Answer
a) $ F=5\times 10^{-4}N $
b) $ T=1.46\times 10^{-3}N $
c) $ q=4.83\times 10^{-9}C $
Work Step by Step
(a) We can find the required electric force as follows:
$ F=mgtan20^{\circ}$
We plug in the known values to obtain:
$ F=(0.14\times 10^{-31}Kg)(9.8m/s^2)tan20^{\circ}$
$ F=5\times 10^{-4}N $
(b) The required tension can be determined as
$ T=\frac{mg}{cos20^{\circ}}$
We plug in the known values to obtain:
$ T=\frac{(0.14\times 10^{-3}Kg)(9.8m/s^2)}{cos20^{\circ}}$
$ T=1.46\times 10^{-3}N $
(c) We know that
$ q=d\sqrt{\frac{mgtan\theta}{K}}$
We plug in the known values to obtain:
$ q=(0.0205m)\sqrt{\frac{(1.4\times 10^{-4}Kg)(9.8m/s^2)tan20^{\circ}}{8.99\times 10^9Nm^2/C^2}}$
$ q=4.83\times 10^{-9}C $
