- #1

Civil_Disobedient

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## Homework Statement

Two small balls, each of mass 5.0 g, are attached to silk threads 50 cm long, which are in turn tied to the same point on the ceiling, as shown below. When the balls are given the same charge Q, the threads hang at 5.0° to the vertical, as shown below. What is the magnitude of Q? What are the signs of the two charges?

## Homework Equations

Coulomb's Law: F = k*q^2 / r^2

## The Attempt at a Solution

Here's the drawing of the problem:

So far I've found distance

*r*by dividing each half into 2 triangles and using trig:

*0.05 * sin5 = r/2*

r = 0.0087m

r = 0.0087m

To find Q, I rearranged Coulomb's Law like so:

*F = k*q^2 / r^2*

F*r^2 = k*q^2

q = sqrt(F*r^2 / k)

F*r^2 = k*q^2

q = sqrt(F*r^2 / k)

To find force, I used F = mg

*F = 5g * 10 = 50N per ball, 100N total for two balls*

From there, I plugged in what I got

*q = sqrt(F*r^2 / k*

q = sqrt(100*0.0087^2 / 9*10^9)

q = 9.17 * 10^-7C

q = sqrt(100*0.0087^2 / 9*10^9)

q = 9.17 * 10^-7C

So I ended up with 9.17 * 10^-7C, which I feel is wrong (I suspect I may have calculated force wrong) but I don't have an answer or solution key and sadly can't check mines or any other solutions. Any help is appreciated!

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