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Honors Mechanics Labs with iOLab for Physics 141, Fall 2020

Alice Quillen, Ryan Semple

December 17, 2020

Acknowledgments This version drew on the book published as ‘iOLab for Scientists and Engineers’, by Tom Hemmick. This version also drew on a manual for PHY 113, summer 2020, written S¸ims¸ek. by Kagan ˘ This version of the manual was done with IoLab device model IOL15A and application version 1.70.1530 on MacOS.

Contents 1 Getting started with the iOLab Device 3 1.1 Inside the box . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Technical specs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Videos and tutorials . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Installing the iOLab application . . . . . . . . . . . . . . . . . 5 1.5 Pairing the dongle to the device . . . . . . . . . . . . . . . . 7 1.6 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.7 Taking and viewing data . . . . . . . . . . . . . . . . . . . . . 7 1.8 Analyzing the data . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.9 Saving data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.10 Sharing data and the iOLab Repository . . . . . . . . . . . . 9 2 Lab #1. Acceleration and Force 11 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Measuring the device mass by lifting it . . . . . . . . . . . . . 12 2.3 Measuring device mass from a parametric plot and with a spring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 The ultimate tensile strength of a hair or another weak narrow object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Discussion and Lab reports . . . . . . . . . . . . . . . . . . . . 20 3 Lab #2. Friction 3.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Coulomb’s laws of friction . . . . . . . . . . . . . . . . . . . . . 3.3 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Measuring the kinetic friction coefficient for different mass objects . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Measuring the kinetic friction coefficient for a different interface . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Discussion and Analysis . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Combining measurements by weighting by σ −2 . . .

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23 23 23 26 26 27 27 28

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CONTENTS

4 Lab #3. Hooke’s law, work loops and elastic hysteresis 31 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Physics Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2.1 Hooke’s law and potential energy . . . . . . . . . . . 33 4.2.2 Work loops and hysteresis . . . . . . . . . . . . . . . . . 34 4.2.3 Simple Harmonic Oscillation . . . . . . . . . . . . . . . 35 4.3 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 Examining Hooke’s Law via measurements of force and displacement . . . . . . . . . . . . . . . . . . . . . 36 4.3.2 Measuring the oscillation period predicted with Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.1 Measuring the spring constant from force and displacement . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.2 Fitting a line to data . . . . . . . . . . . . . . . . . . . . 39 4.4.3 Measuring the spring constant from the oscillation period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4.4 Discussing your spring constant . . . . . . . . . . . . . 40 4.4.5 Discussing your work loops . . . . . . . . . . . . . . . . 40 5 Lab #4. The compound pendulum 43 5.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2 Physics overview . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.2.1 The compound pendulum . . . . . . . . . . . . . . . . 44 5.2.2 The Q-factor . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.4.1 Computing the device’s moment of inertia about the pivot . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.4.2 Interpreting the moment of inertia . . . . . . . . . . . 51 5.4.3 Measuring the Q factor . . . . . . . . . . . . . . . . . . 52 5.4.4 Additional discussion and comments . . . . . . . . . . 53 6 Lab #5. The coefficient of restitution of a bouncing elastic sphere 55 6.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.2 Physics of a bouncing elastic sphere . . . . . . . . . . . . . . 56 6.2.1 The times and velocities of a series of bounces . . . . 56 6.2.2 The coefficient of restitution . . . . . . . . . . . . . . . 57 6.2.3 How much and what type of data? . . . . . . . . . . 58 6.3 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.3.1 If you are using the iOLab device . . . . . . . . . . . . 59 6.3.2 If you are using the Audacity Audio software . . . . . 60 6.4 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . 63 6.4.1 Measuring the coefficient of restitution . . . . . . . . . 63 6.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Chapter 1

Getting started with the iOLab Device 1.1 Inside the box When you have obtained the iOLab device, you should find the following in the box: 1. One device/remote and one dongle (see Figure 1.1), and 2. One screwdriver, one long spring, one eye-bolt, two red felt pads, one plate, and one short spring (and possibly a yellow foam pad) (see Figure 1.2). You may need to free the dongle from the back of the device. Stick the red felt pads onto the bottom of your device so that it will slide on a table top.

