QuickGuide to Conservation of Energy of a Dropped Ball

 

Introduction
The motion of a dropped ball can be examined using a motion detector. As the ball falls to the ground, it speeds up until it strikes the ground. At that point, it reverses direction and bounces off the ground and back into the air. In addition to examining the position and velocity of the ball as it falls and bounces back, the total mechanical energy (ME) of the ball can be found. ME is the sum of the kinetic and gravitational potential energies of the ball.

The ball has gravitational potential energy (PE) if it is some vertical height above a predetermined reference point; the greater the distance, the greater the gravitational potential energy. The ball has kinetic energy (KE) if it has a non-zero velocity; the greater the velocity, the greater the kinetic energy. The mass of the ball also plays a role. For example, these factors can easily be observed by dropping different mass balls from the same height onto sand. All the balls will have the same velocity before hitting the ground.  But, the more mass a ball has, the more work it can do on the sand and the greater the divot (hole) the ball can make.

Putting all of this together, the various energies can be expressed as follows: PEgrav = mgh and KE = ½ mv². There are other types of energy to consider, which we will not directly measure. These include the elastic gravitational potential energy PEelastic of the ball. When the ball strikes the ground, it compresses like a spring, and the kinetic energy is converted to elastic potential energy.
 
If there are no external forces acting on the ball (like friction, air resistance, etc.), then ME is conserved.

Materials
Lab Pro and computer
Motion detector
Rubber ball
Table clamp, rod, and three-finger clamp

Preliminary Questions:

1. Prediction: Sketch a graph of vertical position vs. time for a bouncing ball. Be sure to include a written explanation of why your graph looks the way it does.

2. Prediction: Sketch a graph of velocity vs. time for a bouncing ball. Be sure to include a written explanation of why your graph looks the way it does.

3. Identify the point(s) on your position vs. time graph where kinetic energy is at a maximum and a minimum.

4. Identify the point(s) on your velocity vs. time graph where gravitational potential energy is at a maximum and a minimum.

5. If there is no air resistance acting on the ball, how is the change in gravitational potential energy related to the change in kinetic energy? Describe in words.

Activities:
Measure and record the mass of the ball you plan to use in this experiment. Position a motion detector above the floor or table so that it will be able to map the motion of a bouncing ball.

Because the motion detector is looking down from above, you will need to reverse the direction. You can do this by clicking the LabPro icon in the upper left then going into the sensor setup. If you are using a Go! Motion probe, click the Go! icon in the upper left then the green Go! square in the window that pops up. Once you have reversed direction, zero the probe (ctrl-0) on the top of the ball while it is at rest beneath the motion detector.

Use the motion detector to create a graph of position vs. time and velocity vs. time for a bouncing ball. This will take some practice! Small bounces are recommended.

Analysis:
Using the position data column, create a New Calculated Column that indicates the gravitational potential energy of the ball. To create this new column, please refer to #6 the document on Graphing with Logger Pro. Go to Insert > New Graph and create a graph of PE vs. time. Scale the graph so that three full bounces of the ball are shown.

Using the velocity data column, create a New Calculated Column that indicates the kinetic energy of the ball. Plot KE on the same graph as PE. To show multiple data sets on the same graph, refer to #7 in the document on Graphing with Logger Pro. Be sure to show a legend indicating which line is which.

Make a New Calculated Column that indicates the total mechanical energy (PE + KE) for the ball. Plot ME on the same graph as PE and KE. Print this graph.

Postlab Questions:

1. Describe, in your own words, the transitions of the total mechanical energy of the ball in terms of kinetic energy, gravitational potential energy, and elastic potential energy (see introduction) through one complete bounce of the ball.

2. As the ball bounces upwards, it is said to be in free fall, even though it is moving upward. Why a ball is said to be in free fall even though it is on its way up?

3. What happened to the total mechanical energy of the ball between bounces? Does the total energy remain constant? Should it? Why?

4. What would change in this experiment if you used a very light ball, like a beach ball, that was affected more by air resistance?

5. Try to devise an experiment that would enable you to determine the transition of the mechanical energy of the ball to elastic potential energy when the ball is in contact with the ground.

 

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