## LESSONS: Linear Motion

###### 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 Height and Displacement with Air Pressure

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 ###### Gas Pressure and Speed in an Elevator

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 ###### Describing Acceleration with a Tin Pan

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 ###### Acceleration Due to Gravity

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

Try This

Try This

Using the Accelerometer tool, allow the mobile device to fall straight down onto a soft surface, such as a bed, sofa, 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 ###### 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 ###### G-"Forces"

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

Note: This activity might be best explored after students have studied forces.

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