Answer:
Tetherball is an interesting game in which two players tries to hit the ball hard so that it goes around the
pole.Each time the player hits the ball, it's orbit rises higher off the ground.Let's understand the physics
behind this.The motion of a tetherball is governed by two forces.These two forces combine to generate a
net force, i.e. centripetal force.If the ball is moving more quickly, it requires a greater centripetal force,
which in turn requires a greater tension force.Since the ball's weight hasn't changed, the angle of the
tension force changes until the ball is in vertical equilibrium.
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Ball Mass : This slider controls the mass of the ball. A ball with more mass will have more inertia, requiring
a greater net force to accelerate it. A ball with more mass will ALSO have a greater gravitational force
acting on it. Watch both of these effects occur when you manipulate this slider.
Cable Length : This slider controls the length of the cable. A longer cable is capable of allowing a greater
circular radius of motion for the ball. It is important to remember that the radius of the circular motion is
NOT equal to the length of the cable. Instead, if you want to understand the size of the circle of the ball's
motion, ignore the cable and just imagine the path of the ball.
Ball Speed : This slider controls the speed of the ball - imagine a kid just hit the ball and it sped up. A ball
moving more quickly is also accelerating more quickly because its velocity is changing as it moves in a
circle (remember that changes in DIRECTION of velocity 'count' as changes to velocity).
Force Diagram : This allows you to turn on or off the diagram of the forces acting on the ball. Look for the
ball to be in vertical force balance, which means the vertical component of tension is canceled by the
gravitational force. The ball should NOT be in horizontal force balance - it is accelerating towards the center
of the circle! It is important to note that this free body diagram should really be moving with the ball so that
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the tension force always points along the cord - we are just showing the forces at the moment the ball is at
the furthest-right on this screen.
Centripetal force vs Tetherball speed : This is a plot of centripetal force required to keep the ball in
circular orbit about the pole as a function of its speed. As expected, a more quickly-moving ball is changing
in velocity more often in a given amount of time, and so is accelerating more. This greater (centripetal, or
center-pointing) acceleration requires a greater net force.
Explanation:
to 
(from (-a/2) to
(a/2))