## LESSONS

###### The lesson ideas below require minimal resources other than the smartphone, and are relevant to introductory physics in high school and college. However, creative individuals are using smartphone science in more complex ways, with drones, engineering kits, and much more. Follow us on Twitter @PhysicsToolbox and see our Publications page for additional content.

What are some examples physics topics that can be taught with smartphones?

Try This

Click on the resources below to get some sample worksheets intended for practicing physics teachers to learn about some (but not all) of the capabilities for using smartphones in physics teaching in the context of a 2-hour professional development workshop setting.

Related Resources

Introduction to Smartphone Sensors

What sensors are available in a smarthpone, and what do they measure?

Try This

Download Physics Toolbox Play and complete the 7 challenges to learn about the basic smartphone sensors, what they measure, some fundamental physics, and how sensors are used in STEM careers.

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What is the HEIGHT of any structure?

Try This

To measure the height of a tall object, think about the height as the side of a right-triangle. Standing a good distance away from the object, use the Orientation tool to determine the angle between the horizontal and your line of sight to the top edge of the object. To get the base of the triangle, measure the number of steps between you and the base of the object. (You can find out the length of each of your steps separately using a meter stick). This requires some understanding of trigonometry.

Related Resources

Measurement: Circumference of the Earth

What is the circumference of the Earth?

Try This

Use either equinox to your advantage to measure the circumference of the Earth using a method similar to that used by Eritosthenes! On the Equinox at astronomical noon, the sun is directly overhead at the equator (where the latitude is 0 degrees). At a point not on the equator, use the GPS to determine your latitude and the Inclinometer to determine the angle of the sun at astronomical noon at your location. Considering that the Earth makes up a full 360 degrees around, use the known difference in latitude from the equator, the known distance per latitude degree, and the difference in inclination of the Sun to determine  the total distance around the Earth (approximated for the Earth as a perfect sphere).

Measurement: Precision

What is the PRECISION of our measurement tools?

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Try to measure a small object (such as a leaf or coin) using various tools, including the Ruler mode. To what decimal value does the app provide? (Considering that the smartphone uses pixels, is the measurement actually that precise? Consider how smartphones make estimates about finger position). In reality, what is more accurate and precise, the smartphone or another tool?

Measurement: Gait Patterns

What is the relationship between the HEIGHT and GAIT FREQUENCY for walking humans?

Try This

Attach a mobile device to your back or chest area and collect data while walking using the g-Force or Accelerometer tools. For various subjects, compare dynamic, gait, metrics, symmetry, and variability. Compare these traits in the data to physical characteristics, such as height or leg length. If desired, record video on another camera to compare data to visual observations.

Challenge Yourself

• Create a graph of Gait Frequency vs. Height, and derive a mathematical expression for this relationship.

• If there are any constants in these mathematical expressions, explain their significance.

• Attach the mobile device to other parts of the body (thigh or leg). How does this data differ from that collected on your chest or back? Why?

Related Resources

Measurement: Seismic Vibrations

What is the relationship between SEISMIC VIBRATION STRENGTH and DISTANCE from the "epicenter" of the shake?

Try This

Perform three different investigations from IRIS (Incorporated Research Institutes for Seismology). In these activities, use the Accelerometer tool along with a meter sticktape, and chair or water bottle to simulate the relationship between an earthquake's magnitude and intensity. Calculate the energy released during a weight drop (magnitude) and use the accelerometer to investigate what happens to the energy as the source is moved further and further from the sensor (intensity). Examine USGS ShakeMaps to explore other factors besides event size and distance from the source to the receiver that affect the intensity (i.e. geologic structures and materials).

Challenge Yourself

• Create a graph of Intensity vs. Distance for a "seismic event," and derive a mathematical expression for this relationship.

• If there are any constants in this mathematical expression, explain their significance.

Related Resources

Linear Motion: G-"Forces"

Under what circumstances do G-FORCES read "0" in all dimensions? Why?

Try This

Although used in everyday speech to describe changes in motion, a "g-force" is neither a measure of gravity nor a force! Instead, g-force can be thought of as the unit-less ratio between normal force on an object and its weight (FN/Fg). For example, someone who is experiencing "2 g's" is experiencing a normal force that is twice the strength of the pull of gravity on their body, and the increased normal force is perceived as "apparent heaviness," although there is no actual change in weight.

Investigate g-forces in all dimensions by using the G-Force tool. Try orienting the smartphone or tablet differently, and seeing the effect on the total and individual g-force axes. Try to get the device to read - if only temporarily - a g-force of 0 in all dimension at the same time. Hint: The best place to try this is on a large, padded area such as a bed or sofa. (Be cautious of preventing your phone from colliding with hard surfaces, or bouncing off of a soft surface.)

