Understanding F=ma: How to Prove It with Conical Pendulum Equations"

[wanu]

It's not a problem, it's a proof. The trouble being that I'm not entirely sure what I'm supposed to be proving, which is why I'm getting so confused. Our instructor told us to verify F=ma using the equations that we got from a conical pendulum lab. When further prompted, he said to divide them (which I took to mean finding the tangent) There was also mention of showing the relationship between m (mass), l (length of the string the mass was on), R (the radius of the circle), and P (the period. (In retrospect, that seems to be the most important instruction.)



Although I keep confusing myself, this is what I think I know:
where T refers to the Tension force
T_x =Tsin(theta T) =mv^2/R
T_y= Tcos(theta T)=mg
and from those I got tan(theta)=v^2/Rg=4pi^2R/Pg



And that's where I get stuck, because I'm not entirely sure how to include l in the relationship, and if I do it should have to do with h (the height of the theoretical triangle), right? So if that's true, how do I take that into account and what should I be doing with the tan(theta)?

Any help or guidance would be greatly appreciated-- I really just want to be able to wrap my head around this.

 

[Kurdt]

If you have a look at the circular motion equations you can probably substitute in for acceleration to get all the quantities you want. Just remember your trigonometry as that is where you will get the length of the string into the equation.