Conical pendulum with two charges

[Gabriel Maia]

The sistem above is the one I'm interested in. There is two equally charged spheres spinning on a plane. The line has L=\sqrt{2} m and the spheres weight 0.6Kg. The angular speed is \omega = 2rad/s.

The radius for the circular trajectory is R=1m and so the centripetal force is F_{c}=m\omega^{2}R=2.4N.

I must find the charges q so

2.4=k\frac{q^{2}}{(2R)^{2}}, right? Where k=9*10^{9}N m^{2} C^{-2}.

I found q=32.7\mu C but the problem is said to have an answer 40\mu C.

Where have I commited a mistake if any?

Thank you.

 

[haruspex]

Maybe you mistyped some numbers, but the centripetal force you calculated seems a couple of orders of magnitude off.
Secondly, you show the spheres as having the same charge, not opposite charges, so they are not going to provide a force in the right direction.
Thirdly, the diagram makes it look as though they are suspended from wires. Is that the case?

 

[Gabriel Maia]

Maybe you mistyped some numbers, but the centripetal force you calculated seems a couple of orders of magnitude off.
Secondly, you show the spheres as having the same charge, not opposite charges, so they are not going to provide a force in the right direction.
Thirdly, the diagram makes it look as though they are suspended from wires. Is that the case?

I mistyped the angular velocity. I wrote 0.2... now it's corrected. It should be 2.

They are repelling each other and yes they are suspended from wires. The component of the wire's tension pointing to the center of the circular trajectory balances the Coulomb force. This system is spinning in this configuration.

 

[haruspex]

I mistyped the angular velocity. I wrote 0.2... now it's corrected. It should be 2.

They are repelling each other and yes they are suspended from wires. The component of the wire's tension pointing to the center of the circular trajectory balances the Coulomb force. This system is spinning in this configuration.

Ok, so draw yourself a free body diagram of one charge. What are the forces on it and which way do they act? What do the horizontal and vertical F_net=ma equations tell you?