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

Answer:

The tangential speed of the ball is 11.213 m/s

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:

$Tcos70=mg\\Tsin70=\frac{mv^{2} }{r}$

Replacing:

$\frac{mg}{cos70} sin70=\frac{mv^{2} }{r} \\Clearing-v:\\v=\sqrt{rgtan70}$

Replacing:

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