Calculating Tension and Electric Force in an Electricity Experiment

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Homework Statement


In an electricity experiment, a 1.30 g plastic ball is suspended on a 54.0 cm long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force vector F elec on it, causing the ball to swing out to a 21.0 angle and remain there.

1.) What is the magnitude of vector F?
2.)What is the tension in the string?

Any help would be appreciated!

The Attempt at a Solution


I honestly have no idea how to start it. A step by step on how to solve it would be nice but any help is appreciated.
 
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Draw a picture, put the forces on and resolve.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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