Relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP Physics curriculum.
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.
This active demonstration investigates the law of conservation of momentum using a person on rollerblades and a thrown medicine ball.
Students learn about the physical force of linear momentum movement in a straight line by investigating collisions. They learn an equation that engineers use to describe momentum. Students also investigate the psychological phenomenon of momentum; they see how the "big mo" of the bandwagon effect contributes to the development of fads and manias, and how modern technology and mass media accelerate and intensify the effect.
Watch science come alive in demonstrations of magnetic levitation techniques, ways to rig a sailboat, and much more. See video on: Atomic Physics & Quantum Effects; Circular Motion & Rotation; Conductors, Capacitors, Dielectrics; Electric Circuits; Electromagnetism; Electrostatics; Fluid Mechanics; Geometric Optics; Kinematics; Kinetic Theory & Thermodynamics; Magnetic Fields; Newton's Laws of Motion; Oscillations & Gravitation; Physical Optics; Systems of particles, Linear Momentum; Temperature & Heat; Waves; Work, Energy, Power.
This course is designed to acquaint students with topics in mechanics and classical electricity and magnetism. The materials are assembled from UC College preparatory courses and covers two semesters. The first semester is devoted to Newtonian mechanics including: kinematics, laws of motion, work and energy, systems of particles, momentum, circular motion, oscillations, and gravitation. The second semester discusses the topics of electricity and magnetism. The course emphasizes problem solving including calculus, and there are numerous interactive examples throughout. Students will also gain laboratory experience through interactive lab simulations and wet labs.
The EJS Inelastic Collision of Particles with Structure model displays the inelastic collision between two equal "particles" with structure on a smooth horizontal surface. Each particle has two microscopic elements which interact through a massless spring of stiffness k and natural length L. The mass of one of the microscopic elements and the spring length of the connector spring can be changed via textboxes. You can modify this simulation if you have EJS installed by right-clicking within the plot and selecting "Open EJS Model" from the pop-up menu item.
Second subject of two-term sequence on modeling, analysis and control of dynamic systems. Kinematics and dynamics of mechanical systems including rigid bodies in plane motion. Linear and angular momentum principles. Impact and collision problems. Linearization about equilibrium. Free and forced vibrations. Sensors and actuators. Control of mechanical systems. Integral and derivative action, lead and lag compensators. Root-locus design methods. Frequency-domain design methods. Applications to case-studies of multi-domain systems.
The EJS Elastic Collision Model allows the user to simulate a two-dimensional elastic collision between hard disks. The user can modify the mass, position and velocity of each disk using the sliders. Both disks are draggable and the center of mass is shown a a cross in the simulation.
