AP Physics Energy Lab
The purpose of this investigation is to verify the concept of Conservation of Energy. This will be accomplished by hanging a mass from a spring and allowing it to oscillate vertically. In the absence of nonconservative forces such as friction, the energy of the mass-spring system should remain constant. Force will be measured by a force sensor from which the spring hangs. Time and position will be measured by a Calculator Based Ranger (CBR) connected via Lab Pro Interface to a laptop computer. The program Logger Pro 3 will interpret and graph the data and allows for the calculation of the potential and kinetic energy of the mass-spring system.
Procedure
Set two ring stands on a lab table. Attach a force sensor to one end of a long metal rod and support it between the two ring stands as shown in the diagram. The ring stands should be near each end of the metal rod. The CBR will be placed on the floor directly below the force sensor. A spring will be hung from the force sensor and a mass from the bottom of the spring. IMPORTANT: Great care must be taken not to drop a mass on the CBR!! It would be a good idea to always move the CBR to a safe location and ONLY put it below the mass during the very brief interval of time when it is actually in operation!
1. Connect the LabPro interface to a USB port and plug in its power supply to a wall outlet.
2. Connect the CBR motion detector to DIG/SONIC 1; connect the force sensor to CH 1.
3. Run the Logger Pro program with the file: AP Potential Energy. A message may appear concerning the sensors – click OK.
4. Calibrate the force sensor. Go to the Experiment menu and then Calibrate. Now select the force sensor and then click on the Calibrate Now. You will enter two values to calibrate the sensor. Read the next two steps before you proceed with the calibration.
5. Hang only the spring from the sensor. Click on the button to perform the calibration. Then enter zero as value one and click Keep. This means that the computer will record zero newtons for force when the spring is in this condition and it is not exerting any force on the test object.
6. Hang the test object on the end of the spring and find the position at which it will rest without accelerating. For value two, use the mass of the object to calculate and enter the correct weight (in newtons!) of the test object (not including the spring!) and click Keep. This means that the computer will record a force equal to the weight of the test object when the spring is in this condition and is exerting that much force on the test object. All other readings from the sensor are now adjusted according to the two known force values that have been entered by you – this is done by the program. Click Done.
7. Check that all of the support structure is very secure. The bobbing mass should be about 50 to 60 cm above the location where the CBR will rest.
8. Carefully lift the mass upward and let it go so that it bobs up and down with an amplitude of around 10 cm.
9. Once the mass is already in motion and oscillating smoothly, place the CBR directly below it and click on the Collect button.
10. This should produce smooth graphs showing fluctuations of position and force with respect to time. You may need to click on the Autoscale button to see all of the data. If there are significant glitches in the data you should repeat the experiment.
11. Remove the CBR to a safe location.
12. Use the Save As command to save your data in a file with the last name of one of the persons in your group. Feel free to Save as often as you like so that you could easily recover a previous step if you make mistakes.
Analyses
Position vs. Time, Force vs. Acceleration, and Force vs. Position:
1. Note the Page indicator in the tool bar. Move to Page 3 to view the Position vs. Time graph. Do a regression using a sine model. (click Analyze, Curve Fit ...) If you have done things correctly you should be able to do the regression over the entire graph using all data. (In other words you should not have to select a portion of the data.) Adjust the appearance if necessary – check for appropriate labels, units, etc. Use point protectors but do not connect the points. Under the File Menu use Print Graph to print the graph. In the comment section of Printing Options enter the names of the members of your group.
2. On Page 4 your will find Force vs. Position. Do a regression using a linear model. Adjust the appearance and scales (Autoscale) if necessary – check for appropriate labels, units, etc. Use point protectors but do not connect the points. Use Print Graph to print the graph. Note: you will need the equation describing the force of the spring for correcting your energy graph – this is explained below.
3. On Page 5 you will find a Force vs. Acceleration graph. Do a regression using a linear model. Check the appearance and scales as before. Use Print Graph to print the graph.
Energy vs. Time, Energy vs. Position, and Data Table:
4. You must enter the mass of the test object. To do this use, go to the Data menu, then Column Options – Mass. Under the column definition tab you should see a box labeled “Generate Values”. Use the Numeric Fill option to enter the mass of your object into all 100 rows of the data table.
5. You
will need to modify the equation for potential energy. To do this use, go to
the Data menu, then Column Options – Potential Energy. Under the definition
tab you should see an equation that is used by the computer to calculate the
value. An appropriate type of equation has been entered but you will
need to modify the equation to correctly describe your particular
experiment. Determine an equation that gives the net force on the
object as a function of the position measured by the CBR. Integrate this
function to determine an arbitrary potential energy function relative to the midpoint
of the object’s oscillation. In other words, the reference point for your
potential energy function is the value of the position at which the net force
on the object was zero.
Hints: The net force is the vector sum of the spring force and the
force of gravity. The reference point can be found by using the position vs.
time graph or by solving for the position at which the net force is zero.
Note: Question #1 in your report asks you to show what you did here.
6. Check the equations entered for kinetic energy and total energy and make sure that these are correct.
7. On Page 6 you will find Energy vs. Time. Ensure there is a legend on the graph and that all of the plots have different symbols for the point protectors. Choose to connect the points. There will be no regression equations on this graph. Instead, do a statistical analysis of the total energy by clicking on the Statistics button in the tool bar and choosing ONLY the total energy. If there are stray points for total energy you may choose to select only a portion of the graph for statistical analysis. Adjust the appearance and scales if necessary and use Print Graph to print this graph.
8. On Page 7 you will find Energy vs. Position graph. Adjust the appearance if necessary and use Print Graph to print the graph.
9. Go back to Page 2 and use Print Data Table to print the Data Table – this will be more than one page of paper but each member of your group only needs one page of the data. (You will not need all of the data for your lab report – one page should be sufficient.)
10. Before turning everything off check to see that you have all necessary graphs and Save the file one last time.
Questions
1. (a) Make a free body diagram of the test object. (b) Use the equation from the force vs. position graph to determine a new equation that represents the net force as a function of position. (c) Integrate this function to determine an arbitrary potential energy function relative to the position at which the object was at equilibrium. In other words, the reference point is the value of the position at which the net force on the object was zero. Show all work for parts (b) and (c).
2. Consider
the regression equation of the Force vs. Acceleration graph:
(a) Explain how it is consistent (or not) with Newton’s Laws.
(b) What is the significance of the slope? the y-intercept?
(c) Make any appropriate calculation(s) such as error or deviation that will
quantify the accuracy and/or precision of the slope and/or y-intercept.
3. Use the statistical results on the Energy vs. Time graph to determine the percent deviation in the total energy of the mass-spring system.
4. Discuss whether or not your results support Conservation of Energy and explain how so. Refer specifically to one or more graphs.
5. Discuss how the mass of the spring affects the results. (We are always reading in physics problems about “massless” springs because a spring with mass will impact the results!)
6. Write an intelligent, grammatically correct paragraph or two discussing both the signs of error and the likely sources thereof.
A complete report (50 pts): (pages in this order)
q Data Table (8)
q Position vs. Time graph, with regression equation. (6)
q Force vs. Position graph, with regression equation. (6)
q Force vs. Acceleration graph, with regression equation. (6)
q Energy vs. Time graph, with statistical analysis of total energy (6)
q Energy vs. Position graph (6)
q On separate paper, responses to the questions. (12)