REPORT
Experiment
16
Physics with Computers 16 - 1
Energy of a Tossed Ball When a juggler tosses a bean ball straight upward, the ball slows down until it reaches the top of its path and then speeds up on its way back down. In terms of energy, when the ball is released it has kinetic energy, KE. As it rises during its free-fall phase it slows down, loses kinetic energy, and gains gravitational potential energy, PE. As it starts down, still in free fall, the stored gravitational potential energy is converted back into kinetic energy as the object falls.
If there is no work done by frictional forces, the total energy will remain constant. In this experiment, we will see if this works out for the toss of a ball.
In this experiment, we will study these energy changes using a Motion Detector.
OBJECTIVES • Measure the change in the kinetic and potential energies as a ball moves in free fall. • See how the total energy of the ball changes during free fall.
MATERIALS Power Macintosh or Windows PC LabPro or Universal Lab Interface
volleyball, basketball, or other similar, fairly heavy ball
Logger Pro wire basket Vernier Motion Detector
PRELIMINARY QUESTIONS For each question, consider the free-fall portion of the motion of a ball tossed straight upward, starting just as the ball is released to just before it is caught. Assume that there is very little air resistance.
1. What form or forms of energy does the ball have while momentarily at rest at the top of the path?
Experiment 16
16 - 2 Physics with Computers
2. What form or forms of energy does the ball have while in motion near the bottom of the path?
3. Sketch a graph of velocity vs. time for the ball.
4. Sketch a graph of kinetic energy vs. time for the ball.
5. Sketch a graph of potential energy vs. time for the ball.
6. If there are no frictional forces acting on the ball, how is the change in the ball’s potential energy related to the change in kinetic energy?
PROCEDURE 1. Measure and record the mass of the ball you plan to use in this experiment.
2. Open the file in the Experiment 16 folder of Physics with Computers. Two graphs are initially displayed on the screen. The two graphs are distance vs. time and velocity vs. time. The horizontal axis has time scaled from 0 to 3 s.
3. Connect the Motion Detector to DIG/SONIC 2 of the LabPro or PORT 2 of the Universal Lab Interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it.
4. Hold the ball directly above and about 0.5 m from the Motion Detector. In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. Have your partner click to begin data collection. Toss the ball straight up after you hear the Motion Detector begin to click. Use two hands. Be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it reaches maximum height of about 1.5 m above the Motion Detector. Verify that the distance vs. time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. When you have good data on the screen, proceed to the Analysis section.
DATA TABLE
Mass of the ball (kg)
Position Time Height Velocity PE KE TE
(s) (m) (m/s) (J) (J) (J)
After release
Top of path
Before catch
Energy of a Tossed Ball
Physics with Computers 16 - 3
ANALYSIS 1. Click on the Examine tool, , and move the mouse across the distance or velocity graphs of
the motion of the ball to answer these questions. a. Identify the portion of each graph where the ball had just left your hands and was in free
fall. Determine the height and velocity of the ball at this time. Enter your values in the data table.
b. Identify the point on each graph where the ball was at the top of its path. Determine the time, height, and velocity of the ball at this point. Enter your values in the data table.
c. Find a time where the ball was moving downward, but a short time before it was caught. Measure and record the height and velocity of the ball at that time.
d. For each of the three points in the data table, calculate the Potential Energy (PE), Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion Detector as the zero of your gravitational potential energy.
2. How well does this part of the experiment show conservation of energy? Explain.
3. Logger Pro can graph the ball’s kinetic energy according to KE = ½ mv2 if you supply the ball’s mass. To do this, choose Modify Column Kinetic Energy from the Data menu. You will see a dialog box containing an approximate formula for calculating the KE of the ball. Edit the formula to reflect the mass of the ball and click .
4. Click on the top graph’s vertical axis label and change the display to Kinetic Energy, KE.
5. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.
6. Logger Pro can also calculate the ball’s potential energy according to PE = mgh. Here m is the mass of the ball, g the free-fall acceleration, and h is the vertical height of the ball measured from the position of the Motion Detector. As before, you will need to supply the mass of the ball. To do this, choose Modify Column Potential Energy from the Data menu. You will see a dialog box containing an approximate formula for calculating the PE of the ball. Edit the formula to reflect the mass of the ball and click .
7. Click on the bottom graph’s vertical axis and change the display to the Potential Energy, PE.
8. Inspect your potential energy vs. time graph for the free-fall flight of the ball. Explain its shape.
9. Record the two energy graphs by printing or sketching.
10. Compare your energy graphs predictions (from the Preliminary Questions) to the real data for the ball toss.
11. Logger Pro will also calculate Total Energy, the sum of KE and PE, for plotting. Click on a graph’s vertical axis label and display the Total Energy, TE. Record the graph by printing or sketching.
12. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Does the total energy remain constant? Should the total energy remain constant? Why? If it does not, what sources of extra energy are there or where could the missing energy have gone?
Experiment 16
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EXTENSIONS 1. What would change in this experiment if you used a very light ball, like a beach ball?
2. What would happen to your experimental results if you entered the wrong mass for the ball in this experiment?
3. Try a similar experiment using a bouncing ball. You should mount the Motion Detector high and pointed downward so it can follow the ball through several bounces.