Dynamics and Circular Motion Problem

[Joseph Hotto]

Homework Statement

A 2 kg tetherball swings around a vertical pole attached to two ropes each at a 30 degree angle from vertical. Each supporting rope is 1.5 meters long, and the ball travels at 8 m/s long.

Homework Equations

The question doesn't ask what they're looking for, so I assume they are looking for the tension of the rope.
- Tension is split into a Tx and Ty component
- We draw two free body diagrams, one with a birds eye view and one with a table view.

The Attempt at a Solution

ΣFy = Tcosθ - mg
0 = Tcos(30) - 19.6
Tcos(30) = 19.6
19.6/cos(30) = T
22.6 = T

ΣFx = Tsinθ - mg
0 = Tsin(30)-19.6
0.5T = 19.6
T = 39.2

R = L * sin(30 degrees)
R = 1.5 * 0.5 = 0.75 m

- Did I do anything wrong so far?

 

[kuruman]

Did I do anything wrong so far?

Yes. You did not consider that the tensions in each rope are different.

 

[Chestermiller]

You omitted the mass times centripetal acceleration in the horizontal force balance.

 

[CWatters]

Perhaps draw a free body diagram for the ball.