Physics 2 , two Styrofoam balls on insulated thread

[nathancurtis11]

Homework Statement

Two small .1 gram stryofoam balls are strung like beads on a vertical insulating thread. The lower ball is glued to the thread but the upper ball is free to move. Imagine that both are given an equal amount of negative charge such that the upper ball is suspended about the lower with their centers 4.0 cm apart. (Assume that each ball repels the other as if it were a point charge located at its center.) Roughly how many electrons have been added to each ball? Express your result as a fraction of the total number of electrons initially inside each ball.

Homework Equations

E = (kq1q2) / r^2

One electron = 1.6 x 10^-19 Coulombs

k = 9 X 10^ 9 N m^2 / c^2

The Attempt at a Solution

Assumed the force was now close to zero if the top ball is now suspended in the air instead of being pushed upward. But then you just get both charges to be zero which would be incorrect. Not sure any other way to do this.

 

[mfb]

Don't forget gravity. The upper ball (that is free to move) is in a force equilibrium.

 

[nathancurtis11]

So would force be -9.81 then?? so -9.81 = (kq1q2) / r ^ 2 ?

 

[mfb]

A force is not a number, it has units.
What is the gravitational force on the styrofoam ball?

 

[nathancurtis11]

-9.81 Newtons.

 

[nathancurtis11]

so -9.81e-6 N c = ( 9e9 N m^2 / c ^2 (q^2) ) / ( .04m ^ 2)

solve for q from there?

 

[mfb]

-9.81 Newtons.

How did you get this value? It is wrong.

Another issue: If you set those forces equal, they should have the same sign.

 

[nathancurtis11]

I thought since the ball was stationary then the force by the lower ball on the upper ball had to be exactly equal to the force by gravity, therefore would be the gravitational constant of 9.81

 

[mfb]

The gravitational constant is something different.
Check the equation for the gravitational force. And please do not forget units. They are exactly the right tool to avoid the mistakes you make.

In particular, do you expect all objects on Earth to have the same force? An elephant as much as a mouse? Do you see the issue?