The first four labs plus the out of lab assignment introduced you in a systematic way to some ideas and conventions related to;

• how to compare measured values in a scientifically meaningful way,
• how to evaluate data by looking at plots of the residuals and,
• least squares curve fitting and reduced Chi-square as a measure of goodness of fit.

These are all tools which you will make use of throughout your physics lab courses.

For the final two labs of the Autumn quarter we will shift gears a bit and introduce you to an instrument which can record data using many different sensors and send that data to a computer for analysis. You will then use this instrument to design and execute two experiments.

In this lab you will use instrument called the iOLab. The iOLab contains a wide array of instruments and sensors which are useful for doing physics experiments.

• 3-axis Magnetometers.
• 3-axis Accelerometers.
• 3-axis Gyroscopes.
• A Force sensor.
• Position encoders.
• Light and Sound sensors

Interestingly, most of the sensors in these devices are also found in your cell phone. The difference is that the sensors in the iOLab are designed to be used for scientific experimentation and can provide much more precise and accurate data than what your phone can achieve. You will use this device in a number of future labs in the PHYS140s sequence. The first part of this lab is an exercise to get you familiar with the device, what its capabilities are and how to use it. Work through the following tutorial.

Doing experimental physics is not a matter of setting up some equipment, taking and analyzing data, and getting an answer. A considerable amount of time and effort goes into developing experimental apparatus and techniques. This process involves designing and conducting sub-experiments to more fully understand the capabilities of your apparatus. The rest of todays lab will be a guided exercise in this process.

For the sake of the lab exercise, assume that you plan to use the iOLabs wheel sensor to measure the acceleration of an object as one part of a larger experiment. It would be important to understand how accurately the iOLab is able to measure acceleration. No measurement device is perfect, there are always systematic biases present in how they operate which must be understood and often times accounted for.

This is what you will do for this lab. Since this is a learning exercise we will guide you through the process. In future labs you will be expected to know how and when to do this as part of an experiment.

The first step is to test the performance of the apparatus under conditions where you can predict what the result of the measurement should be.

A straight forward method of testing the ability of the iOLabs wheel sensors to measure acceleration is to allow it to roll down an inclined plane under the influence of gravity. This method has the advantage that it is easy to predict what acceleration using Newton's Laws.

1. Develop a model that predicts what the acceleration of the iOLab should be when it rolls down a ramp. In developing this model you will be making some assumptions, take a moment to consider what they are.
   • Record the most important assumptions which went into your model in your lab notebook. Do not resort to making wild guesses, your assumptions should be scientifically plausible.
2. Do a few trial runs. Observe what is happening and look at the data. Consider how you will release the iOLab so that it travels smoothly and in as straight a line as possible. The goal is to ensure that your data are repeatable and reliable.
   • Consider what part of the data stream from the iOLab to select for analysis. It is not arbitrary which portions of the data you select, your choices have consequences for how you interpret the results. You will be asked to describe how you made this selection and why for your Individual Analysis. A screen shot illustrating your selection can be helpful for this and should be included in your lab notebook for later use. As an example you would not want to select a region of the velocity plot which begins before you release the device, that would clearly not yield a sensible result.
3. Do the measurement. You could just take data for a single run of the iOLab down the incline and analyze that. But doing this would be sloppy and unprofessional, to say the least.
   • Collect enough data to establish repeatability, and show the range of fluctuations (i.e. you want enough measurements to be able to get an average value with a meaningful error of the mean).
4. Analyze the data. Use the tools built into the iOLab software to measure the acceleration of the device for multiple trials. Record your measurements with uncertainties in your lab notebook.
5. Compare your measured acceleration with the predictions from your model. You will find that the two do not agree within experimental uncertainty. If you have been paying attention to the system you are working with, you probably have a pretty good idea why the results do not agree with the prediction. Discuss with your instructor what is going on here.
   • Record what you conclude is the most likely effect that is the source of the disagreement.

At this point you will have identified a significant source of bias (systematic uncertainty) present in your data. The next step is to continue your investigation to see if you can confirm and account for this effect.

Your task now is to come up with another experiment that will allow you to determine a correction factor for the effect that is causing your results to deviate from the expectation.

1. Come up with a way of independently verifying and quantifying the source of your bias. By this point you, possibly with the assistance of your instructor, will have concluded that there is energy loss due to friction in the wheels. In physics terms this means we have a non-conservative system. Friction is a non-conservative force which would you would plausibly expect might cause an effect like what you observe. If this is indeed the case you should be able to modify your model to include a frictional force term, and then come up with a way to independently verify and quantify its presence. Consider the following hint. A frictional force always acts in a direction that opposes the motion of the object. The force of gravity however always acts in the same direction, regardless of the motion of the object. This should suggest a simple test which can be done that will both confirm the presence of a frictional force and determine its magnitude. Ideally you want to change as little about your experimental setup as possible so that you can isolate the effect of friction only. I.e. you do not want to change the angle of the ramp for example, because that could have an independent effect on the effect of friction. Consult with your TA about how to approach this part of the problem to make sure you are on the right track.
2. Conduct the experiment you developed above. Collect enough data to establish repeatability and get a good average.
3. Analyze your data and see if you are able to confirm the hypothesis of a frictional force being present.
4. Use the data to determine a correction factor. Apply this correction factor to your original measurement and assess it's impact. Does this improve the accuracy of the first acceleration measurement?

Now do one final test of your modified model. If you have properly accounted for friction, your model should work to predict how quickly the iOLab decelerates when given an initial velocity on a horizontal surface.

• Conduct an experiment to test out this hypothesis.
• Record your data and calculations showing how well your modified model predicts the deceleration of the iOLab.