17 Lab 2: Torque and Speed of Muscle

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.

PHY255 Stay-At-home Experiment 2

Measuring the Torque and Speed of the Biceps Muscle

What you will do

Use the built-in accelerometer of the phone to estimate the maximum force and speed that can be produced by your biceps muscle.

What you will need

• A smart phone installed with the Phyphox app

Theoretical Background

• For a point mass [latex]m[/latex] rotating around a point that is [latex]r[/latex] distance away from the point charge, the moment of inertia of the point mass is [latex]I=mr^{2}[/latex].
• For a uniform rod of mass [latex]m[/latex] and length [latex]l[/latex] that is rotating around one of its ends, the moment of inertia of the rod is [latex]I=ml^{2}[/latex].
• A torque [latex]\tau[/latex] acting on an object that has a moment of inertia [latex]I[/latex] will generate an angular acceleration [latex]\alpha=\tau/I[/latex].
• The torque [latex]\tau[/latex] generated by a force [latex]F[/latex] can be written as [latex]\tau=Fl\sin\theta[/latex], where [latex]l[/latex] is the distance from the action point of the force to the pivot point of the object, and [latex]\theta[/latex] is the angle between the vector of the force [latex]F[/latex] and the vector of the displacement vector [latex]l[/latex].

Procedures

1. In the Phyphox app, click on the “acceleration without g” sensor.
2. (Optional Step) You can conveniently access your data through remote control of the Phyphox app with a web browser on your computer. (Follow this video to start remote control.)
3. Switch to the “ABSOLUTE” tab, then start a measurement.
4. With the measurement running, hold the phone in one hand, then curl your forearm as fast as you can (making the biceps contract). Slowly extend your arm then curl as fast as you can again. Repeat for at least five times. (Be careful not to damage your phone!)
5. Stop the measurement. Save a screenshot to help you navigate through your data quickly. Use the remote control to export the data as a csv file (comma, decimal point) for further analysis. If you did not use remote control, you can save the data to your phone first then transfer the file to your computer.
6. Find the mass of your cell phone ([latex]m_{phone}[/latex]) online. If you were using a protective case on the phone, you should try your best to find the mass of the case, too.
7. With the help of internet, estimate the mass of your forearm ([latex]m_{arm}[/latex]).
8. Find the length from the center of your palm to your elbow joint ([latex]l_{arm}[/latex]). If you do not have a ruler, you can estimate the length by comparing it to the length of the phone, then find the length of the phone online.

Data Analysis

Part I: the maximal force of your biceps

1. Read the maximal acceleration experienced by the phone ([latex]a_{max}[/latex]) during each trial, then take the average.
2. Calculate the maximal angular acceleration of the forearm ([latex]\alpha_{max}[/latex]) using [latex]a_{max}[/latex] and [latex]l_{arm}[/latex] that you found above.
3. Assume the center of mass of the forearm is located at [latex]frac{1}{2}l_{arm}[/latex], calculate the moment of inertia of the forearm ([latex]I_{arm}[/latex]) with the elbow as the pivot point. (Hint: check your 1st year physics textbook for the calculation of moment of inertia.)
4. Calculate the moment of inertia of the phone ([latex]I_{phone}[/latex]) with the elbow as the pivot point, treating the phone as a point mass.
5. Calculate the maximal torque that your biceps produced ([latex]\tau_{max}[/latex]).
6. Assuming that the lever arm of the biceps is a constant 4cm, calculate the maximal force ([latex]F_{max}[/latex]) that your biceps produced.

Part II: the maximal contraction speed of your biceps

1. Crop the data and plot the acceleration-time curve for one complete “pulse”.
2. On the plot, indicate the time point at which the phone reaches the maximal speed.
3. Using the time point that you identified above, integrate (i.e., sum up) the acceleration-time data to find the maximal speed of the phone ([latex]v_{max}[/latex]) for five of the trials, then take the average.
4. Still assume that 4cm is the distance from the attachment point of the biceps tendon to the elbow joint, estimate the maximal speed at which the length of your biceps was contracting.

Requirements of the experimental report:

• Font size: 12
• Line spacing: 1.5
• Only write these sections: Results, Discussions, and Suggestions of improvement.
• Total marks: 20/20
• Results (12/20):
  • Complete all the calculations that are required in the procedures and data analysis sections above.
  • Show sample calculations.
  • Attach graphs or tables when necessary.
  • If you write a program for calculations, attach the code in the appendix.
• Discussions (8/20):
  • Find the uncertainty values for each of the calculation in your results section.
  • 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).
• Suggestions of improvement (+2 bonus; total marks capped at 20/20):
  • 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?
  • Did you enjoy this experiment? What are the aspects that you dislike the most about this experiment?
• No page limit. But please try to be straightforward and concise!