## 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?

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