5 Lab 5: Simple Pendulum

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 5

Simple Pendulum

What you will do:

Set the phone up as a simple pendulum, then use the accelerometer that is built in the phone to study the simple harmonic motion of the phone.

What you will need:

• A smart phone installed with the Phyphox app
• A bag that can hold your phone and tie to a string
• A piece of string that is at least 80cm in length
• Another device to remotely access your phone

Demonstration Video: https://youtu.be/hmI_GF4oH2c

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.
3. Try to place/wrap the phone in a way so that when the bag is hung by a string, the phone stays vertical. (If you lost remote access at any point during the process, try operating the phone through the bag or taking the phone out from the bag and repeat.)
4. Use a piece of string that is about 1 meter long. Tie one end of the string to the bag. 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 30 cm, 40 cm, 50 cm, 60 cm, and 70 cm away from the center of the cell phone.
5. Hold or tie the string at the 70cm mark firmly to an object that is high enough so that the phone will not hit the ground or any other obstacle.
6. Wait for the phone to stop spinning. Displace the phone from its equilibrium position by a small angle and then release, so that the phone starts swinging in a small angle.
7. After the motion of the phone appears regular, start an “acceleration with g” measurement with remote access. Count to a total of 10 full oscillations, and then stop the measurement.
8. Count how many periods are shown on the X / Y / Z accelerometer readings. You will notice that one of these axes has about twice more periods than what you counted. Identify this axis on the phone, and explain why the acceleration on this axis reaches maxima twice as frequent.
9. Set the phone on a small angle swing first, after the motion of the phone appears regular, start an “acceleration with g” measurement. Stop the measurement after more than 10 full oscillations. Export the data as a csv file.
10. Repeat Step 9 with string lengths of 60cm, 50cm, 40cm, and 30cm.
11. Put a small object with known mass into the bag with the phone. (If you purchased the experimental kit, you can use the 500g hex mass.) Repeat Step 9 with string lengths of 70cm, 50cm, and 30cm. Note: if you did not purchase the kit, find another small heavy object that will fit in the bag with the phone (such as a rock) and record its mass using a kitchen scale.
12. For each trial, calculate the average period of the 10 oscillations. State which axis was used to identify the periods. To obtain the uncertainty of the periods, you can calculate the standard deviation in the periods of the 10 oscillations.
13. For the trials without the added mass, plot the square of the period against the length of the string. Find the gravitational acceleration using your plot. You may find it useful to refer to this video https://www.youtube.com/watch?v=WPa5IgLgDyQ
14. For the trials with the added mass, compare the period values with those from the trials without the added mass.
15. Should the added mass affect the period? Does your data match your expectation? If it doesn’t, (bonus) come up with a hypothesis and test your hypothesis with some simple calculations and measurements.

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.
• 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 5” on the discussion board on Quercus! We may award the most helpful inputs with +1 bonus mark for the lab report!

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.