Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Whirling a ball on a string

Joe ties a ball of mass m = 0.5 kg onto a string of radius R = 1.5 m. He then whirls the ball around in a horizontal circle so that it completes 2 revolutions each second.

For the moment, assume that the string is perfectly horizontal, and ignore the force of gravity.

  1. What is the speed v of the ball?
  2. What is the tension in the string?

Of course, in real life, the string is not perfectly horizontal. Instead, it dips slightly from Joe's hand to the ball, at some angle below the horizontal.

Suppose that all else remains the same: m = 0.5 kg, R = 1.5 m, and the ball completes 2 revolutions per second.

  1. Make a picture showing all forces on the ball.
  2. Make a table which describes all the forces on the ball in each direction, horizontal and vertical.
  3. Write down Newton's Second Law in each direction.
  4. You should find two equations for two unknowns, the tension of the string T and the angle theta. Solve for both the angle and the tension.

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.