Answer to Question #85229 in Physics for Jasmina Ahmetovic

Question

A 5.29 kg ball is attached to the top of a vertical pole with a 2.31 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.41 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole.

Answer 1

We can calculate the components of the tension of the string:

T_x=T sin⁡θ=(mv^2)/r

T_y=T cos⁡θ=mg

r=l sin⁡θ

Thus,

sin⁡θ/cos⁡θ =v^2/gr=v^2/(gl sin⁡θ )

v^2/gl=sin^2⁡θ/cos⁡θ =(1-cos^2⁡θ)/cos⁡θ

(1-cos^2⁡θ)/cos⁡θ =〖4.41〗^2/(9.8∙2.31)=0.8591

cos⁡θ=0.6588

The angle, between 0° and 90°, that the string makes with the pole.

θ=cos^(-1)⁡0.6588=48.8°