a tetherball is on a 21.0 m string which makes an angle of 44.0 degree with the vertical as it moves around the pole in a horizontal plane. If the mass of the ball is 1.30 kg what is the ball's speed?
See the attached image with the explanations.
The ball has a circular motion in the horizontal plane. It is subjected to centripetal acceleration. This acceleration is given by the centripetal force which acts towards the center of the circle of motion by the horizontal component of the tension of the string.
T = tension of the string
F = centrifugal force
For the vertical equilibrium of the ball
`Tsin46 = 1.3g`
`T = 17.73N`
For the circular motion using F = ma (Newton second law of motion)
`Tcos46 = 1.3xxv^2/R`
The radius of circular motion is given by;
`R = 21cos46 = 14.59`
`17.73cos46 = 1.3xxv^2/14.59`
`v = 11.76m/s`
So the speed of the ball at this moment is 11.76m/s.