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# Exploration 6.4: Change the Direction of the Force Applied

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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.

- How does the work done by the pulling force change as you vary the pulling force for a constant angle?
- How does the work done by the pulling force change as you vary the angle for a constant pulling force?
- Combine your answers above to obtain a general mathematical formula for the work done on the ball due to an arbitrary pulling force.
- 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.

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