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- Homework Statement
- One pith ball is mounted on an insulating stick and the other is hung on a string from the ceiling. The two balls are brought together such that they are barely touching, the initial tension is only vertical. Upon introducing a charged object to the stationary pith ball, charge is equally distributed to both of the balls. The hanging ball swings out from the mounted ball and eventually comes to rest. Your task is to determine the magnitude of charge on the balls given the following measurements:

-A pith ball has a diameter of 40mm

-The hanging ball is hung from the ceiling with a 147.3cm long string. Note: this measurement is to the top of the pith ball, not to the ball's center.

-After charging, the two pith balls have a center-center displacement of 6.40cm

- Relevant Equations
- ##F_{c} = \frac{\left ( k\left ( q_{1} \right )\left ( q_{2} \right ) \right )}{r^{2}}##

##F_{g} = m*g##

I actually found most of it out I'm just struggling with how to find the mass of the balls. I'm not sure how you would do that since could only derive two equations from the information given or are we assuming the mass is so small that it doesn't matter?

Q = charge of one pith ball

d = distance between the COM of the two balls

L = length of the string plus the radius of the ball

h = change in height after the swing (though I suppose this is probably negligible)

m = mass of pith ball

##\frac{F_{c}}{F_{g}} = \frac{d}{2} * \frac{1}{L-h}##

## F_{c} = \frac{d}{2} * \frac{1}{L-h} * F_{g}##

##\frac{d*m*g}{2(L-h))} = \frac{k*Q^{2}}{d^{2}}##

√##\frac{d^{3} * m * g}{2(L-h) * k)}## = Q

Any help would be appreciated. Thanks in advance!

Q = charge of one pith ball

d = distance between the COM of the two balls

L = length of the string plus the radius of the ball

h = change in height after the swing (though I suppose this is probably negligible)

m = mass of pith ball

##\frac{F_{c}}{F_{g}} = \frac{d}{2} * \frac{1}{L-h}##

## F_{c} = \frac{d}{2} * \frac{1}{L-h} * F_{g}##

##\frac{d*m*g}{2(L-h))} = \frac{k*Q^{2}}{d^{2}}##

√##\frac{d^{3} * m * g}{2(L-h) * k)}## = Q

Any help would be appreciated. Thanks in advance!