Unit 2 - Motion

Lab 2A: Linear motion on an air track

UCLA Physics Department

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University of California, Los Angeles

Department of Physics and Astronomy

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Physics 4AL

JupyterLab Repository Updated

Log in link:

https://physhub.oarc.ucla.edu/hub/login?next=%2Fhub%2F

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Physics 4AL:

https://physhub.oarc.ucla.edu/hub/user-redirect/git-pull?repo=https%3A%2F%2Fgithub.com%2Fuclaphysics4labs%2FPhysics_4AL_2023-24&urlpath=lab%2Ftree%2FPhysics_4AL_2023-24%2F

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Please note that material pulled from this link will be periodically updated as the course is changing throughout the quarter.

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UCLA Physics Department

Outline of Lab 2A

• 2A In-Lab
• Mount bluetooth Arduino ultrasonic sensor setup on airtrack
• Measure the position of the glider under constant acceleration
• Use polyfit to fit position vs. time data to a quadratic polynomial
• Obtain the elevation angle from the acceleration of the glider

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UCLA Physics Department

Setting up the Glider

UCLA Physics Department

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Bluetooth connection

• We will be working with just one team member’s setup for this lab.
• Take out one setup and attach the bluetooth module.
• Add the batteries to the battery holder and power your setup.
• Connect the bluetooth module of your setup with your computer.
• Open serial monitor on the Arduino IDE and verify if you are able to see the elapsed time and ultrasound readings (the previously uploaded code into the Arduino from Lab 1D should still work).

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UCLA Physics Department

Mount ESP32 setup

• Place ESP32 in plastic holder with ultrasonic sensor flush with opening and battery clipped in
• Put rubber band holder (with rubber bands attached as shown in picture) facing downwards (so the rubberband lessens the fall).

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Plastic holder

Note ultrasonic sensor not covered

ESP setup mounted on plastic platform, note rubber band

Reflecting surface setup

• Attach a piece cardboard to the end of the air track using tape. The Arduino will be bouncing ultrasound signals off of this cardboard. If the cardboard is unstable, cut it smaller using scissors or box cutters.

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Cardboard

Air supply to Air track

• Turn on the air track using the device shown shown in the figure. Look under the table to find it.
• The dial goes from 0 to 6 to control how much air is flowing to the air track.
• Try different settings of the dial to see how the airflow controls the motion of the glider.

Air track glider stability

• If the glider is not stable, the air track is not leveled.
• Use the screws at the bottom of the air track so that the glider is stable when the air glider is set to max air flow.

Sensor limitation (Checkpoint 1)

• Open the serial monitor of your bluetooth port. (Since your code is already uploaded during lab 1D you don’t have to upload any code.)
• Start with the ultrasound sensor close to the reflecting surface (around 5 cm) and move the glider away increasing the distance from the reflecting surface.
• At some point, the signal will become noisy. Determine the maximum distance that the glider can go before the signal is too noisy.
• Note down the output from the Arduino right before the output becomes noisy. Compare the output in your serial monitor with the ruler on the airtrack. Provide both values to your TA.

Obtaining acceleration data

UCLA Physics Department

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Elevating the air track

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• Tilt the airtrack using an appropriate measure, use the metallic block, stacks of cardboard etc.
• Measure your angle by measuring the height and length of your air track as shown below
• Use trigonometry to determine the elevation angle of the air track

θ

Length = L

Height = h

Obtaining acceleration data

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• Set the airflow to maximum and move the glider to the max distance before data gets noisy. Release the glider and capture the data.
• Collect data once for each group member at the same elevation angle. Save these into different files. Each group member should perform analysis on their own data file, but you can use the same Arduino for all data sets.

TA Checkpoint 2 - constant acceleration plot

• Calculate the elevation angle of the air track using trigonometry
• Show this angle to your TA.
• Use the lab 2A notebook to plot and analyze the data collected. Analysis must be done by each group member. (each member analyzes one of the datasets collected)
• You should be able to estimate the acceleration of the glider with uncertainty using np.polyfit
• Extract the acceleration of your glider and the associated uncertainty.
• Show this result to your TA.

Finding the elevation angle

UCLA Physics Department

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Aside - Representing Measurements with Error

• Generally, we give measurements as some value ± uncertainty, followed by the units�
• However, it is important to properly represent values given the error that we know. Consider these two measurement representations:

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• Since the error in our measurement here is of the order 0.1 cm, our measurement results that are more precise than 0.1 cm are meaningless�
• Therefore, we should represent our measurements like those presented on the right. Presenting our measurements like those presented on the left implies that we know more about the measurement than we actually know

Obtaining the elevation angle

• The elevation angle can be obtained directly from the acceleration

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• Since the equation for the angle is not a simple function of the acceleration, we need more robust error analysis
• In general, for a function f of independent variables, we have

TA Checkpoint 3 - obtain the elevation angle

• Using this, we can calculate the uncertainty in the elevation angle

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• Using the derivative of arcsin, we obtain (if the angle is given in radians. Convert it to degrees if you report your angle in degrees.)

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• Using the acceleration of the glider you found for TA checkpoint 2, determine the elevation angle and associated uncertainty of the air track. Show your result to your TA.

Post-Lab Requirements for lab 2A

• Record the maximum reading in cm given by the ultrasonic sensor before the ultrasonic data became noisy
• Record the maximum reading in cm given by the ruler on the air track before the ultrasonic data became noisy
• Provide the plot of distance vs. time of the glider for constant acceleration. Be sure to include axis labels, a title, and a legend
• Obtain the acceleration of the glider and the associated uncertainty. Be sure to include units in your measurement
• Obtain the elevation angle of your air track and the associated uncertainty. Be sure to include units in your measurement

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• You don’t have to include your elevation angle measured from trigonometry, but you will need it for the Unit 2 Report.