# User Lesson Plans

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

## Determining the Radius of Curvature of a Gradual Street Turn

### Investigating Boyle's Law with PocketLab

### Investigating Ampere's Law for a Long Current Carrying Wire

### K-8 Lesson (Acceleration & Mean, Median, & Mode)

This lesson has been developed for Grade 8 students.

Please see video link as well as attached Hyperdoc.

### PocketLab Experiment on Centripetal Acceleration with a 3-speed Ceiling Fan

### 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.

### The Inverse Cube Law for a Neodymium Dipole Magnet

PocketLab makes is quite easy to investigate and verify the inverse cube law for the magnetic field of a neodymium magnet as a function of distance from the magnet. All that is needed in addition to The PocketLab is a centimeter ruler, small neodymium magnet, a small block of wood and a little double stick tape. The photo below shows how the neodymium magnet is taped to the block of wood with the magnet located at the 10 cm mark on the NSTA ruler. The height of the center of the magnet is at about the height of the circuit board inside of PocketLab. The X on the front face of PocketLab is very close to the location of the magnetic field sensor inside of PocketLab, 0.5 cm from the left edge of Pocket Lab, in line with the Y-axis of PocketLab.

The photo below shows the set up from above with the left edge of Pocket lab at the 15 cm mark. The distance between the dipole and the sensor is therefore about 5.5 cm in this photo.

In preparation for data collection, PocketLab is set to display magnetic field magnitude. It is then moved far from the neodymium magnet and zeroed. It is then placed at the 12 cm mark on the ruler, making the distance between magnet and sensor 2.5 cm. After a few seconds, PocketLab is moved to the 13 cm mark, thus increasing the distance by 1 cm to 3.5 cm. This process is continued through a distance of 8.5 cm. The magnetic field magnitude can be read directly from the movie, shown below, at each of the known distances.

(Distance, magnetic field magnitude) data pairs are then entered into an Excel spreadsheet, and a chart of Magnetic Field vs. Distance is created. The chart, shown below, appears to show some sort of an inverse relationship between magnetic field and distance. The Excel "Add trendline" feature is then used and the "Power" regression fit is applied. It is found that the power is -2.832, very close to the -3 expected for an inverse cube relationship.

A copy of the Excel spreadsheet is included in the attachments for anyone interested in viewing it.

### 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.

### PocketLab Investigation of Fuel Efficiency

### Using PocketLab to Investigate Newton's Law of Cooling

### PocketLab on an Oscillating Cart

An oscillating cart with a PocketLab provides an interesting way to study Newton's Second Law of Motion as well as some principles of damped harmonic motion. The apparatus setup is shown in the figure below. The small dynamics cart that can quickly be made from parts included in the PocketLab Maker Kit is shown in its equilibrium position. Rubber bands are attached to each side of the cart and to two ring stands weighted down with some heavy books. It is best to use rubber bands that provide as small Newton/meter as possible. PocketLab is attached to the cart with its x-axis parallel to the rubber bands.

The close-up in the figure below shows that two small pieces of wire are threaded into holes in the cart with the rubber bands attached. The ends of each wire are twisted together to tighten the rubber band on the cart.

The movie below shows a typical run, with 20 data points per second and acceleration selected in single-graph mode. The red trace on the graph is the acceleration of interest, namely acceleration in the X-direction. The blue and green traces, representing acceleration in the Y and Z directions, are quite erratic due to slight jiggling of the cart, and are not of interest here. The red curve shows a very regular pattern, in which it can be observed that the magnitude of the acceleration is greatest when the cart is at each end of its swing and zero in the center of the swing. It is also noted that the magnitude of the acceleration decreases with time in a pattern that suggests exponential decay.

The image shown below contains a graph of x acceleration from data produced by the PocketLab app. The graph was obtained by importing data from the PocketLab app into Logger Pro, an exceptional educational scientific analysis software from Vernier Software & Technology (vernier.com). A model involving the sine function and exponential function was created. It is seen that the model (the black curve) follows the red acceleration X curve very well.

### Negative Exponentially Damped Harmonic Motion from a PocketLab Pendulum

This experiment allows one to do a quantitative investigation of the damped harmonic motion of a swinging pendulum. The pendulum is a piece of wood about a yard long from a Michael's hobby shop one end of which has been attached to a PocketLab by a rubber band. The other end is taped to the top of a doorway, allowing the resultant pendulum to swing back-and-forth as shown in the image below.

The y-axis is perpendicular to the XZ plane of the swinging pendulum. Therefore, the main item of interest is the magnitude of the angular velocity vector in the Y direction (shown as a blue curve in the movie).

The image shown below contains a graph of the Y angular velocity (shown in blue). The X and Z angular velocities (shown in red and green in the video, respectively) are small and erratic due to slight wobble in the swinging pendulum and are not included in the graph. The graph was obtained by importing the data from the PocketLab app into Logger Pro, an exceptional educational scientific analysis software from Vernier Software & Technology (vernier.com). A model involving the sine function and the exponential function was created. It is seen that the model (the black curve) follows the blue angular velocity curve very well.

### Using a 33-45-78 Turntable to Show that Centripetal Acceleration is Proportional to the Square of the Velocity and Inversely Proportional to Radius

PocketLab in conjunction with a 33-45-78 RPM turntable is an ideal setup for studying centripetal acceleration. There are two videos that can be found in the Videos page of this web site. They show that (1) keeping radius constant implies that centripetal acceleration is proportional to the square of the velocity, (2) keeping velocity constant while varying the radius implies that centripetal acceleration is inversely proportional to the radius.

The PocketLab is placed in its silicone protective case to provide greater friction so that it doesn't slide off the turntable. Y is toward the center of the turntable, and X is in the direction of rotational motion of the turntable. Single-graph mode is used with acceleration selected to be graphed.

From the accel X data in the videos students can then use Excel, Google Sheets, or any other analysis software to make graphs of (1) accel X vs. velocity-squared, and (2) accel X vs. the reciprocal of the radius. Both of the graphs should be pretty close to straight lines, giving support for the desired outcomes.