Challenge Yourself

• Describe the kind of motion that is necessary for all axes to read "0" g-force. Explain why this is the case.

• Describe the kind of motion that would be necessary for all axes to read "1" g-force. Explain why this is the case.

• For a device at rest, is it ever possible for the total g-force to be higher or lower than 1-g? Explain.

Related Resources

Linear Motion: Describing Acceleration

What is the relationship between the POSITION of objects and the TIME they take to fall?

Try This

Attach 6 or more hex nuts with uniform spacing, using a ruler, to a single strand of string, suspend the string vertically from one end, and then drop it onto a pie pan. Listen to the pattern of the sound produced. What does this suggest about the motion of things as they fall? Try to re-position the hex nuts along the string so that the sound produced is a uniform series of beats (equal time intervals). Using the Sound Meter mode of Physics Toolbox Suite, record these sounds, and refine your spacings until the time intervals are as uniform as possible.

Challenge Yourself

• What do you notice about the physical spacing between each of the nuts in order to produce a uniform series of beats?

• Create a graph of Distance of each hex nut (from the first hex nut) versus the beat number. What mathematical model describes the curve produced?

Related Resources

Linear Motion: Acceleration due to Gravity

What is the ACCELERATION DUE TO GRAVITY near the surface of the Earth?

Try This

Using the Accelerometer tool, allow the mobile device to fall straight down onto a soft surface, such as a bedsofa, or very large pillow. Using the data recorded, determine the acceleration due to gravity near the surface of the Earth.

Challenge Yourself

• Is the acceleration due to gravity recorded as positive or negative on your device? Why?

• Is the acceleration of devices of different mass and size the same or different? Why?

Related Resources

Linear Motion: Displacement, Velocity, and Acceleration

What is the vertical DISPLACEMENT traveled during an elevator ride?

Try This

Few mobile devices have the capability to measure small-scale displacements inside of buildings - when it is measured, it is typically done through comparing GPS coordinates. However, another method is to use "dead-reckoning." In this case, a simple example of linear dead-reckoning can be accomplished by taking the double integration of acceleration data.

While using the Accelerometer tool on a mobile device that is lying flat on the floor of an elevator, ride up or down a reasonable number of levels. Export this data as a .csv file into a data analysis program, such as Logger Pro, Data Studio, or Excel. Take the double integral of the data from the moment you started accelerating at the start of the ride to the moment you stoppped accelerating at the end of the ride. This double integration gives the displacement of the elevator. If possible, compare this double integration to a physically measured value (i.e. counting and measure stair steps) to evaluation.

Challenge Yourself

• If you went up in your elevator ride, how would your results (graph, integral, and total displacement) be different if you went down?

• How would the results above be different if your mobile device was oriented differently? Explain.

• What is the percent error in your double integration compared to the physically measured displacement? Explain what factors might account for these differences.

Related Resources

Periodic Motion: Springs

What is the relationship between MASS and PERIOD of an oscillating spring?

Try This

Using the Accelerometer tool, record the period of oscillation of your smartphone when attached to a vertical spring. Determine the graphical and mathematical relationship between mass and period of the spring. (If a spring is not available, a set of uniform rubber bands will suffice). Known masses can be attached to the mobile device, and additional objects can be massed using a balance. Determine the effect of using different uniforma sets of rubber bands.

Challenge Yourself

• Create a graph of Period vs. Math, and derive a mathematical expression for this relationship.

• If there are any constants in these mathematical expressions, explain their significance.

• The "type" of spring affects the quantitive relationship of mass and period by a factor known as the "spring coefficient." Do thicker, stiffer rubber bands results in a higher or lower spring coefficient? Explain how you know.

• Predict the unit(s) associated with the spring coefficient by doing unit analysis. Explain.

Related Resources

Periodic Motion: Spring Systems

What is the relationship between effective SPRING CONSTANT and SPRING SYSTEMS (series/parallel)?

Try This

Using the Accelerometer tool, record the period of oscillation of your smartphone when attached oscillating springs in a series or parallel configuration. Determine the effective spring constant in each scenario.

Related Resources

Periodic Motion: Pendula

What is the relationship between LENGTH, MASS, and PERIOD of a simple pendulum?

Try This

Using the Proximeter tool, measure the period of a simple pendulum constructed from a suspended string attached firmly to the mobile device. Use a meter stick to determine the relationship between pendulum length and period (if any). Use a balance to determine the relationship between the pendulum mass and period (if any).

Challenge Yourself

• Create a graph of Period vs. Mass, and derive a mathematical expression for this relationship.

