Question

A tetherball is tied to the end of a string of negligible mass. The ball is struck so that it moves in uniform circular motion in a horizontal plane, and the string makes an angle of 26° with the vertical pole. The mass of the ball is 1.3 kg. What is the ball's speed

Answer 1

The centripetal force is directed parallel to the string and the weight of the ball is always directed downwards. Making a force balance along the direction of vertical axis:
Fc cos 26 = W
where Fc is the centripetal force which is equal to mv2/r
W is the weight which is equal to mg

m v2 /r cos 26= mg
v2 /r cos 26 = g
v2 = rg cos 26
v2 = 2.1(9.81) cos 26
v = 4.30 m/s

The ball's speed is 4.30 m/s.

Answer 2

Answer:

v =  24sqrt{r} m/s

Explanation:

as vertical force is equal to weight,

hence W= Fc Cos 26

now ,   mass= mg

and Fc= mv^{2}/r

where r is the length of string.

putting all the values together in equation 1 :

mg = mv^{2}/r Cos 26

v^{2} = rg Cos 26

v^{2} = r (9.8) Cos 26

v^{2} = 9.8 * (.64691) r

   v =  24sqrt{r} m/s