1.2 Technical specs Take a look at the specifications of the device: Specs! Relevant for many of our experiments is • 3D accelerometer (14 bit signed, 2/4/8g ranges, 1.56 800 Hz sample) • Force probe (Range ± 10 N parallel to Y axis, 12 bits) The 800 Hz sample means a data point every 1/800 of a second. 1/800 = 0.00125 s. That’s a little longer than a millisecond. The actual 3

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CHAPTER 1. GETTING STARTED WITH THE IOLAB DEVICE

Figure 1.1: The device/remote and the dongle.

Figure 1.2: From left to right, the screwdriver, the long spring, the eyebolt, the red felt pads (two of them), the plate, and the short spring.

1.3. VIDEOS AND TUTORIALS

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sampling rate of your data depends on the number of sensors you are recording. The sampling frequency is shown in the plotting windows in the software application. I don’t know what the number 1.56 on the accelerometer refers to. Maybe some kind of lower frequency limit? We can’t measure very high g values (acceleration values) and the three axes are not exactly the same. This probably has to do with the design of the sensor chip. Chips are often not the same in all 3 dimensions. The maximum force we can measure is 10 N (Newtons). If you exert a larger force, the device might break. 14 bits: The numbers span 214 = 16384. 1/16384 = 6.1e-05. So we get an accuracy about about 10 −4 as a fraction of the range. We can probably measure with an accuracy of ± milli-g. 12 bits: The numbers span 212 = 4096. 1/4096 = 2.4e-04. We multiply this by the range which is about 20 N, giving us an accuracy about about 4 × 10 −3 N per data number. We can probably measure ±0.01 N. I suspect vibrations in the mount screw reduce the accuracy. These estimates are meant to give you a feel for the capability of the device. Experimentalists can often instantly recount a lot of information about the capabilities of their instrumentation.1

1.3 Videos and tutorials You can follow videos and tutorials here: link for instructions on getting started!

1.4 Installing the iOLab application The device connects to your computer through a wireless connection. You need to install an application on your computer in order to control your device and take data. 1. If you are installing the software on a Mac see link for installing software on MacOS. 2. If you are installing on a Windows machine see link for installing software on Windows. You will also need to install a driver. 1 As a writer of this manual I need to know the capabilities of the device in order to design feasible labs.

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CHAPTER 1. GETTING STARTED WITH THE IOLAB DEVICE

Figure 1.3: A view of the application.

1.5. PAIRING THE DONGLE TO THE DEVICE

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1.5 Pairing the dongle to the device When you have downloaded the iOLab application, launch it. Insert the USB dongle into your computer. Pressing the power button on the device (this is labelled with a circle that has a vertical bar on it) to power on the device. Select Remote 1 in the application (on top right), and it should automatically pair the dongle to the device. Now the device can be controlled by the application.

1.6 Calibration You must calibrate the device on every computer you use to take data with the iOLab device. Calibrations are necessary to ensure you are getting accurate data. First make sure your device is turned on and the dongle is plugged into your computer and the two are paired. You can follow this: link about how to calibrate the sensors. Figure 1.3 shows a view of the application. Click on the tools button in top right corner of the applications page (This is a small gear-shaped icon). This will give you a drop-down menu. One of the options in this menu is Calibration. You will be able to click on either Accel - magn - gyro or Force under Calibration. You will do two calibrations: one for the Accelerometer - Magnetometer - Gyroscope and one for the Force sensor. You will need to attach the eyebolt to the force probe (on the bottom of the device) in order to complete the calibration of the force sensor. To calibrate the accelerometer, the eyebolt must not be attached. Once you select a calibration type, follow the directions given in the application. Once you are done with the calibration, make sure you hit the save button so that you don’t need to do it again! If you make a mistake, you can quit and restart the calibration sequence. How is the mechanism calibrated? The accelerometer is calibrated using the direction and strength of gravitational acceleration, g. The force probe is calibrated using the mass of the device.