• Create a graph of Period vs. Length, and derive a mathematical expression for this relationship.

• If there are any constants in these mathematical expressions, explain their significance.

• Does the angle of release have any impact on the pendulum? Explain how you know.

Related Resources

• Eureka Magazine. "Obtaining Acceleration Due to Gravity with a Pendulum."

• Mobile Science Wiki. "Measurement of Acceleration of Gravity and Angle of Release."

• Lesson

• Video

• * Note: The lesson plan above refers to a "Mobile Science Pendulum" app, and is no longer available. However, this lab can be fully completed with Physics Toolbox Accelerometer alone and with or without any data analysis tool that can accept .csv files. Essentially, the app, developed by Forinash and Wisman, used Physics Toolbox Magnetometer to directly export data into a data analysis tool. Vieyra Software hopes to soon have direct data analysis capabilities in the future.*

Periodic Motion: Inertial Balance

What is the relationship between MASS and PERIOD of an oscillating inertial balance?

Try This

Using the Accelerometer tool, measure the period of an oscillating inertial balance (either commercially obtained or fashioned out of two electrical boxes, metal strips, and screws) and masses

Challenge Yourself

• Create a graph of Period vs. Mass, and derive a mathematical expression for this relationship.

Related Resources

Circular Motion: Acceleration and Tangential Velocity

What is the relationship between centripetal ACCELERATION and tangential VELOCITY?

Try This

Using the Accelerometer tool, hold the mobile device outward at arm's length and pirouette or spin as uniformly as possible. Determine the direction of the net acceleration on the mobile device. Explain why this makes sense. Determine the qualitative relationship between velocity and net acceleration. Calculate the tangential velocity of the mobile device during the spin using a meter stick to measure your arm length. Estimate total net force after measuring the mass of your device with a balance.

Related Resources - Click the image to get a lesson plan!

Circular Motion: Locating an Accelerometer

Where is the ACCELEROMETER located in my smartphone?

Try This

Measure the centripetal acceleration on a smartphone using the Accelerometer tool when placed on a record player moving at a constant speed. Determine the location of the accelerometer from the acceleration reading and the radius, measured with a meter stick.

Challenge Yourself

• How would the experiment be different if the speed of the record player was uniformaly faster or slower? Explain.

Related Resources

What is the relationship between the PRESSURE and HEIGHT above ground?

Try This

Using the Barometer tool, determine the relationship between air pressure and height above ground. A meter stick can be employed to determine the height above ground (by measuring and counting the heights of stair steps, for example).

Related Resources - Click the image to get a lesson plan!

Force: Forces on an Inclined Plane

What is the relationship between the INCLINE ANGLE and FORCES on an object placed on an inclined plane?

Try This

Using the G-Force and Orientation tools, determine how the components of the forces acting on an object change as the angle of incline changes,

Related Resources

Force: Liquid Pressure and Stevin's Law

What is the relationship between PRESSURE and DEPTH below the surface of a liquid?

Try This

Using the Barometer tool, place the smartphone inside of a water-proof case and submerge it under a still container of water. Use a meter stick to measure the depth of the device below the surface. Determine the relationship between pressure and depth for water. Perform the same experiment with different fluids (soap, saturated salt water, oil, alcohol, etc.)

Challenge Yourself

• Create a graph of Pressure vs. Depth for water, and derive a mathematical expression for this relationship.

• Create additional graphs of Pressure vs. Depth for other fluids, and derive mathematical expressions for these relationships.

• If there are any constants in these mathematical expressions, explain their significance.

• Using prior understandings about fluid pressure, determine the density of each fluid studied.

Related Resources

Force: Air Pressure in a Balloon

What is the relationship between PRESSURE and RADIUS of an inflated rubber balloon?

Try This

Using the Barometer tool, place the smartphone inside of a spherical translucent latex balloon. (Alternatively, us an app such as Airmore to display Physics Toolbox on your computer via a bluetooth connection). Inflate the balloon, and periodically measure the radius of the spherical balloon using a meter stick.

Challenge Yourself

• Create a graph of Pressure versus Radius. and derive a mathematical expression to model the relationship.

• If there are any constants in these mathematical expressions, explain their significance.

Related Resources

Force: Investigating Elements of Bernoulli's Principle

What is the relationship between PRESSURE and TUNNEL RADIUS in a wind tunnel of flowing air?

Try This

Using the Barometer tool, place the smartphone inside of a "wind tunnel" constructed from PVC tubes and a hair dryer. Observe changes in pressure as a result of changes in tunnel radius.

