Answer to Question #163042 in Physics for mia

Question

A tetherball as shown is moving in a horizontal circular fashion around a poleThe rope makes an angle of with the pole. The tension on the rope is 4.25 N. What is the mass of the ball? What is the centripetal acceleration (ac) of the ball?

Answer 1

The mass of the ball can be found from the fact that the ball does not change its height above the ground: the weight is equal to the vertical component of tension:

$$mg=T\text{ cos}\theta,\\\space\\ m=\frac{T\text{ cos}\theta}{g}=0.434{ cos}\theta.$$

The centripetal force is equal in magnitude to the horizontal component of tension:

$$F_C=ma_c=T\text{ sin}\theta,\\\space\\ a_c=\frac{T\text{ sin}\theta}{m}=9.8\text{tan}\theta.$$