Charged particle suspended from elastic cord

[jspeese]

Homework Statement

A charged particle with mass m = 200g and charge q = 25 µC is suspended from an elastic cord with force constant K = 5 N/m in a vertically upward electric field E of magnitude 3.7 x 10^5 N/C. What is extension of the cord when the particle is in equilibrium?

Homework Equations

The Attempt at a Solution

 

[issacnewton]

Hi

first draw a free body diagram. there are three forces acting on the body. $mg$ downwards , the force of restoration due to the elastic cord , according to Hook's law is
$kx$ upward and the force due to electric field $F_e$ upward. when in equilibrium, they balance.

$$F_e+kx = mg$$

solve for x, the extension.