Related Resources

Newton's Laws: Atwood's Machine

What is the relationship between MASS, NET FORCE, and ACCELERATION for an object?

Try This

The relationship between mass, net force, and acceleration of an object is frequently displayed using an Atwood's Machine (two masses suspended over a pulley sustem) or a modified Atwood's Machine (one mass suspended over a pulley system, pulling on a frictionless object over a horizontal surface).

Using the Accelerometer tool, place the mobile device in a plastic bag and suspend it from a traditional or modified Atwood's Machine composed of pulleys and string. Using known masses and mass of the mobile device using a balance, determine the net force on each object. Use the data to determine the acceleration. Perform experiments in which acceleration is measured resulting from changes in mass and net force on the system.

Challenge Yourself

• Create a graph of Net Force vs. Acceleration, and derive a mathematical expression for this relationship.

• Creat a graph of Mass vs. Acceleration, and derive a mathematical expression for this relationship.

• If there are any constants in the mathematical expressions above, explain their significance.

• Combine the two expressions into a single expression.

• Using the expression and a new system of given mass, estimate the expected acceleration. Compare to the actual acceleration observed using the smartphone data.

Related Resources

Newton's Laws: Force Pairs

When two objects interact, how do the forces on each of them compare?

Try This

Place two mobile devices in g-Force mode. While lying flat on a smooth surface or carefully adhered to moving carts, tap the two devices together on their edges (either top-top, side-side, or bottom-bottom). Observe the g-force readings on each device that result. How do they compare?

Challenge Yourself

• What happens to the g-force experienced by each device when one device is larger/more massive than other?

• What happens to the g-force experienced by each device if one of the devices is moving and the other is at rest when the collision occurs?

Related Resources

• Under Construction

Newton's Laws: Elevator Ride

How does the NORMAL FORCE on my body change during an elevator ride?

Try This

Use the Accelerometer tool and place the mobile device flat on the floor of an elevator during a ride up and a ride down. Use a body scale to determine your mass. For each part of the elevator ride (accelerating up, moving up at constant velocity, accelerating down on the way up, etc.), draw a quantitative force diagram for your body by calculating the net force, normal force, and weight acting on you.

Challenge Yourself

• Complete the worksheet listed below in "Resources."

• How would this experience be different if you were on another planet, or if you weighed more?

Related Resources

Linear Motion, Force, & Newton's Laws: Gas Pressure and Speed

What is the speed of an elevator shaft?

Try This

Using the Barometer tool, measure changes in atmospheric pressure up and down a long elevator ride. Using Stevin's Law, which relates fluid pressure and depth (or altitude), determine the displacement of the elevator in the given time, and calculate average velocity during the constant velocity portion of the ride.

Challenge Yourself

• Create a graph of Pressure vs. Time for a ride up and down the elevator.

• Perform column calculations to create a graph of Position vs. Time

• From the Position vs. Time graph, determine the average velocity of the elevator during each major segment of motion (going up at a constant speed, going down at a constant speed, stopped).

• Collect accelerometer and barometer data at the same time (in Multi Record mode), and compare the graphs of Position vs. Time, Velocity vs. Time from the barometric data and the Acceleration vs. Time from the accelerometer data.

Related Resources

Energy: Potential & Kinetic

What is the relationship between POTENTIAL ENERGY and KINETIC ENERGY of a simple pedulum?

Try This

Using the Accelerometer tool, fix the smartphone to the end of a simple pendulum made from a string attached to a point. Before releasing the pendulum from a given height (measured from the bottom of the pendulum swing), determine the potential energy using the mass of the smartphone and a ruler. Release the smartphone. Using data from the acceleration when at the lowest point, determine the tangential velocity at the lowest point (and hence, the kinetic energy).

Challenge Yourself

• How did the starting potential energy at the top of the swing compare to the kinetic energy at the bottom of the swing?

• How would this relationship differ if potential energy had been measured from the ground, and not from the bottom of the pendulum swing? Why?

• Draw energy pie charts for systems in which potential energy is measured from both frames of reference.

Related Resources

Impulse: Collisions

How well do different materials decrease the FORCE OF IMPACT between two objects?

Try This

Using the Accelerometer tool, determine which bumper materials decrease the average force of impact on a cart rolling down an inclined plane into a barrier

Challenge Yourself

• Which material most decreased the force? Why?

• Would it be beneficial for the bumper and the barrier to have material properties that caused the cart to bounce? Why or why not?

Related Resources

Amusement Park Physics

Amusement Park Ride Analysis

Try This

Use the Accelerometer, Barometer, and/or Roller Coaster tools to investigate G-forces, acceleration, and circular motion on a variety of amusement park rides.

