17 Lab 2: Torque and Speed of Muscle
liyuchon
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
- In the Phyphox app, click on the “acceleration without g” sensor.
- (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.)
- Switch to the “ABSOLUTE” tab, then start a measurement.
- 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!)
- 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.
- 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.
- With the help of internet, estimate the mass of your forearm ([latex]m_{arm}[/latex]).
- 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
- Read the maximal acceleration e