Electric Charge Applied on Two Wires of Electroscope?

[TrivialPants]

Homework Statement

A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 24-g spheres at the ends. When charged, nearly all the charge resides on the ends of the spheres. (See diagram attached)

If the wires each make a 26° angle with the vertical, what total charge Q must have been applied to the electroscope? Ignore the mass of the wires?

Diagram of the Electroscope:

Homework Equations

What does it mean to ignore the mass of 24g? Does that mean that I can find the charge by finding the distance between the two points?

The Attempt at a Solution

I split the triangle into two right triangles. Then I used the trig properties to deduce that:

sin26° = opp/hyp = .4387, opp/78cm = .4387 = opp =.4387*(78cm) =34cm
cos26° = adj/hyp = .8988, adj/78cm = .8988 = adj =.8988*(78cm) =70cm

Now using this data, I would input the distance between the repelling positive charges into the Coulombs Law:

F = (k|Q1||Q2|)/(r12)^2 Where k = 8.988x10^9 N*m^2 / C^2 and r = 68 which is derived above
(34*2) = 68 cm or 68*10-2m

How do I find the value of Force? I will be needing it to complete the problem this way. Thank you!

 

[Doc Al]

What does it mean to ignore the mass of 24g?

You are to ignore the mass of the wire, not the spheres. You'll need their mass to solve the problem.

How do I find the value of Force?

Analyze the forces acting on each sphere. Hint: Three forces act.

 

[TrivialPants]

You are to ignore the mass of the wire, not the spheres. You'll need their mass to solve the problem.Analyze the forces acting on each sphere. Hint: Three forces act.

Is the method I am using thus far correct to find the value of the Q? Since there is no mention of an electric field in this problem I assume I will be using the coulombs law equation I stated above: $$k\bullet\mid Q_1\mid\bullet\mid Q_2\mid\\r_{1,2}^2$$

 

[Doc Al]

Is the method I am using thus far correct to find the value of the Q? Since there is no mention of an electric field in this problem I assume I will be using the coulombs law equation I stated above: $$k\bullet\mid Q_1\mid\bullet\mid Q_2\mid\\r_{1,2}^2$$

Sure, you need to use Coulomb's law to calculate the total charge. (Note that Q_1 = Q_2 = Q/2.)

But you first need to do the force analysis to find the electrostatic force.