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Transcript
Computing in the introductory physics course Ruth Chabay and Bruce Sherwood North Carolina State University VPython 3D programming for ordinary mortals Programming language (Python) Easy to learn Vector computations Navigable 3D animations are a side effect Object-oriented Free, open source, runs on all platforms http://vpython.org Student program to compute and display the motion of a proton in a cyclotron. The orange arrow represents the electric field in the gap at this instant. The graph displays kinetic energy of the proton vs. time. Student program to compute and display the motion of a 3D massspring system. The Newtonian synthesis The momentum principle + force law + initial conditions Iterative update of momentum and position, for two or more interacting objects Student program to compute and display the motion of a proton in a uniform magnetic field. Arrows represent momentum and magnetic force. Simple Euler algorithm is quite adequate: computers are fast, so step size can be decreased if behavior is erratic. Student program to compute and display the motion of a spacecraft near a fixed Earth and Moon. The green arrow represents momentum. Vector algebra VPython code Student program to calculate and display the electric field due to a uniformly charged rod at various locations. The rod is approximated by a number of discrete point charges; students vary the number of charges, and study the effect on their computed results. Student program to compute and display the magnetic field of a moving proton at many locations, dynamically. Programs written by students include (Intro course, 2 semesters): Student program to compute and display the trajectory of an alpha particle scattering off a gold nucleus, and to plot x and y components of the momentum of each object vs. time. (In the program the gold nucleus does recoil, but it has not moved far enough to leave a visible trail.) The basic algorithm for Rutherford scattering, spacecraft orbits, and the 3D massspring system is the same; only the force law changes. Motion of a fancart (constant force) Spacecraft orbit Spacecraft orbit with energy graphs 3D Mass-spring 3D Mass-spring with energy graphs Rutherford scattering with momentum graphs Statistical mechanics of Einstein solid Electric field of point charge Electric field of dipole Electric field of uniformly charged rod Magnetic field of moving proton Charge motion in uniform magnetic field Positron motion in electromagnetic plane wave New features in VPython (beta): transparency, textures, lighting Lecture demo program illustrating the electric field on a transparent Gaussian surface. Matter & Interactions Modern calculus-based introductory physics course 20th century physics integrated throughout both semesters Computation integrated to strengthen conceptual understanding, aid visualization R. Chabay & B. Sherwood, John Wiley & Sons, 2002, 2005 http://www4.ncsu.edu/~rwchabay/mi These new features in VPython were added by Jonathan Brandmeyer. The development of VPython and Matter & Interactions has been supported in part by the National Science Foundation. VPython was originated by David Scherer.