Coulomb's Law and point charges

[absolutezer0es]

Two m = 6.0g point charges on 1.0-m-long threads repel each other after being charged to q = 120nC , as shown in the figure.

What is the angle θ? You can assume that θ is a small angle.

Hopefully the image will work.

I feel like something is missing. I've gotten 7.4 and 3.4 degrees - both wrong. I know the sum of the forces in all directions must equal zero. My equations then are:

Fx = -Tsinθ+Felectric
Fy = Tcosθ - mg

We know m, g, and q. I know that coulomb's law is:

F = Kq^2/r^2 ... but we don't know r.

Any ideas?

 

[ZetaOfThree]

You are given the length of the string and the angle. Do you see a right triangle you could make in order to determine r?

 

[absolutezer0es]

Ah, yes ... a little clearer now.

So sinθ = r/1 = r. Alright let me run with that. Let's see if I can get it now.

Thanks for the nudge!

 

[ZetaOfThree]

Wait! Are you sure $\sin{\theta}=r$? Remember $r$ is the distance between the charges...

 

[absolutezer0es]

When I replied, I realized I made a mistake, like you said. It's not r, but rather r/2!

I was able to boil down the equation to:

(sinθ)^2*(tanθ) = kq^2/(4mg)

I'm pretty sure you can't boil it down anymore than that, so I used my old grapher to find the intersection point between both sides.

Got it!

Thanks a ton Zeta! I appreciate the insight!

 

[nrqed]

When I replied, I realized I made a mistake, like you said. It's not r, but rather r/2!

I was able to boil down the equation to:

(sinθ)^2*(tanθ) = kq^2/(4mg)

I'm pretty sure you can't boil it down anymore than that, so I used my old grapher to find the intersection point between both sides.

Got it!

Thanks a ton Zeta! I appreciate the insight!

You can actually do it withOUT using a graph. Note the hint: you may assume that the angle is small. In that approximation, what can you say about $\tan \theta$ and $\sin \theta$ ?

 

[danielhep]

You can actually do it withOUT using a graph. Note the hint: you may assume that the angle is small. In that approximation, what can you say about $\tan \theta$ and $\sin \theta$ ?

Can you help? I worked through this and plugged my numbers in but when I try to solve for theta I don't get any kind of real number. Here's what I put in Wolfram Alpha:
http://www.wolframalpha.com/input/?...*(8*10^-9)^2/(4*4*10^-3*9.8)+for+x+in+degrees

Thanks!

 

[gneill]

Can you help? I worked through this and plugged my numbers in but when I try to solve for theta I don't get any kind of real number. Here's what I put in Wolfram Alpha:
http://www.wolframalpha.com/input/?i=(sin(x))^2*tan(x)=8.99*10^9*(8*10^-9)^2/(4*4*10^-3*9.8)+for+x+in+degrees

Thanks!

Wolfram says:

Can you explain those numbers? I recognize k and g but the rest is a mystery given the data in the problem statement of post #1.

If you are actually working on a different problem with different data please start a new thread of your own. Hijacking old threads is against the rules.