Finding Angle of String with Two Charged Balls

[Quinn Pochekailo]

Homework Statement

http://loncapa.vcu.edu/res/vcu/phys202/zzImages/Ch25_TB.jpg
A charged ball with charge Q1 = 0.1 μC and mass 0.05 kg is suspended from a ceiling with a thin massless string as shown in the figure. The second charged ball has a net charge Q2 = -0.5 μC and it is located d = 0.3 m away from the suspended ball. What is the angle θ that the string makes with the vertical (dahsed vertical line) as shown in the figure? Provide your answer in degrees. (Note: The dashed horizontal line is not a string or rod, it only designates the distance d between the two spheres)

Homework Equations

F=(K*Q1*Q2)/ (d^2)

The Attempt at a Solution

I converted the charges to C first, getting 1e-7 and -.5e-7. Because the charges are attracting, I found that the force is equal to 5.6e-14, which would be my force in the x component. The y force component would be equal to F=mg, which is (.05 * 10). How would I go about finding the angle with these 2 values?

 

[jbriggs444]

I converted the charges to C first, getting 1e-7 and -.5e-7. Because the charges are attracting, I found that the force is equal to 5.6e-14, which would be my force in the x component. The y force component would be equal to F=mg, which is (.05 * 10). How would I go about finding the angle with these 2 values?

You have a force whose x component is known and whose y component is known, right?

There is an easy way to do this and a hard way. The hard way is to compute the magnitude of the tension force first. You know its x and y components, so you should be able to find its magnitude. Then write down an equation for the x component of the tension force in terms of its angle and magnitude.

The easy way is to think about the ratio of the two components. There is a trig function that is equal to that ratio...

Edit: Or, there is a slightly easier way, if you are comfortable with small angle approximations.