Did I Approach the Electrostatic Force Derivative Correctly?

[a_ng116]

Well,I've tried attempting this problem but I am not sure if I approached it the right way. Here is a link for the diagram and the question.

[PLAIN]http://img.photobucket.com/albums/v367/crazy_cat_lady/physics/diagram1.bmp[/URL]

If anyone could check it over and point out any mistakes and tell me if I make any sense what so ever,then you would make my day.

My solution:

Fe=Fg therefore
qE=mg ------> E=mg/q

x-component: Ex¹= Ecosø
= Fe/q cosø
= mg/q cosø

y-component: Ey¹= Esinø
= Fe/q sinø
= mg/q sinø

E¹= square root of (mg/cosø)² + (mg/sinø)²

Another solution that I thought up of:

Isn't tension just the sum of all forces acting on a object...therefore:

Ft= Fe+Fg
Fe= Fg-Ft
= mgsinø- Ft

 

[cepheid]

Fe=Fg

Just wondering why this very first step? I didn't see that in the problem, although I could be blind

Also, just as an FYI, it should be a 'derivation' in the thread title, since that is the term for arriving at an equation by deriving it. A "derivative" is something else in calculus, and so that confused me initially.

If you explain that first step, I should be able to help further...

As for this question:

Isn't tension just the sum of all forces acting on a object...

I'm afraid that the answer, in general, is no. Tension is just the name given to a force tending to 'stretch' an object, i.e. pull it apart. When referring to some object suspended by a rope, the object pulls on the rope, which pulls back up on the object, keeping it suspended. The rope is taut, not slack, so it is in tension.

 

[Nylex]

Yeah, the first line of your working should be Fe = Ftsin θ.

Also, how are you getting x and y components of the electric field? E is in the direction of Fe and from the diagram, Fe is only in the x direction.

 

[a_ng116]

Hmmm...alright.It actually somewhat makes sense. There is only an x-component to the electrostatic force so starting with what nylex suggested Fe=Ftsinø,would it be true then to say that:

Fe=Ft-Fgsinø
= ma- mgsinø

My rationale for this is that Earth exerts a downward force F=-mg on the test body correct?So the test body exerts and upward force F=+mg on the earth. The upward force is caused by the tension on the thread holding the test body and this is working against gravity keeping it suspended, hence Ft=ma. Anyways...more feedback would be much appreciated even despite not making much sense before in my previous derivation. And you know, if I'm completely wrong again here.