Clarification on calculating Electrical Force and charge

[yudi]

Please see the following question and the answer. I don't understand how Fe/Fw = 0.12/0.43

Question?
Two small metal-coated styrofoam spheres each of mass 2.80e-6 kg are
attached to nylon threads 45.0 cm long and hung from a common point. The
spheres are then charged equally negative and the angle each supporting thread
makes with the vertical is 16°. Calculate the charge on each sphere.

Answer:

let Fe = electrical force
Fw = Weight force = 2.8e-6 X 9.8 = 2.744e-5 N
if θ = 16°, then hypotenuse = 0.45m, Opposite = 0.12 m, and adjacent = 0.43m

If the system is blanced:

Fe/Fw = 0.12/0.43

Can someone please explain the above equation?

Thank You.
Yudi

 

[berkeman]

Please see the following question and the answer. I don't understand how Fe/Fw = 0.12/0.43

Question?
Two small metal-coated styrofoam spheres each of mass 2.80e-6 kg are
attached to nylon threads 45.0 cm long and hung from a common point. The
spheres are then charged equally negative and the angle each supporting thread
makes with the vertical is 16°. Calculate the charge on each sphere.

Answer:

let Fe = electrical force
Fw = Weight force = 2.8e-6 X 9.8 = 2.744e-5 N
if θ = 16°, then hypotenuse = 0.45m, Opposite = 0.12 m, and adjacent = 0.43m

If the system is blanced:

Fe/Fw = 0.12/0.43

Can someone please explain the above equation?

Thank You.
Yudi

Welcome to the PF.

Is there a diagram included with this problem? It would be easier to explain it if you showed the diagram.

Also, what are the relevant equations when solving problems that involve charges and forces? There is an equation that relates the force to the two charges and the distance between them. Can you list that equation please?

 

[yudi]

Is there a diagram included with this problem? It would be easier to explain it if you showed the diagram.

No. There is no diagram given with the question. I used the info in the question to draw the triangle. With 32° at the apex and as the included angle and 0.45 m as the sides.

Also, what are the relevant equations when solving problems that involve charges and forces? There is an equation that relates the force to the two charges and the distance between them. Can you list that equation please?

Fe = kq₁q₂/d²

To use the above equation, I need the Electrical force. This is where I am stuck.

I looked at the answer and it has the following:
In a balanced system:

F₁/F₂ = s₂/s₁

How is F_e/F_w = 0.12/0.43

If the forces are in a straight line, the above equation makes sense but in this case, they are at an angle.

 

[SammyS]

Draw a free body diagram for each sphere.

The gravitational force is at a right angle to the electric force. Each sphere is in equilibrium, so there must be a third force acting on each sphere.

 

[yudi]

No extra information other than what's in the question is given.
Can someone please explain the logic in solving this problem.
I don't need the answer, just pointers on how to solve this question.

 

[berkeman]

No extra information other than what's in the question is given.
Can someone please explain the logic in solving this problem.
I don't need the answer, just pointers on how to solve this question.

Did you read SammyS' post?