1.7 Taking and viewing data Open the iOLab software. On the left hand side of the page, you will see a menu listing the possible sensors (with check boxes next to each). To take data, first make sure the dongle is plugged into the computer and the device is turned on.

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CHAPTER 1. GETTING STARTED WITH THE IOLAB DEVICE

Record data by selecting one or more sensors from the checklist at the left of the the iOLab application, then clicking the Record button at the top. Click Stop in the same place as Record to finish recording. This nice video shows how to record and view Force and Accelerometer data. The Remove button on the top of the application will clear the plots and allow you to retake the data. You can find where the data is stored by clicking on the file icon. This tutorial explains how to view data. You can turn off the device by holding down the power button for 2 seconds. I found this was useful as the USB input slowed down my computer. The top of the application shows you whether the device and dongle are paired and whether the device is on.

1.8 Analyzing the data Watch this this video to see an example of the types of analysis you can do with the application. In the application, there are three connected buttons that look like a bar graph, a magnifier, and two arrows orthogonal to each other. The “bar graph” is the analysis mode. The middle one is the zoom button. It has actually a dropdown menu: The first option allows you to choose a box section of the plot on which to zoom. The second option allows you to zoom horizontally only, and the last option allows you to zoom vertically only. To unzoom, click on the plot while in Zoom mode. The last button in this block of three is a ’pan’ and allows you to move the central position of the plot by clicking, holding and dragging. The analysis mode of the software allows you to highlight specific sections of the plots to analyze. When a section of the plot is highlighted, the following information will be given to you: ∆t, µ, σ, a, and s: 1. ∆t is the duration of the selected interval. 2. µ is the average value of the highlighted portion. 3. σ is the standard deviation of points in the highlighted portion. 4. a is the area under the curve. 5. s is the slope of the highlighted section. Note σ is not the uncertainty in the measurement of the average value. To estimate the uncertainty in the average value you need to take into account the number of points in the interval. The number of points in the interval is N = ∆t × S where S is the sampling frequency in Hz. A √ measurement of the average would be µ ± σ/ N.

1.9. SAVING DATA

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1.9 Saving data All data that you record will be saved on your computer. If you take data in the iOLab application, click on the folder button and you will see all the data you have taken in the order you have taken it. The most recent data will be at the top of the list and each item in the list will be time stamped and marked by which sensors were used. However, keep in mind that highlighting and the analysis will not be saved here. You can click the snapshot button on the lower right of the application to save the view. This does not give you an image but does restore some information, such as the zoom state of the window and which region is highlighted for analysis. I recommend take notes in your lab notebook and write down which data matches each set of experiments you carried out.

1.10 Sharing data and the iOLab Repository The iOLab repository can be used to share data with a lab partner. To find out more, in the iOLab ap, click on the cloud icon and then click on Documentation.

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CHAPTER 1. GETTING STARTED WITH THE IOLAB DEVICE

Chapter 2

Lab #1. Acceleration and Force 2.1 Overview Newton’s 2nd law Newton’s second law is a relation between force, mass and acceleration. F = ma. Objectives In this lab, we are going to 1. Use Newton’s 2nd law, F = ma, to measure the mass of the iOLab device. We will measure the device mass in two ways. • By lifting the device and measuring mg where g is the gravitational acceleration. • Using the relation between force and acceleration for harmonic motion with a spring. In your lab report you will compare these mass measurements. You will need to estimate the uncertainty in each of your mass measurements!

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CHAPTER 2. LAB #1. ACCELERATION AND FORCE

Figure 2.1: To measure the device mass, first record the force and acceleration while it is resting on the table top. Then lift it and hold it steady while recording the force. 2. After we have confidence in our ability to accurately measure force, we will measure an unknown force. We measure the ultimate tensile strength of a human hair or another weak and narrow object. Things you need to do this lab Find a long narrow object that is easy to break. It must be easy to break as we don’t want to overload and break the force sensor. I found the following objects: a human hair, a thin blade of grass and a very narrow slip of paper.

