Two pith balls hang from a string and are equally charged. Mass of each ball: .0

Question

Two pith balls hang from a string and are equally charged.

Mass of each ball: .05g

Distance bewteen the balls: 8cm

Angle between the vertical and one string: 6 degrees

Between the two strings: 12 degrees

How many electrons are on each pith ball?

What is the gravitational attraction?

What is the electrical force?

What are the horizontal and vertical force vectors?

What is the theoretical charge on each pith ball?

When asked to draw a free body diagram showing gravity (weight), string tension, and coulomb force - how do you calculate the string tension?

I've run through a bunch of calculations but it's all jumbled and I'm struggling to relate different equations and components. So please list equations used to calculate values and give a detailed explanation.

Thank you!

Explanation / Answer

here ,

for number of electrons ,

N = charge on the balls/charge of 1 electron

N = 6.168 *10^-9/( 1.602 *10^-19)

N = 3.849 *10^10
---------------------------------------

the number of electrons on each ball is 3.849 *10^10

gravitational attraction force = G*m*m/d^2

gravitational attraction force = 6.673 *10^-11 * (0.05 *10^-3)^2/(0.08)^2

gravitational attraction force = 2.61 *10^-17 N

the gravitational attraction force between the balls is 2.61 *10^-17 N

---------------------------------------

electrical force = k * q*q/d^2

electrical force = 9*10^9 * (6.168*10^-9)^2 /.08^2

electrical force = 5.35 *10^-5 N

the electrical force between the ball is 5.35 *10^-5 N

----------------------------
horizontal force , Fh = mg*tan(6)

horizontal force , Fh = 0.05 *10^-3 * tan(6)

horizontal force , Fh = 5.26 *10^-5 N

----------------------------
vertical force = mg

vertical force = 0.05 *10^-3 * 9.8

vertical force = 4.9 *10^-3 N

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