Physics Lab – Conservation of Energy
Overview
The purpose of this activity is to measure the energy of a bouncing ball and to verify its conservation. Unlike previous lab reports you will use the computer to do all the tedious work. The computer will: collect the data, graph the data, analyze the data, and print out the graphs and data tables for your report. In this regard a secondary goal of this activity is for you to learn about current scientific methods and technologies for collecting and analyzing experimental data.
In this experiment you will drop a ball and let it bounce several times beneath a Calculator Based Ranger (CBR). As the ball bounces the CBR will collect data about the ball’s position and velocity and this data will be fed via Universal Lab Interface (ULI) into a laptop computer running Logger Pro software. After the data is collected you will use Logger Pro to edit and modify the position and velocity data so as to produce graphs and data tables showing the ball’s kinetic, potential, and total energy.
1. Measure and record the mass of the ball.
2. Make all connections BEFORE turning the equipment on. The CBR is connected to Port 2 on the front of the ULI. The ULI is connected to the serial port on the back of the computer. Once all connections are secure, and only then, turn on the ULI and turn on the computer. At the log on screen enter name: student, password: student.
3. Start the Logger Pro program and open the file called “Ball”.
4. The file contains formatting information that sets up the CBR to measure distance and velocity. Once the file is opened the CBR is ready to collect data. Simply click on the collect button. If the results are not satisfactory just run it again – the old data is automatically deleted and the new data is collected and displayed each time you click on the collect button.
5. To perform the experiment the CBR is held about head high and the ball is dropped beneath it. One person should hold the CBR while another drops the ball. TAKE GREAT CARE NOT TO DROP THE CBR! The ball should be released from a point at least 40 cm (15 in) below the CBR. The CBR cannot properly measure objects that are too close to it. It may be necessary for the person holding the CBR to “follow” the bouncing ball – make sure the CBR is always the same height above the floor.
6. If the experiment is successful you should now see two graphs. Use the autoscale tool button if the data goes off the edge of the window.
7. The distance graph should have a series of smooth-curved humps showing the rising, falling, and bouncing of the ball. The velocity graph will look a little like a saw tooth consisting of connected linear segments. If this is not the case, try again.
8. Once you have an acceptable set of data you are through with the ball and are ready to do some analysis using the Logger Pro program. Use the Save As command from the File menu to save your file on the floppy disk, giving it a unique and recognizable name (like your last name). Make frequent Saves to your file as you proceed.
The steps below will lead you through the process of analyzing the data collected by the CBR. If you look at the Table Window and use the scroll buttons you can see that the data at this point consists of three columns: time, distance, and velocity. Since our goal is to test the conservation of energy you need to “tell” the computer to make and graph four additional columns: height, potential energy, kinetic energy, and total energy. And you will get the computer to print out a hard copy of the results.
Analyzing the distance data and producing a height graph:
1. First you will change the distance graph into a height graph. The data in its original form is the distance measured downward from the CBR. However, for potential energy it is more convenient and easier to understand if height is measured upward from the floor or lowest point.
2. First determine the maximum distance measured by the CBR. This would correspond to the lowest point in the ball’s bouncing. This is done by scrolling through the data in the Table Window or by using the x=? tool button and moving across the graph with the mouse. This maximum distance should be around 1.5 m to 2.0 m.
3. Now you will make the computer calculate the ball’s height above its lowest point. This will be done by subtracting the maximum distance (found above) from the rest of the distance data. Keep reading.
4. Make sure the distance graph is selected. Keep reading.
5. Now carefully do the following: Under the Data menu choose New Column and Formula. Under the Options tab enter: Long Name: Height; Short Name: h; Units: m. Under the Definition tab enter for the equation: your maximum distance – “Distance”. For example if your maximum distance was 1.600 m you would enter: 1.6 – “Distance” in the equation box. There is a “drop-down” box that you can use to “type” previously defined variables into your equation.
6. Now you should see a graph showing the height values determined by your equation. You also should find a new column showing height in the Table Window.
7. You can choose what values to show on a particular graph. Click on the y-axis label of this graph. You should see a dialog box appear. Choose to plot only the height and not the distance. Finally, you should have a nice graph showing a serious of smooth curves that show the bounces of the ball.
8. Click on the title of the graph. Change the title to something more appropriate.
9. Under the View menu choose Graph Options and select Point Protector Every 1 Points and Grid; then unselect Connecting Line. This should result in a graph that shows only the actual data points.
