of the two balls : .2620/2
L is the length of string to the pith ball, bascially the height or radius. Pith ball is hanging from a stand. (.1524 meters)

Homework Equations

Fgravitational=Gm1m2/(r^2) Felectricalfield = kq1q2/(r^2)

The Attempt at a Solution

I've got nothing.

 

[collinsmark]

I've got nothing.

Can I assume that the angle θ is the average angle between a given strand and the vertical (as opposed to the total angle between both strands)?

The fist place to start is by drawing a free body diagram.

Then work with the x-components and y-components separately. Since nothing is accelerating, the sum of all forces along a given component must be equal to zero. (For example, the y-component of the tension of a given strand must equal the force of gravity from the corresponding ball). Once you have the force equations for both x and y components, you can combine equations and solve for q (assuming that each ball has the same charge q on it).

Another hint: One of the relevant equations you posted was

Fgravitational=Gm1m2/(r^2)​

There's no need to make it so complicated. Just use

F_grav = mg​

where m is the mass of the ball, and g ≈ 9.81 m/s².