Estimating charges coulomb's law

[mussgo]

this is my first time posting here in the forums right now I am really stuck with this problem
i already tried solving it on my own but i can't i will really apreciate any feedback or hint i could use to solve it U_U


Estimating Charge Two hard rubber spheres of mass ~20 g are rubbed vigorously with fur on a dry day. They are then suspended from a rod with two insulating strings of length 10 cm. They are observed to hang at equilibrium, 19° from vertical, as shown in Fig. 22-41. Estimate the amount of charge that is found on each sphere







3. The Attempt at a Solution i saw a somewhat similar problem on my text and i tried ths equation

x= (2*k*L*q^2 / mg )^1/3

where L is the length of the cord and x the separation of the balls and my final answer was wrong :S did i use the right equation :S?

 

[Mindscrape]

You shouldn't ever use an equation derived in a problem because it will almost never relate to the problem you are doing. I mean, what does x represent? Where the hell did the the cube root come from? Just as in mechanics you don't want to stray too far from F=ma or other fundamental laws, in EM you don't want to stray do far from its fundamental laws.

Let's get you on your own start. There are two forces acting in the problem. There is a force from gravity, acting on each of the masses, and there is the electric force acting on the charges the masses contain. I think you are allowed to assume that the charges have an equal amount of charge.

So when you draw the two vectors, which ones point in which direction? Where do you think the angle fits in?

 

[mussgo]

i think the angle is given so we can solve use sin(19) = x/10
and get how much the ball is being pushed by the other charge
and i see that both charges have the same amount and same charge that means
the are pushing away on each other but i really can figure out what equation to use U_U

 

[Mindscrape]

Well, yes, you will eventually need to find x, but let's first help you with the equation to use. So, if I have a gravitational force pointing downwards, and electric force pointing to the right, then what kind trig function will describe the ratio of those?

 

[mussgo]

can i get like an m*g*tan(19)

 

[Mindscrape]

Yep, so tanø = Fe/Fg

So now that we know that Fe = Fgtanø then we can look at the Fe equation more closely.

F_e = kq*q/d^2

I think you can take it from here. :)

(Make sure you use the correct distance!)

 

[mussgo]

wahhhh thxx alot
you really helpd me a whole lot xD
im pretty sure i would never have gotten the right answer alone thanks (: