How Does Coulomb's Law Explain the Movement of a Cobweb?

[Shilly]

Homework Statement

A dust cobweb is drawn from an initial vertical position toward a nearby wall by an electrostatic force. Assume the cobweb to be like a single dust ball of mass 2.0 x 10^-7g suspended on a massless string of length 0.42 m connected a horizontal distance of 0.35 m from the wall, as shown below. The tethered dust ball is drawn to the wall by another similar dust ball of opposite charge, -q = -3.0 x 10^-6C, as shown.

a) Draw a free-body diagram for the tethered dust ball in its final resting position.

b) Transfer the force information from the free-body diagram to a triangle. (I think they mean a component triangle)

c) What is the final charge on the cobweb?

Homework Equations

F_e = $$\frac{Kq_{1}q_{2}}{d^{2}}$$

where F_e is the electric force between two objects
K is Coulomb's constant (9.0 x 10⁹ Nm²/C²)
q₁ is object 1's electric charge
q₂ is object 2's electric charge
d is the distance between centers of charged objects

The Attempt at a Solution

a) just draw the Normal Force, Force of Gravity, and the Electric force?

b)unsure, but i could figure this out alone

c) Would I just solve for the distance between the two dust balls and then sub that into the equation above, using +q for q₁ and -q for q₂ and 9.0 x 10⁹ for K?

edit: bah, nevermind that failed. need help for c)

 

[Doc Al]

The Attempt at a Solution

a) just draw the Normal Force, Force of Gravity, and the Electric force?

Instead of "normal force", that should be tension.

c) Would I just solve for the distance between the two dust balls and then sub that into the equation above, using +q for q₁ and -q for q₂ and 9.0 x 10⁹ for K?

You would use that formula (Coulomb's law) to solve for the magnitude of the electric force in terms of the charges. (In what direction does that force act?) The negative charge is given; the positive charge is unknown--that's what you are trying to solve for. (It's a bit confusing that they called the charges +q and -q. If that were true, you wouldn't need to solve for anything!)

Yes, you'll have to compute the distance between the charges.

Hint: You'll need to analyze both vertical and horizontal force components on the tethered dustball.