Solving Tetherball Problem: Find Tension & Angle θ

[ybgl]

Homework Statement

A .3 kg ball is attached to a string that is 50.0 cm in length, and completes 2 circles every second. Find the tension required to whirl the ball with the given constraints and also find the angle θ

2. The attempt at a solution
I only have that Ftcosθ = Mg and that mv^2/r = ftsinθ
I don't know where to go from there since all I have is the length and mass because to find the radius it is r=Lsinθ which I cannot find without θ...

 

[Andrew Mason]

Homework Statement

A .3 kg ball is attached to a string that is 50.0 cm in length, and completes 2 circles every second. Find the tension required to whirl the ball with the given constraints and also find the angle θ

2. The attempt at a solution
I only have that Ftcosθ = Mg and that mv^2/r = ftsinθ
I don't know where to go from there since all I have is the length and mass because to find the radius it is r=Lsinθ which I cannot find without θ...

Welcome to PF!

This is just an algebra problem now. You have done the physics!

2 equations. 2 unknowns. Solve. Hint: try dividing the two equations.

AM

 

[ybgl]

I have tried, it gives me (g)(r)sinθ/cosθ=v^2 which is 3 unknowns since I don't know radius, velocity, or θ

 

[Andrew Mason]

I have tried, it gives me (g)(r)sinθ/cosθ=v^2 which is 3 unknowns since I don't know radius, velocity, or θ

You can work out r from L and θ. θ is the downward angle that the tether makes as measured from the horizontal, so r = Lcosθ. Just substitute into your equation.

v can be determined from the period and radius. Or you can just use mω²r for centripetal force.

AM

 

[Lesleyanne]

You can work out r from L and θ. θ is the downward angle that the tether makes as measured from the horizontal, so r = Lcosθ. Just substitute into your equation.

v can be determined from the period and radius. Or you can just use mω²r for centripetal force.

AM

And where do the solution go from here .Kind of stuck somewhere

 

[berkeman]

Welcome to PF, @Lesleyanne

This thread is over 8 years old, so it's best if you start a new thread here in the Homework Help, Introductory Physics forum and show your work on your problem. That's the best way to get tutorial help with your schoolwork here. Thanks.