- #1

tmanderson

- 4

- 0

## Homework Statement

A 0.020-kg mass is attached to a 1.2-m string and moves in a horizontal circle with a constant speed of 1.50 m/s, as shown in the figure. What is the measure of angle

*θ*?

What is given:

- m = 0.020kg
- v = 1.50 m/s
- L = 1.2 m

## Homework Equations

Lengths

- L = 1.2m
- Lsinθ = r

- Tx = Tsinθ = Fc
- Ty = Tcosθ
- T = mg/cosθ

## The Attempt at a Solution

What would solve this:

- atan(Fc/mg) – (Fc needs r)
- atan(r/h) –(r is unknown, and h would require knowing θ or r)

- T = mg/cosθ
- Fc = Tsinθ
- Fc = mg/cosθ * sinθ
- Fc = mg*sinθ/cosθ
- Fc = mv
^{2}/r - mv
^{2}/r = mg*sinθ/cosθ - r is unknown, but r = Lsinθ
- mv
^{2}/Lsinθ = mg*sinθ/cosθ - mv
^{2}/L = mg*sin^{2}θ/cosθ - mv
^{2}/mgL = sin^{2}θ/cosθ - v
^{2}/gL = sin^{2}θ/cosθ

My problem continually being the sin

^{2}θ/cosθ, making that not tanθ. If there's something I missed, I feel like it might be some trig identity or sloppy algebra? Nothing came to mind immediately. Every solution path I went, I always ended up needing θ or 'r'. Would really appreciate some help with this one, as I've been consuming too much time with this single scenario. Thank you!