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 L129. Energy Curves for a Pendulum In this lab, you'll use Logger Pro to analyze the motion of a swinging pendulum. You'll make decisions about how you'll use the software tools to meet the goal of the lab. Your report will be submitted in two parts to WebAssign. The first part will be the prelab, and the second parts will be the predictions, analysis, and discussion.

Goal

To investigate energy changes of a simple pendulum and determine whether mechanical energy is conserved

Prelab

Students with last names beginning with A-L will use file penopt_2pach. The other students will use file penopt_3pach. Either the .mov or .mp4 file may be used.

Download your assigned video clip from the page below. Right click on the file and save it file to your hard drive.

• Note the scaling data given on the above page. Record this value.
• Record the filename of the file assigned you.
• Record the mass of the pendulum bob:  0.100 kg.
• Start Logger Pro. Insert the video clip using the Insert -> Movie command. Drag the corners of the clip to make it as large as possible. Play the video to see the motion of the pendulum.

For the following questions, take the system to be the bob and the Earth. Assume the string has negligible mass and does not stretch.

1. Open WebAssign L129PL and answer the following.

1. Are there any external forces that don't do work on the system? If so, what are the forces and why don't they do work on the system?

2. Are there any external forces that do work on the system? If so, what are the forces and why do they do work on the system?

3. Do you expect the total mechanical energy ΔEsys of the system to be conserved? Why or why not?

4. Stop the video at some point intermediate between the lowest and highest positions. What information could you obtain from the video clip in order to help determine a numerical value for the gravitational potential energy of the system at that point?

5. For the point above, what information could you obtain from the video clip in order to help determine a numerical value for the kinetic energy of the system at that point? Be specific--consider what you would actually need to do in order to determine the velocity, which, of course, is needed to determine the kinetic energy. (Note that an incorrect response would be to assume that mechanical energy is conserved and hence, the change in kinetic energy was equal to the negative of the change in potential energy. That approach would amount to assuming what you're trying to determine.)

6. What additional information (not obtainable from the video clip) would you need in order to determine the gravitational potential energy and the kinetic energy?

2. Next you'll predict the energy curves for the one-half cycle of the pendulum as a function of horizontal position.

1. On the PencilPad, draw your prediction of the graph of the gravitational potential energy as a function of the horizontal position for one-half cycle of the motion from extreme right to extreme left. (Hint: Think about where you expect the Ug to greatest and least. Also, assume that the lowest position of the bob is a vertical position of 0.)

2. On the same axes as above, sketch and label a line representing your prediction for the kinetic energy as a function of horizontal position.

3. On the same axes as above, sketch and label a line representing the total mechanical energy of the system as a function of horizontal position.

Data and Analysis

After the prelab assignment comes due, open the assignment and view the key as well as any comments from the instructor. Use these to help guide you in the analysis.

The items below provide some guidance but are not intended to be a complete procedure for the lab. Many decisions are left up to you. You won't need to do curve fits in Logger Pro; therefore, a matching table isn't required. However, you're expected to format graphs and tables in a manner consistent with the expectations of previous Logger Pro analyses.

1. Let the bob swing all the way to the right before starting to mark frames. Then mark all the frames from the right extreme of the motion to the left extreme.
2. Advance to the last frame of the clip to see a ruler that you can use to apply a scale factor.
3. Set the origin of the coordinate system conveniently.
4. Logger Pro automatically creates columns for the horizontal and vertical positions and velocities. In order to see where these numbers come from, select Analyze -> Tangent. Then run your cursor along the data points.
5. As you create new calculated columns in the data table, label them clearly. You can use shorthand symbols as long as they're standard symbols. Use SI units.
6. Create calculated columns for the kinetic energy, gravitational potential energy, and total mechanical energy. Of course, you'll need to decide what equations and variables to use for this. This is where the physics comes in.
7. Plot on the same graph the kinetic energy, gravitational potential energy, and total mechanical energy as a function of horizontal position.

Make sure everything is labeled and formatted appropriately in your analysis. Then upload your file to WebAssign L129 and continue with the discussion below.

Discussion and Conclusion

Continue in WebAssign L29.

Write a well-composed and comprehensive discussion in which you compare your graph obtained in the Logger Pro analysis to your predictions in Predictions Item #2. Expect to see some deviations from your predictions. Describe these deviations. Give three specific sources of error that could explain the deviations. As part of your response, consider your answer to Predictions 1b. Also consider the method that LP uses to calculate velocities.

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