The graph below represents the height above the floor of a bouncing ball. Before we actually take our own data in lab, it is most important that we understand what the data reveals…..

Ignoring air friction, the bouncing ball is in free fall whenever it is not colliding with the floor. The consequence is that the acceleration is constant, the velocity changes linearly with time, and the position changes in a quadratic (parabolic) manner with time while the ball is in flight through the air.

a) Below the given height (above the floor) vs. time graph for a bouncing ball, you are to sketch the corresponding VELOCITY vs. time graph. Make certain that the height and velocity graphs align carefully with respect to time. Pay particular attention to the velocity values that correspond to the PEAKS of the arcs. Also indicate how the velocities just before and just after the collisions with the floor compare to one another.

While the precise values of the velocities are not important for the graph, you DO need to indicate the (+) and

(-) regions, places where velocity is zero, and relative magnitudes of the velocities involved.

b) Create the corresponding acceleration vs. time graph below the velocity graph. Again, be sure the time axes of all three graphs line up.

The bouncing ball (mass = m) is undergoing a collision with the earth (mass = M). When m and M are so vastly different, we can make the following mathematical approximations:

a) Use the equations you already know for a perfectly elastic collision and the approximations above to derive the result that the ball will leave the floor with the same speed (opposite direction) as it hit the floor. Be organized in your work. State any additional valid assumptions you use.

b) In reality, the collision will likely not be totally elastic. Describe how the speed of the ball just before and just after the collision will compare with one another in this case.

a) What is the gravitational potential energy of the ball at each of the heights labeled in the given bounce graph? Be sure to show the equation used.

GPE at h₁: __________ GPE at h₂: __________ GPE at h₃: __________

2. Using what you know about gravitational (potential) energy, kinetic energy, and conservation of energy, predict the velocity of the ball just before it contacts the floor after it falls from each of the labeled heights. Ignore air friction. Use "up" as the positive direction. State the concept and the general equation(s) used. Be sure to solve for the unknown before plugging in numbers.