Related Resources

Thermodynamics: Gases, Gay-Lussac's Law, and Humidity

What is the relationship between the TEMPERATURE, PRESSURE, and RELATIVE HUMIDITY of a constant volume of air?

Try This

Place a smartphone inside of a sealed jar while recording data on the BarometerThermometer, and Hygrometer tools. Place the jar inside of a refrigerator or freezer for a few minutes. Analyze the data and describe the changes in all of the variables throughout the experiment.

Related Resources - Click the image to get a lesson plan!

Related Resources

Waves: Wave Properties

What do physical WAVES look like?

Try This

Use the Tone Generator, a speaker, and a small tray of liquid to observe Faraday waves and Couder spheres.

Related Resources

Sound: Waveforms

What kind of WAVEFORMS are representative of HIGH/LOW PITCH and HIGH/LOW VOLUME?

Try This

Use the Oscilloscope to observe waveforms for produced by simple tones (such as tuning forks) and more complex sounds (such as your voice).

• Draw a sketch for a high/low frequency sound

• Draw a sketch for a high/low amplitude sound

• Compare sounds of the same tone that have a different timbre

Sound: Natural Resonance

What is the relationship between resonant FREQUENCY of a bottle and the LENGTH of the resonating air column? (or the PROPERTIES of a resonating rod?)

Try This

Acquire a bottle with a small mouth that can easily resonate by blowing over it. Using the Tone Detector tool, record the resonating frequency produced by the bottle. Record the pitches produced in the bottle at various length (measured with a meter stick) modified by adding or removing water from the bottle. (It is also possible to study the physical properties of resonating rods, including their density/material, length, and Young's Modulus value).

Challenge Yourself

• Create a graph of Frequency  vs. Length of the resonant column of air, and derive a mathematical expression for this relationship.

• If there are any constants in this mathematical expression, explain their significance.

• Try the experiment again, and do this instead with a resonating wine glass, using your wetted finger to make the glass resonate. (Note: In the case of wine glass resonance, it is the actual glass - not the column of air - that resonates). Consider how it might be appropriate to measure the variable in question. Try this with glasses of various shapes, sizes, and thicknesses.

Related Resources

Sound: Forced Resonance

How many harmonics can be created in a straw?

Try This

Use the Tone Generator at around 800 Hz. Submerge one end of a large straw (such as a "Giant Pixie Stick" straw) into a cup of water so that you can easily modify the length of the closed-end tube. Place the smartphone speaker near the end of the open part of the tube. What length of tube is necessary to generate resonance? Why?

Challenge Yourself

• How many harmonics can be created in a straw with only one tone?

• What happens to the necessary length of tube as the frequency of the Tone Generator is increased/decreased?

Related Resources

Sound: Interference

What is the relationship between POSITION between two sound sources and INTENSITY?

Try This

Use the Tone Generator tool on a single smartphone with attached earbuds at 3440 Hz. Separate the earbuds by about 40 cm, and fasten them to a meter stick. Pull the meter stick with the attached earbuds along the length of your ear. What do you hear? Do the same, but pull it along the microphone of another smartphone that records the intensity with the Sound Meter tool. You will notice that the sound intensity increases and decreases multiple times along the length between the earbuds. Why?

Challenge Yourself

• What happens to the interference pattern when the frequency is higher or lower? Why?

Related Resources

Sound: Beats

What is the relationship between TWO FREQUENCIES played at once and the observed BEAT?

Try This

Use the Tone Generator tool on two different smartphones (ideally, they should be similar phones, so that the microphones are as similar as possible).

Related Resources - Click the image to get a lesson plan!

Sound: Speed of Sound in Air

What is the speed of sound in air?

Try This

Use the Tone Generator tool to cause resonance in a column of air. Use the Oscilloscope to visually observe resonance. Determine the speed of sound in air by measuring the length of a fraction of a wave as it resonates in a column.

Related Resources - Click the image to get a lesson plan!

Image provided by https://t.co/96hM9HtwKL

Sound: Ambient Noise

How loud is my environment?

Try This

Using the Sound Meter tool, measure the average intensity of ambient noise to determine the level of noise pollution that surrounds you. Record values in quiet and loud environments, and compare these values to charts online to determine if hearing damage might result in particular environments.

Challenge Yourself

• What is the quietest environment that you can possible find?

• What is the loudest environment that you found?

Related Resources

Sound: Noise Insulators

What types of MATERIALS block out sound waves?

Try This

Using the Sound Meter tool, construct a sonically insulated box using any materials available to you.

Challenge Yourself

• What materials are best at insulating noise? Why?

Related Resources

• Under Construction