Question

A tetherball swings around a pole, making a full circle once every 2s. The total length of the rope is 2 m. Calculate the angle θ that the rope makes with the pole. The rope has negligible mass.

Answer 1

here is the force diagram

using Newton's second law

In x - direction

Tsin = ma_x

a_x = Tsin / m ----------- (1)

In y - direction

Tcos - mg = ma_y ---------------- (2)

there is no acceleration in y - direction

so,

equation (2) becomes

Tcos - mg = 0

and

a_x = v² / r

where

r = L sin

and

v = 2r/ t

so,

a_x = 4r² / t² r

a_x = 4²r / t²

a_x = 4² L sin / t²

so,

4² L sin / t² = Tsin / m

T/m = 4² L / t² ----------- (3)

and from y - equation

T/m = g / cos ----------- (4)

from (3) and (4)

= arccos ( gt² / 4² L )

= arccos ( 9.8 * 2² / 4² 2)

= 60.233 degree