LESSONS: Measurement

The majority of 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.
Measuring Heights​

What is the HEIGHT of any structure?

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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.

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Circumference of the Earth​

What is the circumference of the Earth?

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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).

Precision and Accuracy

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?

Gait Patterns​

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

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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?

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Seismic Vibrations​

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

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Perform three different investigations from IRIS (Incorporated Research Institutes for Seismology). In these activities, use the Accelerometer tool along with a meter stick, tape, 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.

 

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Solute Concentration and Color Intensity

What is the relationship between solute concentration and color?

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Using the Color Detector tool, measure the HEX values of various known concentrations of copper sulfate in an aqueous solution. Convert the HEX values to HSV (Hue, Saturation, Value) using an online converter. Plot mass of dissolved copper sulfate versus hue, and develop a mathematical model to describe the relationship.

 

Challenge Yourself

  • Determine the concentration of an unknown amount of copper sulfate based upon its hue value.

  • Determine what will happen to the relationship after the saturation point has been reached.

 

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Beer's Law

What is the relationship between SOLUTE CONCENTRATION and LIGHT ABSORPTION?

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Using the Light Meter tool, measure the light intensity as it passes through various cuvettes filled with different known concentrations of colored soda (or other solute). Plot absorbance (as measured by log (I0/I), the log of the intensity of light as observed through a control cuvette filled with water divided by the intensity of light observed through a cuvette filled with the solution) versus concentration.

 

Challenge Yourself

  • Determine the mathematical relationship between absorbance and concentration.

  • What is the meaning of the slope and y-intercept of the linear relationship observed?

 

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Image Credit: Glen Gilchrist

Identifying Permanent Magnets

What kinds of common METALS can be permanent magnets?

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People frequently confuse permanent magnets with non-magnetic materials that can be polarized by a nearby permanent magnet. 

 

Collect a number of metallic objects from around the house. Using the Magnetometer tool, determine which materials are magnetic and which materials are not. (Note: Because the phone produces a magnetic field itself, even non-magnetic materials moved near the mobile device might interfere with the field and given a false impression that the item is magnetic. For the best result, hold the object steady, and compare with the magnetic field recorded by the mobile device when no object is present).

 

Challenge Yourself

  • What kinds of metals seem to make up permanent magnets?

  • Can you ever get the mobile device to record a magnetic field of 0 in all directions? Why or why not?

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Magnetic Field Intensity

What is the relationship between the MAGNETIC FIELD STRENGTH and the DISTANCE from a magnetic "point source"?

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The strength of a magnetic field is dependent upon the distance between the sensor and the "point-source" of the magnet. Using the Magnetometer tool, record the magneti field at various distances away from a strong but small permanent magnet.

 

Challenge Yourself

  • Create a graph of Magnetic Field Strength vs. Distance from the magnet, and derive a mathematical expression for this relationship.

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

  • Try performing the same experiment above, but use a fairly large, strong bar magnet. How does the graph of the magnetic field strength compare to before? Why might the nature of the relationship be different?

 

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Magnetic Poles

Where are the POLES of a bar magnet? A horseshoe magnet? A spherical or irregular magnet?

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Acquire a collection of regular and irregularly-shaped strong magnets. Use the Magnetometer tool to determine where the poles of the magnets are. You might be surprised to find where they are located!

 

Challenge Yourself

  • Using data from the surface of the magnet, attempt to sketch the magnetic fields lines produced by each type of magnet.

  • Acquire a refrigerator magnet. How does the magnetic field of the "front" face compare to the "back" face of the magnet? Where are its poles located?

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Earth's Magnetic Field

Which way does the EARTH's MAGNETIC FIELD point at my latitude and longitude?

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Using the Magnetometer tool, determine the strength of the Earth's magnetic field in three dimensions. Using an understanding of vectors, determine the direction of the Earth's magnetic field. 

 

Challenge Yourself

  • Share magnetic field values with students across the globe, noting respective latitude and longitude values.

  • Create a vector array of magnetic field values to observe the Earth's whole gravitational field.

  • Collect data over time, and observe changes in the Earth's magnetic field due to solar activity.

 

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Planetary Magnetism

What do magnetic fields look like around planets?

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Using the AR setting that makes use of the magnetometer, accelerometer, and gyroscope, visualize the Earth's magnetic field and explore a model "Earth" and a model "Planet X." 

 

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Electromagnetism and the Oersted Effect

What is the relationship between CURRENT and MAGNETIC FIELD deflection?

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Using the Compass tool, place a wire across the top of the compass, along the "North-South" direction. Send a variable current through through the wire using a series of batteries or a power source. Observe what happens to the compass when the current is traveling through the wire.

 

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Electromagnetism and Helmholtz Coil

What is the relationship between CURRENT and MAGNETIC FIELD magnitude in three dimensions?

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Using the Magnetometer tool, place the smartphone inside of a Helmholtz coil attached to a power source. Measure the magnetic field strength as a function of current in the coil.

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Electromagnetism and the Bio-Savart Law

What is the value of PERMEABILITY OF FREE SPACE?

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Evaluate the Bio-Savart Law  by taking a smartphone while recording Magnetometer and Accelerometer data by mounting it on a cart on a frictionless track through a current-carrying coil of known numbers of turns, radius, and current. 

 

Challenge Yourself

  • Double integrate the accelerometer data after export as a .csv to determine the position of the smartphone with respect to the center of the coil.

  • Create a graph of magnetic field strength, B, versus position with respect to the center of the coil, y.

  • Modify the graph to linearize the data. (i.e., plot B^(-2/3) versus y^2.)

  • Determine permeability of free space using the known Bio-Savart Law.

 

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Binary Messages with Light

How can INFORMATION be conveyed via DIGITAL SIGNALS?

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Create a simple message after learning how to convert it to binary code. Use a piece of clear tape or an overhead projector laminate to make a translucent strip, then create bars with masking or electrical tape. Slowly pull the barcode across the light sensor while in Light Meter mode. Observe the shape of the light intensity graph.

 

Challenge Yourself

  • Make barcodes with a partner. Use the graphs to de-code each others' messages.

 

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