Static system + a second long distance force

In summary, when an electrically charged object is placed in an electric field, a proportional electric force acts on the object. In the given scenario, a pendulum with a charged bob is hanging at a 20 degree angle due to the forces acting on it. The ambient electric field is uniform and has a magnitude of 2 × 10^5 N/C. To find the charge on the bob, the net force equation is used, with the known forces being the tension in the rope and the force of gravity. The tension in the rope can be found by taking components perpendicular to the unknown force, and then solving for the charge using the equation F = qE.
  • #1
imzkris
2
0

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).

diagram.png


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. :'(
 
Last edited:
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  • #2
Welcome to PF!

imzkris said:
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! :smile:

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. :wink:
 
  • #3
I'm... not following. :shy:
 
  • #4
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 … ? :smile:
 

What is a static system?

A static system is a system in which all forces are balanced and there is no net movement or acceleration.

What is a long distance force?

A long distance force is a force that acts on an object from a distance, such as gravity or electrostatic force.

How does a second long distance force affect a static system?

A second long distance force can disrupt the balance of forces in a static system, causing movement or acceleration.

Can a static system have more than one long distance force?

Yes, a static system can have multiple long distance forces acting on it as long as the forces are balanced.

What is the mathematical equation for determining the net force in a static system with multiple long distance forces?

The mathematical equation for determining the net force in a static system with multiple long distance forces is Fnet = ΣFlong distance, where ΣFlong distance represents the sum of all the long distance forces acting on the system.

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