Forces in a homogeneous electric field

[tomkoolen]

Hello everyone,

I was wondering if anyone could help me out with this one:

Problem statement:
A charged metal ball is hanging from a nylon wire in the space between both plates of a loaded capacitor. The ball has a mass of 9.2 grams. The distance between the hanging point and the ball's centre of mass equals 71.7 cm. After the ball has been charged, it horizontally moves 4.3 cm. See this illustration for the forces working on the ball:

Calculate the electrical force working on the ball.

My attempt at solution:
The gravitational force equals 0.0903 N which is equal to the vertical component of the tensile force. I'm actually already stuck right now because of the following problems:

1. I don't see how to calculate the angle α because I only have one side of the triangle.
2. I don't know how to write an equation for F_el because the presence of a nett force doesn't allow me to set it equal to the horizontal component of the tensile force.

Thank you very much in advance!

 

[gneill]

1. You have two sides; the length of the wire and the horizontal displacement.

2. Think about similar triangles and ratios.

 

[tomkoolen]

Thank you for your reponse! I see how to work it out with similar triangles now :)