Question

A 0.700-kg ball is on the end of a rope that is 2.30 m in length. The ball and rope are attached to a pole and the entire apparatus, including the pole, rotates about the pole’s symmetry axis. The rope makes a constant angle of 70.0° with respect to the vertical. What is the tangential speed of the ball?

Answer 1

The tangential speed of the ball is 11.213 m/s

Step-by-step explanation:

The radius is equal:

`r=2.3*sin70=2.161m` (ball rotates in a circle)

If the system is in equilibrium, the tension is:

`Tcos70=mg\\Tsin70=(mv^(2) )/(r)`

Replacing:

`(mg)/(cos70) sin70=(mv^(2) )/(r) \\Clearing-v:\\v=√(rgtan70)`

Replacing:

`v=\sqrt{2.161x^(2)*9.8*tan70 } =11.213m/s`