Accelerometers

JOHNS HOPKINS UNIVERSITY,PHYSICSAND ASTRONOMY AS.173.111 – GENERAL PHYSICS LABORATORY I

Accelerometers

1L EARNING OBJECTIVES At the conclusion of this activity you should be able to: • Use your smartphone to collect acceleration data. • Use measured acceleration to estimate the distance of a free fall • Use measured acceleration to estimate kinematic quantities that describe an elevator ride.

2B ACKGROUND

2.1A CCELERATION,VELOCITY, AND POSITION We know from Classical Mechanics that we can move between position, velocity, and acceleration by repeatedly taking time derivatives of the position of an object. Similarly, starting from acceleration, we can take subsequent integrals with respect to time to obtain velocity and position respectively.

Description Differential Form Integral Form Z Position ~x ~x ~vdt = d~x Z Velocity ~v ~v ~adt = dt = d 2~x d~v Acceleration ~a ~a = dt 2 = dt

2.2C OLLECTING DATA WITH A SMARTPHONE Most modern smart phones come packed with sensors that make them ideal to use as physics instru- ments. Many cell phones come packaged with an air pressure sensor, light meter, 3-axis accelerometers, 3-axis magnetometer, gyroscope, and of course a microphone. Many great physics measurements can be made using your smart phone. Several apps exist for collecting data from these packaged sensors. For this lab activity, we will use the PhyPhox app. You may download the app to your phone here: https://phyphox.org/

2.3A CCELEROMETERS Your smartphone is packaged with a small integrated circuit package called a Microelectromechanical Systems (MEMS). Accelerometers are used in nearly all smartphones. For example, the accelerometer is used to tell your phone whether to display the screen in portrait or landscape mode depending on the orientation of the phone. Accelerometer MEMS contain small springs attached to small “proof masses” to measure accelerations. Generally, the accelerometer can measure the acceleration in three axes simultaneously. Figures 2.1 and 2.2 show microscope pictures of an accelerometer.

Figure 2.1: A microscope picture of an accelerometer MEMS chip. For this picture, the chips packaging has been removed. The motion of the proof mass is measured using capacitors (labeled “cap’s” in the image). The x and y accelerations are measured using one system and the z direction is measured with another. Image Credit: https://memsblog.wordpress.com/ 2011/01/05/chipworks-2/

2.4E XPORTING PLOTSFROM LOGGER PRO The easiest way to get a plot from Logger Pro into your lab note is to copy and paste the graph. However, this method results in an extremely large ﬁle size in Microsoft Word. Turnitin will only accept ﬁles that

2 Figure 2.2: A close-up microscope picture of the etched spring and proof mass in an accelerometer MEMS. Motion of the proof mass – under acceleration – changes the spacing between the capacitor plates which can be measured electrically. Image Credit: https: //memsblog.wordpress.com/2011/01/05/chipworks-2/ are less than 40 MB; large ﬁles can often lead to submission problems. The following link gives instructions on how best to save a Logger Pro graph as a reasonably sized image ﬁle (.jpg or .png) that can be imported into your lab note. http://www.vernier.com/til/2358/

3 3P ROCEDURE ! ! ! CAUTION ! ! ! You will be dropping your smartphone to make acceleration measurements in this lab. To avoid damaging your phone, only drop it onto a soft surface. In the laboratory we drop phones into boxes ﬁlled with packing peanuts. At home you might try dropping your phone onto a mattress, folded soft blanket, couch, or pillows.

To avoid damaging your phone, limit the height your phone drops to no more than 1 meter (roughly 3 feet).

If you feel nervous about dropping your device, please check in with us – before continuing – to conﬁrm that your setup will not cause damage. If you would rather NOT drop your phone, we can provide you with the data required to complete the assignment.

3.1P HONE DROP Using accelerometer data collected by your smart phone, determine how far the phone falls when dropped. • Using the PhyPhox app, record acceleration data when your phone is dropped from a known height. Drop your phone into one of the “foam pits” in the laboratory to avoid damaging your phone. • Use the accelerometer data collected with your phone to measure the height of the drop.

3.2E LEVATOR RIDE • Using the PhyPhox app, record acceleration data while riding an elevator in the Bloomberg build- ing. • Using the accelerometer data collected with your phone develop an analysis to answer at least one of the following questions: – What is the distance between two ﬂoors? – Is the spacing between each ﬂoor the same? – What is the maximum velocity of the elevator? – Is the speed of the elevator the same when going up as going down?

4L AB REFLECTION Write a brief reflection to document and summarize your lab work. Your work will be evaluated using the following rubric: • Data Analysis & Plots (4 points) – State what you intend to accomplish with your experiment. What are you trying to measure? – Briefly describe how the apparatus will be used to make the measurement. A well-labeled photograph or diagram is an efficient way to explain the details of the experimental setup. – Analyze your data using well-formatted plot(s).

4 – Describe the models that were used to make sense of your data. • Result(s) and Comparison (4 points) – Clearly state the final result(s) of your experiment with an associated uncertainty estimate. – Report your result with measurement units and the appropriate significant digits. – Compare your result to another relevant quantity. For example, you might compare your measurement to an accepted value or another another group’s value. – Choose the best tools available to make the comparison meaningful. • Dominant Source of Uncertainty (4 points) – Identify and discuss the dominant source(s) of uncertainty in your result. – Use error propagation calculations (as appropriate) to support your explanation. • Experiment Reflection (4 points) – Interpret the evidence (plots, results, calculations, error estimates, etc) that you have pre- sented. – Explain how your experimental findings relate to the underlying physical principles. – Emphasize interesting features of your experiment and/or highlight unanswered questions that you identified in the course of the experiment. – Remember that we are interested in the details of your experiment and not vague theoretical statements.