Static system + a second long distance force

[imzkris]

Homework Statement

When an electrically charged object (a proton, an electron, a balloon after you’ve rubbed it
on your hair) is placed in an electric field, E , an electric force proportional to this field acts
on the object. Specifically,

F = qE

where q is the charge on the object and is in units called Coulombs (C).

The figure shows a pendulum, the bob of which is charged. The ambient electric field is
uniform, directed toward the right, and has a magnitude of 2 × 10^5 N/C. The pendulum
hangs at an angle of 20 degrees as a result of the forces acting on it. What is the charge on the bob of the pendulum? The string can be considered of negligible mass and uncharged.

So:

(theta) = 20 degrees
E = 2 x 10^5 N/C
m = 5.0g (or 0.005kg)
a(g) (acceleration due to gravity) = -9.8m/s
F(e) (force of electric... thing) = ?
T(xy) (x and y component of tension in rope) = ?
F(net) (net force) = 0

Homework Equations

F = ma
F = qE
probably like four I can't remember

The Attempt at a Solution

I know that F(net) is zero, 'cause it's a static system. So:

F(net) = T(xy) - F(e) - F(g) = 0

The force of gravity is 0.049N (0.005kg*9.8m/s^2).

But I have no idea how to find the tension in the rope. If I could get it, the only thing left would be to solve for F(e) using the net force equation, and then rearrange the F(e) = qE equation to solve for q, but that's the easy part.

The second long-distance force is throwing me off. Also, I forget all of high school trig (it's been like, four years) and even then I'm not sure how I would apply it. cos(theta)*T(xy) = T(y), sin(theta)*T(xy) = T(x) (which, I'm kind of grabbing at straws here, so I give myself a 50/50 chance on being right). So what - I can't see a way for me to get or apply either of those. I'm stuck. :<

Thanks for reading.

EDIT: Is the magnitude of T(x) just the same as F(g)? If it is I'm going to be mad, 'cause this took way too long. :'(

 

[tiny-tim]

Welcome to PF!

The ambient electric field is
uniform, directed toward the right, and has a magnitude of 2 × 10^5 N/C. The pendulum
hangs at an angle of 20 degrees as a result of the forces acting on it. What is the charge on the bob of the pendulum?

Hi imzkris! Welcome to PF!

You could find T by taking vertical components …

but you don't need to find T …

when there's an unknown force in a known direction, like T, just take components perpendicular to that unknown force.

 

[imzkris]

I'm... not following. :shy:

 

[tiny-tim]

ok … the tension force, T, is along the string, at 20º to the vertical.

So take components perpendicular to that (at 20º to the horizontal).

Then the component of T in that direction will be Tcos90º = 0,

and the components of the other forces are … ?