Effective measurement techniques include the concept of measurement uncertainty. Students may make erroneous conclusions analyzing data using measurements that do not include the uncertainty of the measurement. In this lab, students determine a density range for a metal and identify the material based on this range.
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This is a lab activity that allows students to collect data to practice using effective measurement. While other authors have produced similar labs, this version includes uncertainty analysis consistent with effective measurement technique as presented in the module Measurement and Uncertainty.
One video clip, with embedded graphs, can be used to help students understand the mathematical relationships that describe simple harmonic motion.
The EJS Anisotropic Oscillator model displays the dynamics of a mass connected to two opposing springs. The simulation displays the motion of the mass as well as the trajectory plot. The initial position of the mass can be changed by dragging. The unstretched lengths of the springs can changed as well via textboxes.
The Balls in a Box model shows a system of particles is very sensitive to its initial conditions. In general, an isolated system of many particles that is prepared in a nonrandom configuration will change in time so as to approach its most random configuration where it is in equilibrium. What happens if we choose the initial conditions in a very special way?
The default initial condition corresponds to eight stationary particles perfectly aligned on the x-axis. Two particles approach from the left and the right. What happens when these particles collide with the eight stationary particles? The EJS model solves Newton's second law of motion numerically but pauses when a collision is detected. This is called an EJS event. Conservation of energy and momentum are applied at the event and the simulation is resumed.
The EJS Barrier Scattering model shows a quantum mechanical experiment in which an incident wave (particle) traveling from the left is transmitted and reflected from a potential step at x=0. Although the analytic solution to this standard problem is well known, its visualization shows how the incident and reflected waves form an interference pattern and how the incident wave penetrates the classically forbidden region when its energy is less than the barrier height height V0
The EJS Baton Throw model displays a baton thrown up in the air about its center of mass. The baton is modeled by two masses separated by massless rigid rod. The path of the center of mass of the baton and the red mass are shown in black and red, respectively. The ratio of the two masses can be set via a slider and the initial velocity of the center of mass of the baton and the rotational velocity of the baton can be set via text boxes.
The EJS Beats model displays the result of adding two waves with different frequencies. The simulation displays the superposition of the two waves as well as a phasor diagram that shows how the waves add up at one point in space. The ratio of the wave amplitudes, the ratio of the frequencies, and the phase shift between the two waves can be changed via textboxes.
The Body with Thruster Model shows the motion of a disk with an attached rocket engine. You can drag the engine to change its distance from the center of the disk and you can adjust the thrust of the rocket engine using sliders. The mass of the rocket and its connecting rod are assumed to be negligible. The trajectory of this single-body model is intuitively challenging and difficult to visualize.
The EJS Car on an Inclined Plane model displays a car on an incline plane. When the car reaches the bottom of the incline, it can be set to bounce (elastic collision) with the stop attached to the bottom of the incline. The car consists of the car body, two rotating front wheels, and two rotating rear wheels. The incline angle (in radians) can be changed via a textbox. In addition the car can be dragged to its initial position.
The EJS Charge In B-Field model allows the user to simulate moving charged particles in two identical magnetic field regions separated by a zero magnetic field gap.
The EJS Circumnavigating Pendulum model displays the dynamics of a mechanical oscillator in uniform circular motion. The mechanical oscillator is free to move in two directions. This 2-dimensional simulation displays all the dynamical features of the Foucault pendulum, except for the dependency of the Foucault pendulum precession on latitude. The simulation shows simultaneously the motion with respect to the inertial coordinate system, and the motion as seen from a co-rotating point of view.
The EJS Classical Helium Model is an example of a three-body problem that is similar to the gravitational three-body problem of a heavy sun and two light planets. The important difference is that the helium atom's two electrons repel one another, unlike the planetary case where the intraplanetary interaction is attractive.
The Colliding Galaxies Model is an implementation of Alar and Juri Toomres' 1972 super computer model showing the formation of galactic bridges and tails under the assumption that galactic cores are point masses and that one galactic core is surrounded by 2D concentric rings of orbiting stars. The model assumes is that the stars (test particles) orbiting the galactic cores are non-interacting. When the two galaxies pass one another, tidal forces deform the star distribution into classic tidal features. Our EJS model reproduces this result showing that there is a long curving tail and that only the outermost ring of stars is affected by its companion galaxy. A thin bridge is also formed and some of the stars are captured by the companion galactic core.
A high speed video clip of a roller coaster is used as an example of conservation of mechanical energy. Students use the video to determine whether mechanical energy is conserved while the roller coaster rolls up, and then back down a hil.
This activity describes the construction and use of a pneumatic cannon and free falling target used to teach the concepts of projectile motion in introductory physics.
The EJS Coupled Oscillators and Normal Modes model displays the motion of coupled oscillators, two masses connected by three springs. The initial position of the two masses, the spring constant of the three springs, the damping coefficient for each mass, and the driving force and driving force frequency for the left mass can be changed via text boxes.
The EJS Damped Driven Harmonic Oscillator Phasor model displays the motion of damped driven harmonic oscillator. The resulting differential equation can be extended into the complex plane, and the resulting complex solution is displayed with the real part of this solution being the position of the oscillator. The natural frequency of the oscillator, the damping coefficient, and the driving force and driving frequency can be changed via textboxes.
Data Tool is a data analysis tool for plotting and fitting data from laboratory experiments, simulations, video analysis, or any other data set organized into columns. A click of a checkbox in Data Tool allows the user to change the appearance of plots, see standard statistics for the data set or apply built-in linear, quadratic or cubic fits to the data set. Data Tool also includes a number of standard mathematical functions that can be applied to the data set, allowing for further analysis and extending the range of potential fits to the data.
Easy Java Simulations (EJS) is a Java program that enables both programmers and novices to quickly and easily prototype, test, and distribute packages of Java simulations. Version 4.1 adds grouping and affine transformations to 2D drawing Elements.