Estimate the force a person must exert on a string attached to a 0.200 kg ball to make the ball revolve in a horizontal circle of radius 0.600 m. The ball makes 1.40 revolutions per second. Do not ignore the weight of the ball. In particular, find the magnitude of FT, and the angle θ it makes with the horizontal. [Hint: Set the horizontal component of FT equal to maR; also, since there is no vertical motion, what can you say about the vertical component of FT?]
The Attempt at a Solution
I've made a free body diagram but I was not shown how to solve any problems like this so I'm a little unsure as to how I'm going to begin. I decided to break up tension into horizontal and vertical components
horizontal tension = cos (theta) * t
vertical tension = sin (theta) * t
Then I found the acceleration by converting the revolutions per second into m/s and then finally finding the acceleration which is 1.4*(2*pi*.6)=5.277 then i converted that into acceleration since fnet=ma. v^2/r=a so 27.84/.600=46.41m/s/s
I then take this acceleration and multiply it by mass which is .2kg and I get fnet=9.28.
And here's where I become confused. I'm trying to solve for tension so I can't get rid of that variable but I'm fairly sure I need to substitute something in here for the equation to work.
Since the ball is not moving up or down we can say that
which ends up as
I have 2 variables (tension and theta) and I'm not sure where/how to substitute for this problem.