Calculating Electric Forces with Dangling Objects

[Cory]

How do I calculate Electric forces when objects are dangling from insulated wire. For example
Neutral metal sphere A, of mass 0.10kg hangs from an insulating wire 2.0m long. An identical metal sphere B, with charge -q, is brough into contact with the sphere A. The spheres repel and stelle down as shown in the following figure

.\ <) = 12
...\
...\
...\
(B)...(A)
* <) AB(top) = 90 degrees.
Calculate the initial charge on B.

The formula's are Fe =
k*q1*q2
r^2

 

[ponjavic]

Ok Cory,a are you able to draw a FBD of the forces acting on A?

 

[Cory]

I did with electric force outward, Force of tension angled at 12degrees, and force of gravity. Then I rearranged them to make a triangle.
ie
^
.\ =Ft
...\
...\
...0---->Fe
...|
...| Fg
...\/

 

[ponjavic]

That's perfectly fine, what's your problem with solving the question then?

 

[Cory]

I can't seem to understand how to solve the FBD for fe. I tried using
tan(12) = Fe
.....m*g
but that doesn't seem to work, and I am really just not sure how to go about this.

 

[ponjavic]

That doesn't seem to be right, why would you use sin(12)=Fe?

:)

sin(12)=Fe/Ft isn't it? Think of a triangle. Thus Fe=Ft*sin(12) You can find Ft using Fg

 

[Cory]

Sorry, I edited my last post, I typed the wrong thing. Should I still try Fe = ft*sin12? I don't really understand

 

[ponjavic]

Ft*cos12=Fg help you?

 

[Cory]

I don't think so.. I'm trying to find the initial charge on A

 

[ponjavic]

Nm I see your problem, you do know Fe.

The spheres are equal so q1 = q2

Thus:
Fe = Fg*tan12
and
Fe =k*q^2*r^2

 

[Cory]

so find Fe with mg*tan12 (which is: 0.20830543) then use that to solve for q in Fe =k*q^2*r^2? why does it change from divided by r^2 to multiplied?

 

[ponjavic]

so find Fe with mg*tan12 (which is: 0.20830543) then use that to solve for q in Fe =k*q^2*r^2? why does it change from divided by r^2 to multiplied?

Oh it doesn't, misread your equation sorry ^^

 

[Cory]

I seem to still be missing radius

 

[ponjavic]

Heh sorry, it does not mean radius, r means the distance between the two particles. Are you able to find it using trigonometrics?

 

[Cory]

well yea, but then it's the same as Fe = Fg*tan12 which doesn't work. Maybe I should use the length of the rope?

 

[ponjavic]

What do you mean?

k*q^2*r^2=Fg*tan12

q=sqrt(Fg*tan12/r^2/k)