AP Physics 1 Energy& SHM Lab
Note: You have much control over the appearance of graphs – single click, double click, or right click when you want to change something! Search the menus found in the corners the pane(s).
General tips using the application:
1. The program has multiple viewing “windows” – click on the View Options button in upper right corner to choose what is displayed.
2. Under the File button in the upper left corner there are options to Export your work. When you choose to export Graph Image it creates an image file (.png) of whatever graph or graphs that are currently being displayed. Suggestion: work on one graph at a time and then export to an image file that can be put into Microsoft Word, Google Docs, etc. Also you may want to save the Graphical Analysis file by using Save As and give it a unique name for each graph you create. By saving many versions of the file you can more easily go back and correct or make changes if necessary.
3. The other Export option is Comma-Separated Values. Use this option to save the completed data table in a form that can be opened by other programs such as Microsoft Excel, Google Sheets, etc. You can use this feature if you want to produce the graphs using an application other than Graphical Analysis.
4. Except for
the energy graphs, all other graphs should be adjusted as follows:
Under Graph Tools, choose Apply Curve Fit. Choose an appropriate
model. When doing a curve fit you may choose to select and analyze only a
portion of the graph and data if it results in a more legitimate match between the
data and the curve or line generated by the equation. (However, this may not
be necessary.)
Under Graph Tools and Graph Options choose Points but not
Lines – whenever a curve fit is shown, the data points should be shown as a
scatter plot (no connecting lines). Also adjust the y-axis range as
necessary to produce the best looking graph. The equation should not cover the
data. You can also adjust the x-axis range. It is essential that all
data be showing! And give the graph an appropriate title.
Position vs. Time, Force vs. Acceleration, and Force vs. Position:
5. Position vs. Time graph: use a sine model curve fit.
6. Force vs. Position graph: Click on the x-axis label (Time) and change it to position. Use a linear model.
7. Force vs. Acceleration graph. Change the x-axis to Acceleration. Use a linear model.
Energy vs. Time, Energy vs. Position, and Data Table:
8. Now you will need to add columns to the data table. The goal is to have the computer calculate and graph the energy of the system. It will be convenient under View Options to choose to show graph(s) and the data table at the same time. Click on the three dots at the top of a column in the table to access Column Options and Add Calculated Column. When you add a column it will be inserted immediately to the right, so choose where you want to insert it.
9. Under Add Calculated Column enter an appropriate name and units and then choose an expression type that can be used for the desired operation. For this lab you can use A*X^B, A*X+B, and A*X+B*Y to achieve all necessary calculations.
10. Add a Height column: the h in mgh will be the height above the lowest point in the oscillation. Use the position vs. time graph to determine the lowest position measured by the motion detector. Then use the expression A*X+B to produce the column of height values. For example, if the lowest position were 0.60 m, then you could let A = 1, X = Position, and B = –0.60 to calculate height.
11. Add an Elongation column: the x in ½ kx2 is the amount the spring is stretched. This is the difference in the mass’s measured position and the position at which the force of the spring is zero. Use the linear regression from force vs. position to solve for the position at which the force of the spring is zero. Then use the expression A*X+B to produce the column of elongation values. For example, if the linear regression indicates the force equals zero at a position of 0.85 m, then you could let A = –1, X = Position, and B = 0.85 to calculate elongation.
12. Add a Kinetic Energy column: use the expression A*X^B. The value of A should be half the mass of the object. (What should X and B equal? You should know!)
13. Add a Gravitational Energy column: use the expression A*X^B. The value of A should be the weight of the object. (What should X and B equal? You should know!)
14. Add an Elastic Energy column: use the expression A*X^B. The value of A should be half the value of the spring constant k – determine k from the linear regression of force vs. position. (What should X and B equal? You should know!)
15. Add a Potential Energy column: use the expression A*X+B*Y. X and Y are the two types of potential energy.
16. Add a Total Energy column: use the expression A*X+B*Y. X and Y are potential and kinetic energy. This final column is the sum of all three types of energy present in the mass/spring/earth system.
17. Make a graph of Energy vs. Time. Show 4 plots – the kinetic energy, the gravitational potential energy, the elastic potential energy, and the total energy - make sure there is a legend on the graph. For this graph plot Points and Lines – “connecting the dots” helps illustrate the trends in the variables. There will be no regression equations on this graph. Instead, do a statistical analysis of the total energy by clicking on the View Statistics option under Graph Tools - scroll through the statistics box until you find the information for the total energy. Adjust the overall appearance as necessary – for example, the legend and the statistics boxes should not cover significant features of the graph.
18. Make a graph of Energy vs. Position graph. Again show K, Ug, Us, and E. Adjust as necessary. Note: you do not need to repeat the statistics on this graph because it will be the same result.
Questions
1. Highlight or otherwise indicate one row from the data table and check the computer’s calculations by doing them yourself: calculate kinetic energy, gravitational potential energy, elastic potential energy, and total energy. Show your work!
2. Discuss whether or not your results support Conservation of Energy and explain how so. Refer specifically to one or more graphs.
3. Discuss
whether or not your results support the concepts of Simple Harmonic Motion:
(a) Refer to the Force vs. Position graph and describe specifically whether it
shows that the object was under the conditions that cause SHM.
(b) Refer to the Position vs. Time graph and describe specifically whether it
shows the object exhibited the expected type of motion associated with SHM.
(c) Use the appropriate coefficients from the regression on the Position vs.
Time graph to identify and write down the equilibrium position and amplitude.
Showing your work, plug the equilibrium position into the regression from the
Force vs. Position graph and calculate the amount of force – does the result
make sense? Explain.
4. Show work
as you:
(a) Use an appropriate coefficient from the regression on the Position vs. Time
graph to determine the period of the object’s motion. Show your work.
(b) Use your values for k and m to calculate the theoretical
period.
(c) Calculate the percent error, taking the first value (from the Position graph)
to be the most likely actual “true” period.
5. Consider
the regression equation of the Force vs. Acceleration graph:
(a) Explain how it is consistent (or not) with Newton’s Laws – be specific.
(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.
6. Use the statistical results on the Energy vs. Time graph to determine the percent deviation in the total energy of the mass-spring system. (The standard deviation is what percent of the mean?) This indicates the average fluctuation in the total energy
7. 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)
• Data Table (6)
• Position vs. Time graph, with regression equation. (6)
• Force vs. Position graph, with regression equation. (6)
• Force vs. Acceleration graph, with regression equation. (6)
• Energy vs. Time graph (K, Ug, Us, and E), with statistical analysis of total energy (6)
• Energy vs. Position graph (K, Ug, Us, and E) (6)
• On separate paper, responses to the questions. (14)