- #1

JJBladester

Gold Member

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## Homework Statement

A 450-g tetherball A is moving along a horizontal circular path at a constant speed of 4m/s. Determine

*(a)*the angle θ that the cord forms with pole BC,

*(b)*the tension in the cord.

## Homework Equations

[tex]\sum F_{y}=ma_{y}[/tex]

[tex]\sum F_{n}=ma_{n}=m\frac{v^{2}}{r}[/tex]

## The Attempt at a Solution

Find θ and T.

__Given__:

m=0.45kg

v=4m/s

__FBD__:

__Sum of forces equations__:

(1)[tex]\sum F_{y}=-mg+Tsin\theta =0 \to Tsin\theta =mg[/tex]

(2)[tex]\sum F_{n}=Tcos\theta =m\frac{v^{2}}{r} \to T=m\frac{v^{2}}{rcos\theta}[/tex]

Substitute expression for T found in (2) into (1):

[tex]\left (m\frac{v^{2}}{r} \right )tan\theta =mg[/tex]

[tex]\theta =tan^{-1}\left (\frac{gr}{v^{2}} \right )[/tex]

This is where I get stuck. I know that if I can find r, I can find θ and subsequently T. How do I find r?