COLUMBIA UNIVERSITY - DEPARTMENT OF PHYSICS

# SIMULATIONS

## Introduction

Each of the other experiments you perform in this laboratory involve a physical apparatus which you use to make measurements of various phenomena. This is the usual way in which physical laws such as Newton's Second Law, Hooke's Law and Snell's Law were discovered and verified. Other situations arise where we may have a very good understanding of many (if not all) of the laws governing some system, yet we may wish to determine how the application of these laws affects its behavior. Often a simulation offers a powerful method for such situations.

Rather than actually building an apparatus to measure its properties, we can program a computer to simulate the behavior of the system of interest. Obviously, the results of the computer are only as good as the accuracy of the simulation. Simulations are of great importance in physics; for example, they are widely used in particle physics to account for the interactions of particles with the measurement apparatus. They allow one, at little cost, to perform a wide range of experiments on many different systems. Combined with an actual experiment, simulations allow one to determine the behavior of the physical system through comparison of measured results to those from the simulation.

Simulation programs are often highly specialized, designed for a specific situation. In this experiment, we will be using a commercial program called Interactive Physics for the simulation of various mechanical systems. This program allows us to ``build'' different apparatuses and ``perform experiments'' on them. It is important to understand that this program isn't magic, it is only applying Newton's Laws to systems; all of the calculations it does are based on material you learned in Physics lecture courses. What the simulations do allow is the rapid computation of the dynamics and kinematics of systems of particles. It can perform many calculations (which would be quite tedious for us to do by hand) and therefore allows us to look at more complicated situations than we would calculate manually. It also allows us to vary the properties of the systems at will (without having to have new parts built etc.) and allows us to study the behavior of ideal systems (say without friction), or to introduce such phenomena as friction in a controlled way to study their effects. Of course, the cost of this flexibility is that we cannot discover new physical laws as we could with a real apparatus; laws which were not programmed into the simulation clearly won't be revealed in its use.