# Force and Motion Lessons

## Middle School Science Balloon Powered Car

Phenomena or Driving Question: Make a vehicle that travels one meter powered only by two balloons

Lesson description:  In this unit of study, Newton’s Laws will be used to explain the forces and motions of objects on Earth and in Space.  This Lesson is the Engineering design project at the end of the unit.

PE’s addressed: MS-PS2-1, MS-PS-2-2, MS-ETS1-1, MS-ETS1-4

This lesson is courtesy of Heather Wygant and Susan Paulsen, Santa Clara, CA

You can find an overview of the lesson here: http://bit.ly/2oeSMvL

And a template for the activity here: http://bit.ly/2p6Oynb

## Newton's Laws of Motion with PocketLab and Estes T-Bolt Air Rocket

See attached PDF for activity.

### Linear Motion: Position, Velocity, and Acceleration

See attached PDF for activity.

### Understanding Newton's Laws with Atwood's Machine

See attached PDF for activity.

### Newton's First and Second Laws of Motion with Rockets

See attached PDF for activity.

### Quantitative Experiment to Determine the Relationship Between a Pendulum's Length and Period

PocketLab is a perfect device for determining the quantitative relationship between the length of a pendulum and its period of oscillation.  Pendulums of known lengths were made from balsa wood strips such as those available from Michaels and other hobby stores.  The photo below shows six such pendulums of lengths 15, 30, 45, 60, 75, and 90 cm alongside a meter stick.  The picture shows that PocketLab was taped with double-stick mounting tape to the pendulum whose length is 45 cm.

The photo below shows the apparatus setup. The balsa wood pendulum with PocketLab attached is hung with masking tape from a ring stand supported by the weight of several books to keep it stable.  The orientation of PocketLab shows that it will be swinging in the XZ plane.  Therefore, the Y angular velocity data will provide information necessary to compute the period of the pendulum.

The video below shows the PocketLab graphs superimposed on the actual moving pendulums.  The Y angular velocity, shown in blue, contains the data of interest in the analysis.

The Excel graph below shows the Y angular velocity in deg/s obtained from the gyroscope data file for the pendulum of length 15 cm.  (Note that half the length (3.2 cm) of PocketLab is subtracted from 15 cm, giving a length of 11.8 cm to the approximate center of mass of PocketLab.)   As shown in red in the graph, the period is calculated by averaging the time for ten complete oscillations.  This process is repeated for all six pendulum lengths.  All gyroscope data for these six pendulums can be found in the attached gyroscope Excel file.

Below is shown an Excel chart the summarizes the results of the experiment.  When a power regression type is applied to the data, it is seen that the power turned out to be 0.4773, very close to the theoretical 0.5 expected for such a pendulum.  It can be concluded that the period of a simple pendulum is proportional to the square root of the length of the pendulum.

### PocketLab Joins Ozobot to Study Position, Velocity and Acceleration Concepts

Ozobot (ozobot.com) is a tiny one inch diameter line-traveling robot that can be used in conjunction with PocketLab to easily study the physics concepts of position, velocity, and acceleration and their time graphs.  PocketLab is simply taped to the top of an Ozobot using double-sided mounting tape.  In other words, Ozobot gives Pocket lab a ride.  The photo below shows this setup, with Ozobot following a 1/4" heavy black line drawn with a chisel tip marking pen.

A magnetic ruler can be easily constructed to capture position/time information on the Ozobot/PocketLab duo. The photo below shows the magnetic ruler.  Small neodymium magnets are taped 15 cm apart on a stick that can be purchased at hobby shops such a Michaels.  PocketLab is set to record values of magnetic field magnitude.  As the PocketLab/Ozobot pair travel along the line, the magnetic field magnitude rises to a peak when reaching each of the magnets on the ruler.  The data file created by the PocketLab app can then be used to determine the times for each of the peaks.  With position and time known, a graph of position and time can then be constructed, perhaps in Microsoft Excel.

CONSTANT SPEED EXAMPLE

The movie below shows data captured when Ozobot/PocketLab move at a constant speed along the line.
The two charts below were created using Excel with raw data from the PocketLab app magnetometer magnitude.  It is seen that the peaks are very close to being equally spaced in time, roughly 2 seconds apart.  With the distance between magnets fixed at 15 cm, velocity is therefore constant. The slope of the position versus time chart tells us that the velocity is about 7.546 cm/s, as shown by the linear regression data from Excel.  The Excel file is attached for anyone interested in viewing its details.
CONSTANT ACCELERATION EXAMPLE
Ozobot can be programmed using OzoBlockly (ozoblockly.com) in a way that causes Ozobot to accelerate rather than travel at constant velocity.  The OzoBlockly program shown in the figure below was used in this investigation.  Ozobot begins at a speed of 35 mm/s and then increases as it approaches each of line intersections at the magnets by 10 mm/s.  Because Ozobot is carrying the weight of PocketLab, the speeds are actually somewhat less.
The movie below shows data captured with Ozobot/PocketLab traveling with  acceleration.  You will note that as its speed increases, the distance between peaks of magnetic field magnitude decrease.
The two charts below were created using Excel with raw data from the PocketLab app magnetometer magnitude.  Again, we note that the peaks are more closely spaced as time progresses.  The thin black straight line on the position vs. time graph clearly shows that the curved blue line implies acceleration.  When a linear fit is done on the velocity vs. time chart, we find that the average acceleration is about 0.2932 cm/s/s.  The Excel file is attached for anyone interested in viewing its details.

### PocketLab on a Skier's Edge Machine

The PocketLab is an ideal device for measuring user performance for a variety of exercise equipment.  One example of such equipment is the Skier's Edge, whose company was founded in 1987.  This machine was designed for non-impact lateral conditioning that simulates the experience of downhill skiing.  The photo below shows the skiing machine.  The skier stands on the two black platforms, holding poles and moves the carriage back-and-forth on the curved white tracks.

A close-up view of the carriage in the photo below shows that a Pocket Lab has been mounted to the carriage with tabs provide in the PocketLab Maker Kit.  The carriage moves back-and-forth on the curved track in the XZ plane.  Therefore, the Y angular velocity would be a variable of interest to measure.  In addition, the X acceleration would be of interest as it is the major component of the back-and-forth motion provided by the skier's legs.

An iPhone snapshot of the data and video combined is shown below.  The acceleration graph (red) shows that the maximum acceleration is about 4g.  This is a true measure of the skier's power.  The angular velocity graph (blue) shows that the maximum angular velocity is about 75 degrees/sec.  From study of the time axis, both graphs show that the  back-and-forth movements of the skier has a frequency of about 75 per minute.  Increasing this rate while keeping the amplitude of the swings the same would suggest that the maximum g "force" could be increased for a more powerful skier.

The action movie shown below includes an overlay of both the acceleration and angular velocity graphs, with maximum acceleration occurring at the ends of the back-and-forth motion, and maximum angular velocity occurring at the center of each swing.

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