3 Lab 3: Conservation of Energy

Acknowledgment

This project is made possible with funding by the Government of Ontario and through eCampusOntario’s support of the Virtual Learning Strategy. To learn more about the Virtual Learning Strategy visit: https://vls.ecampusontario.ca.

PHY136 Stay-At-home Experiment 3

Conservation of Energy

What you will do:

Put your phone on a swing. Then use the accelerometer that is built into the phone to verify the conservation of energy during the swinging motion.

What you will need:

• A smart phone installed with the Phyphox app
• Another device to remotely access the Phyphox app
• A bag that can hold the phone
• A long piece of string

Demonstration Video: https://youtu.be/Pv5l_CEDNYE

Procedures:

1. In the Phyphox app, open the “acceleration with g” sensor. On your computer, use a browser to remote access the Phyphox app.
2. Put the phone in a bag (if you purchased the experimental kit, use the velvet drawstring bag). If the bag does not fit the phone perfectly, you can wrap an elastic band on the outside of the bag around the phone. It’s important that your phone doesn’t move around too much in the bag.
3. Cut a piece of string that is about 1 meter long. Tie one end of the string to the bag. Tie the string at least twice to make sure the knot does not unravel.  Pull the string tight. (Important: if you are using a drawstring bag that came with the experimental kit, make sure the drawstring is also tight.) Measure and make five marks on the string that are 20cm, 30 cm, 40 cm, 50 cm, and 60 cm away from the center of the cell phone. Why should measurements be taken from the centre of the phone?
4. Hold the string at the 60cm mark at the edge of a table that is high enough so that the phone will not hit the ground. Start an acceleration with g measurement using remote access. Keep the string tight and lift the phone to the height of the table, then release the phone so that it swings with the string. Note: you must start the measurement before releasing the phone!
5. Repeat the swing for a total of 3 times before stopping the measurement. Then export the data as a csv file.
6. Repeat Steps 4-5 with string lengths of 50cm, 40cm, 30cm, and 20cm.
7. In each csv file, create a scatter plot of the absolute acceleration vs. time.
8. On each absolute acceleration vs. time scatter plot, identify the time point that corresponds to when the phone reached the lowest point of the swing for the first time. Explain how you identified the points.
9. Pick one length of string, and calculate the theoretical acceleration that should be measured by the phone at the lowest point of the swing. Does the experimental value match the theoretical value? Explain if you see any difference.
10. The absolute acceleration at the lowest point of the swing is the sum of the gravitational acceleration and the centripetal acceleration. Assume that the gravitational acceleration is 9.81 m/s2, calculate the speed of the phone when it reached the lowest point of the swing for the first time for all lengths.
11. For each length of string, calculate the maximum kinetic energy Ek of the phone per unit mass. I.e. Find Ek/m = 1/2 v2
12. Summarizing all five sets of data, plot the maximum kinetic energy per unit mass Ek/m against the initial gravitational potential energy per unit mass Eg/m = gh. Use the lowest point of swing as the reference height for the gravitational potential energy.
13. Fit the Ek/m vs. Eg/m data with a straight line. What value should be the slope of the line? What value should be the intercept of line? Do the results match your expectations? Briefly explain.
14. (Bonus) Can you use this method to find the approximate location of the accelerometer in your phone? Briefly explain.

Tips for data analysis:

• Complete all calculations that are required in the procedures above. Show sample calculations in the appendix.
• Answer all questions in the procedures section above.
• Attach graphs or tables when necessary. (Do NOT attach the raw data!)
• If you write a program for calculations, attach the code in the appendix.

Suggested topics for discussion:

• Find the uncertainty values for each calculation in the results section. Show a sample calculation of your error propagation in the appendix.
• Identify the sources of error in your measurements.
• Feel free to do more tests to verify your claims if possible.
• Make a reasonable conclusion based on your results.
• Compare your results with literature values (and add citations). You may reference the textbook.
• What other quantities can be determined with the same experimental design?
• What can be done to reduce the uncertainties at no cost while staying at home?

We value your feedback!

Did you enjoy this experiment? What are the aspects that you dislike the most about this experiment? – Let me know in the “Student Feedback Survey for Lab 3” on the discussion board on Quercus! We may award the most helpful inputs with +1 bonus mark for the lab report!

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