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

In summary, the conversation discusses a conceptual question about pendulum problems and the confusion around finding the tension using trigonometry. The speaker shares their approach of using the equation m*g = F (of the Tension) * cos(theta) and how it conflicts with their realization that the force of tension must also equal the gravitational force in the direction of the string. This is clarified by another speaker who explains that the forces balance in the direction of the string, but not in the vertical direction.
  • #1
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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!
 

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  • #2
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).
 
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  • #3
Oh, thanks. Of course this makes absolute sense. Thank you !
 

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