One of the classes of problems dealing with magnetic fields concerns the production of a magnetic field by a current-carrying conductor or by moving charges. It was Oersted who discovered back in the early 1800's that currents produce magnetic effects. The quantitative relationship between the magnetic field strength and the current was later embodied in Ampere's Law, an extension of which made by Maxwell is one of the four basic equations of electromagnetism.
In this lesson students will find that a current-carrying loop can be regarded as a magnetic dipole, as it generates a magnetic field for points on its axis. The figure below shows a diagram and the equation for the magnetic field B. Derivation of this equation requries knowledge of the Biot-Savart Law, calculus and trigonometry. But in this lesson we are interested only in comparing experimental results from PocketLab's magnetometer to the theoretical equation in the figure below. More advanced students can consider derivation of the equation, if they wish.
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.
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 t
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.
In this experiment students will use PocketLab to collect data related to the cooling of a container of hot water as time goes on. Sir Isaac Newton modeled this process under the assumption that the rate at which heat moves from one object to another is proportional to the difference in temperature between the two objects, i.e., the cooling rate = -k*TempDiff. In the case of this experiment, the two objects are water and air. Newton showed that TempDiff = To * exp(-kt), where TempDiff is the temperature difference at time t and To is the temperature difference at time zero.
With a pressure sensor built into PocketLab, there must surely be some way to investigate Boyle's Law. This law states that pressure and volume of an ideal gas are inversely proportional to one another provided that the temperature and amount of gas are kept constant within a closed system. What is needed is a closed system that is large enough to hold PocketLab in a way that pressure can be sensed while changing the volume of the enclosed gas (in our case, air).
Gay-Lussac's Law states that when the volume of a container of gas is held constant, while the temperature of the gas is increased, then the pressure of the gas will also increase. In other words, pressure is directly proportional to the absolute temperature for a given mass of gas at constant volume. Although this is, strictly speaking, true only for an ideal gas, most gases that surround us behave much like an ideal gas. Even ordinary air, which is a mixture of gases, can behave like an ideal gas.
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.