Charges on two small spheres suspended from a thread

[OmegaFury]

Homework Statement

Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point by threads of length L = 0.30 m. What is the charge on each sphere if the threads make an angle θ = 20° with the vertical?

Homework Equations

F=k|q₁q₂|/r²

The Attempt at a Solution

I found the opposite side of one of the triangles to be around 0.10m (0.30mSin(20°)=opp). So the radius between the two charges would be 2 x opposite side length= 0.20m. Without knowing the force between the two charges, I'm at a loss as to how to find the charge on each sphere. I do have an idea: I find it strange to have two spheres floating without coming together due to gravity, so I'm guessing that for this to happen, the electric force may be equal to and in opposition to the gravitational force. Is this the right line of thinking?

 

[Villyer]

Yes, that line of thinking is correct.

 

[OmegaFury]

Alright. So. I can't use the equation F_g=Gm₁m₂/r² since I do not know the position of the spheres relative to the earth. So I set up a coordinate system, of which the origin is in the middle where the two threads meet. Gravity only affects the y-direction, so the x-components are irrelevant. I labeled the two spheres m1 and m2 respectively. I made the y-direction below the origin to be the positive y-direction, therefore the sum of the forces in the y direction is equal to F_ym1+F_ym2. F_ym1=mgsin(20°)=0.05N. F_ym2 is equal to the same thing, therefore the sum of the forces in the y-direction is equal to 0.10N. I'm assuming that the charges on both of the spheres are equal, so q₁ times q₂ is equal to q². Rearranging the electric force equation, I got q=sqrt(Fr²/K). q=sqrt(0.10N x (0.20m)²/k)= 6.67 x 10^-7C. Unfortunately, this is not the correct answer.

 

[darkxponent]

how can electrostatic force oppose gravitational force when both are at right angles. Further electrostatic force is an internal force for the 'system of two charged spheres' so it cannot effect the state of 'system'. You are missing one more force.

 

[OmegaFury]

how can electrostatic force oppose gravitational force when both are at right angles. Further electrostatic force is an internal force for the 'system of two charged spheres' so it cannot effect the state of 'system'. You are missing one more force.

I was wondering about that, direction-wise. The electrical force is only affecting the x-direction... If there is a missing force, I do not know of what it may be.

 

[darkxponent]

Can you show me the FBD. Always draw FBD(free body diagram) when you are solvimg mechanics questions

 

[OmegaFury]

Can you show me the FBD. Always draw FBD(free body diagram) when you are solvimg mechanics questions

Well, it's not necessarily a mechanics question. I just thought a mechanics approach could solve the problem. The problem here is that I have to find the charge on the two spheres, even though I don't even know the electrical force between them. If F_g-F_e does not equal zero (F_g=F_e), as they don't work in the same direction, then I can't use the electrical force equation to solve for q. That makes a FBD kind of useless, doesn't it?

 

[Darth Frodo]

I've attempted this but I'm not sure I'm right. Do you happen to have the correct answer?

 

[OmegaFury]

I've attempted this but I'm not sure I'm right. Do you happen to have the correct answer?

Yes, I do. It's 2.9 x 10^-7C

 

[Darth Frodo]

Ok didn't get it 1st go, but got it now.

So tell me...

What force/s act in the y direction?

What force/s act in the x direction?

What is the angle created by this triangle?

TRY AN FBD. IT WILL HELP GARGANTUANALLY.