## Exploration 6.3: The Gravitational Force and Work

Please wait for the animation to completely load.

A 1-kg ball is subjected to the force of gravity as shown in the animation **(position is given in meters and time is given in seconds)**. The ball starts at x = 0 m and y = 0 m. You can vary the ball's initial velocity and view how this affects the motion of the ball and the ball's kinetic energy. Also shown are the graphs of force cos(θ_{y}) vs. position_{y} and kinetic energy vs. position_{y} where θ_{y} is the angle between the gravitational force and the ball's infinitesimal y displacement. Restart.

With v_{0x} = 0 m/s and v_{0y} = 0 m/s,

- In what direction does the net force on the ball point?
- How would you describe the kinetic energy vs. position graph?

With v_{0x} = 10 m/s and v_{0y} = 0 m/s,

- What is the ball's minimum kinetic energy?

With v_{0x} = 10 m/s and v_{0y} = 10 m/s,

- How would you describe the KE vs. position graph? Be explicit about what happens to the kinetic energy.
- What is the condition for the work done by gravity to be zero?
- What is the ball's minimum kinetic energy?

With v_{0x} = -10 m/s and v_{0y} = 10 m/s,

- How would you describe the kinetic energy vs. position graph? Be explicit about what happens to the kinetic energy.
- What is the condition for the work done by gravity to be zero?
- What is the ball's minimum kinetic energy?