Question

1. A tetherball (aka conical pendulum, like the one we showed in class!) is attached to a string and is rotating around in a horizontal circle. The length of the string is 2.000 meters (which is not

   2 the radius!!) and it takes 0.8000 seconds for the ball to go around once. Use g = 9.807 m/s .

   What angle does the string make relative to vertical? Write your answer to 4 sig figs.

Answer 1

Gravitational acceleration = g = 9.807 m/s²

Mass of the tetherball = m

Length of the string = L = 2 m

Angle the string makes with the vertical =

Radius of the circle = R

R = LSin

Speed of the tetherball = V

Time taken by the ball to go around once = T = 0.8 sec

VT = 2R

Tension in the string = F

The horizontal component of the tension provides the centripetal force for the circular motion of the tetherball.

The vertical component of the tension supports the weight of the tetherball.

FCos = mg

Dividing these two equations,

\

Cos = 0.0795

= 85.44^o

Angle the string makes relative to the vertical = 85.44^o