2.2 Measuring the device mass by lifting it You can look at this tutorial: Finding the mass of the device

2.2. MEASURING THE DEVICE MASS BY LIFTING IT

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Launch the iOLab application, power on your remote and make sure it is paired with the dongle. Insert the eye-bolt into the force probe on the IoLab device. Select the sensors Accelerometer and Force. You are now ready to record data! Reset to clear previous runs on the ap. Put the remote on the table so that the +y axis is downwards and the eye-bolt is upward and start recording data (see Figure 2.1). Wait two seconds. Now grab the remote by the eye-bolt and lift it. Hold steady for two seconds. Put it back. Stop recording data. • You can take screenshots of plots to include in your lab report or to keep a record in a file that would be like a lab notebook. It is a good idea to take notes on your experiments. • In the analysis mode (to the left of the magnifier), choose a region of time before or after you lifted the device. Click on Rezero sensor as shown in Figure 2.2. Check that the force is near zero when the device was at rest on the table. • By using the analysis tool, select a region in the “valley” of your force-time graph (when the device was held by the eye-bolt) and measure (and record into your lab notebook) the average force and the standard deviation of points in the region. • Again using the analysis tool, select the acceleration in the forcefree region and record the average acceleration and its uncertainty. • Using your measurements for acceleration and force, compute the mass of the remote.

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CHAPTER 2. LAB #1. ACCELERATION AND FORCE

Figure 2.2: In analysis mode, choose a region where there should be no force. Click on Rezero sensor to make sure that this region gives a measurement of zero force. In the analysis model, the mean µ and standard deviation σ reported by the application software are the average and standard deviation of the points in the √ selected region. The measurement of the mean itself should be µ ± σ/ N where N is the number of points in the selected region. You can estimate the number of points in the selected region using the sampling rate. For figure 2.2 the region has ∆t = 0.96892 s and the sampling rate is 800 Hz. The time between each sample is dt = 1/800 s so the number of samples in the selected region is N = ∆t/dt = 0.96892 √ × 800 = 775. The measurement of the force would be 0.0000 ± 0.0067/ 775 = 0.0000 ± 0.00024. The relation between force F and acceleration a is F = ma.

(2.1)

The acceleration is vertical and should be equal to a = g. Even though acceleration is vertical, we are measuring the vertical component of acceleration in the y channel (not the z channel) on our accelerometer. Equation 2.1 gives m=

F . g

(2.2)

If you have errors in measurements of both F and g, then you would propagate the errors to estimate the error in m. The error in your mea-

2.3. MEASURING DEVICE MASS FROM A PARAMETRIC PLOT AND WITH A SPRING15 surement of the mass m is s σg2 F σF2 + σm = . g F2 g2

(2.3)

, ∂m You can verify this formula using derivatives∂g∂m ∂ f computed from equation 2.2, propagating errors and summing errors in quadrature. Check that your measured value of the vertical acceleration is consistent with the expected value1 for the gravitational acceleration on Earth g = 9.80665m s −2 . If not then you probably need to investigate2 . How should you use equation 2.3? If σg /g ≪ σF /F then you can ignore σg when computing the uncertainty in m. If you have checked that the vertical acceleration is consistent with g then I would say you can use the known value for g. Equation 2.3 then becomes σm = σF /g. In your lab report, you should describe how you have estimated the standard deviation σm in your mass measurement.

2.3 Measuring device mass from a parametric plot and with a spring Reset the device. Attach the eye-bolt to the force probe (if it isn’t already there), and attach the long spring to it. Attach the spring to something solid so that the device can hang down securely. See Figure 2.3. When it is nearly in equilibrium, start recording data. Give it a small pull and let it oscillate vertically for a while. Stop recording data. See this nice video on making a parametric plot: parametric plot tutorial. The easiest way to do this part of the lab is to watch...