Pendulum's Tension using Force reasoning and Newtons 3rd Law.

[spsch]

Hi, I have a conceptual question.
I was doing some problems on pendulums and found something that confused me.

I attached a drawing. I used to always solve these problems by using some trigonometry and trying to find the Tension.
i.e. $m*g = F (of the Tension) * cos(theta)$ so $\frac {m*g} {cos(theta)} = F$

But then, if I imagine the string continuing and reason that the Force of the Tension has to also equal the gravitational force in that direction I get
$F = m*g*cos(theta)$ which would make $m*g*cos(theta) = \frac {m*g} {cos(theta)}$

Could someone point out where I'm making my thought mistake? Thank you very much!

 

[mjc123]

F = mg cosθ because in the direction of the string the forces balance, there is no acceleration.
mg ≠ F cosθ because the forces don't balance in the vertical direction; the acceleration has a component in this direction (except when θ = 0).

 

[spsch]

Oh, thanks. Of course this makes absolute sense. Thank you !