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A 20-kg ball has a hole with a rod passing through. The rod exerts a force as needed that constrains the ball to move along the rod. An applied force is now added (the "pulling" force) so the ball is pulled as shown (position is given in meters and time is given in seconds). The pulling force vector is shown as a red arrow, and the force makes an angle θ with the horizontal. The velocity is given in meters/second. You may adjust the angle and/or the magnitude of the pulling force (F < 7 N). Restart.

1. How does the work done by the pulling force change as you vary the pulling force for a constant angle?
2. How does the work done by the pulling force change as you vary the angle for a constant pulling force?
3. Combine your answers above to obtain a general mathematical formula for the work done on the ball due to an arbitrary pulling force.
4. Determine the general mathematical formula for the work done by the force the rod exerts on the ball when an arbitrary force is applied to the ball.