10. Now use the mouse to select one of the parabolic parts of the height graph. Under the Analyze menu choose Automatic Curve Fit, Quadratic, and Try Fit. Clicking anywhere on the graph will get rid of the two vertical lines.
11. The height graph has its own window. Use the buttons in the upper right hand corner of its window to maximize its appearance. You may want to move the equation result box to a different place on the graph by clicking and dragging it.
12. The autoscale tool may improve the appearance of your graph. At this point you are ready to print the graph. To do this, under the File menu choose Printing Options. In the Name region put the names of the people in your group. Also you may enter a comment if you wish. Now under the File menu choose Print Window. Make one copy for each person in your group.
Analyzing the Velocity Data:
1. Return the height graph to its original sized window.
2. Now select the velocity graph and maximize its window. Under the View menu choose Graph Options and select Point Protector Every 1 Points and Grid; then unselect Connecting Line. This should result in a graph that shows only the actual data points.
3. This graph is a series of zigs and zags. Use the previously learned steps to get a linear fit for one section of the graph where the ball is in freefall.
4. Repeat the steps necessary to maximize the window and print this graph.
Producing an Energy Graph:
1. Return the velocity graph to its original sized window. Click on the height graph.
2. Use the steps you have learned to make a New Column for potential energy. Use Potential Energy, PE, and J for the names and units. The equation is: your mass*9.8*”Height”. For example if your ball had a mass of 565 grams you would enter: 0.565*9.8*”Height”.
3. Click on the y-axis label and choose to plot only the potential energy.
4. Use a similar process to convert the velocity graph into a kinetic energy graph. You should know the equation!
5. Now click on one of the two energy graphs and maximize its window. Click on the y-axis label and choose to show both the potential and kinetic energy on the same graph.
6. Make one more final New Column for total energy. Total energy is found by adding the two forms of energy for the ball.
7. Now you should have a final single graph that shows three plots: kinetic energy, potential energy, and total energy. Before printing this, take the following steps to “dress it up”. Again, autoscale may improve the appearance.
8. Click on the title of the graph. Change the title to something more appropriate.
9. Under the View menu choose Graph Options and then select the following: Point Protector Every 1 Points, Legend, Connecting Line, and Grid. Now you should see a nice final graph. You may want to click and drag the legend box to a more convenient location on the graph.
10. Since there are three different energy plots on this one graph the point protector symbols must be different (so that one can distinguish the plots from one another). Under the Data menu choose Column Options and then make the desired changes to the point protectors and colors.
11. Print out this energy graph using the same steps as before.
12. As a final step return this graph to its original size and then click on the Table Window that shows the numerical data. Maximize this window.
13. Print this table of numerical data and on it write the mass of the ball.
14. Make a final Save of the file that you created and then exit the program.
A complete report (50 pts): (Put in this order!)
q Data table including mass of the ball. (9)
q Height vs. Time graph with regression equation. (9)
q Velocity vs. Time graph with regression equation. (9)
q Energy vs. Time graph with legend showing kinetic, potential, and total energy. (9)
q On separate paper, answers to the questions using complete sentences and showing any necessary numerical calculations. (14)
1. Based on the velocity graph and its regression equation what was the acceleration of the ball as it rose and fell through the air? Determine the percent error in this value.
2. Based on the height graph and its regression equation, what was the acceleration of the ball as it rose and fell through the air? Determine the percent error in this value.
3. In the data table choose a single row in which there are no zero values. Highlight or otherwise indicate which row you choose. Then check the computer’s three energy values by doing the appropriate calculations yourself. In other words, I am asking you to show a single example of the calculations that you had the computer do for you. Note: the program rounds numerical values off to a particular number of decimal places and so you may find some slight discrepancies here!
4. You should find that certain parts of the energy graph appear to support the idea that energy is conserved. Explain how the graph supports conservation of energy.
5. You should also find that certain sections of the energy graph appear to show that the total energy of the ball decreases. Describe any such sections and explain what became of that energy assuming that it was, in fact, conserved (and not destroyed – though this is something that can not be proven by the graph).
6. The graph takes on a “stepped” appearance or a series of “plateaus”. In the data table find the numerical values for total energy that make up one of the plateaus besides the first one. Highlight or otherwise indicate the section of the table that represents the plateau you have chosen. Copy those total energy values and determine the best value and average relative (percent) deviation. The deviation indicates “how well” your data shows that energy was conserved.
7. Discuss error. As always this means to note the signs of error in your graphs and other numerical results and then to make an attempt to explain the probable sources of the errors that are apparent.