The Physics of Computer ScienceBy Matthew Pinney

A Brief look at how physics is related to Computer Science and a sample

application of problem solution.

What is Computer Science

• To fully understand the connection between computer science and physics, let’s look at the definition of computer science.

• Wikipedia defines: Computer science (or computing science) is the study and the science of the theoretical foundations of information and computation and their implementation and application in computer systems.

What is Computer Science

• Edsger Dijkstra, a renowned computer scientist, once stated, "Computer science is no more about computers than astronomy is about telescopes."

• Computer science spans a range of topics from theoretical studies of algorithms and the limits of computation to the practical issues of implementing computing systems in hardware and software

Physically Relevant• John P. Hayes, founding director of Michigan's

Advanced Computer Architecture Laboratory and author of several books

• “There's a different form of computation that can be based on quantum physics. That turns out to be a very rich area, at least from the theoretical viewpoint. It's particularly exciting because -- although it's at a primitive stage of development -- it has a killer application. Namely, there is an algorithm for factoring numbers that is exponentially faster than any known classical algorithm for that problem. Quantum computing raises the possibility of very fast factoring, which has an immediate application in code breaking.”

Physically Relevant

• Physical based modeling animation is one of the methods of 3D graphics.

• Uses principals of physics and non-linear motion equations to determine the animation path

• Physics fundamentals are also the basis for lighting a scene.

Physically Relevant

• Along with graphics, physics is related to Computer Science with the need for simulation.

• Simulations can be used to test many different types of designs.

• Simulators also prepare people for future tasks.

The Solution to the Problem

• We are given a track that is 100 meters long. For ease of working the problem, I would let the center be 0 with the left end being -50 and the right end being 50. I will also assume that moving left will be a negative velocity, right being positive.

• We will also be given the cart’s mass (m) , velocity(v), location on the track (x = position-50), and coefficient of friction (mu)

The Solution to the Problem

• We are also given the eight rules to apply:– 1. If in the middle and standing still then no force– 2. If left then push– 3. If right then pull– 4. If middle then no force– 5. If moving left then push– 6. If standing still then none– 7. If moving right then push– 8. If right and moving right then pull

The Solution to the Problem

• My algorithm for solving the problem would be to use a while loop with the condition that it would repeat until the cart is at center position(or the cart moves off of the track). For ease of equations, each pass of the loop would simulate one second of time.

• The first part of the loop would be to examine what rule should be applied based off the current velocity and position.

The Solution to the Problem

• The next part of the loop would be to determine the direction and strength of the force to apply. This would be done by using Newton’s second law: F = m * a.

• Reworking of the equation and allotting for all forces gives us the equation a = (F[friction]+F[applied])/m.

• Also needed would be the equation v = v + a*t

The Solution to the Problem

• Assuming the time to be one second, the result would be v = v + a.

• Using branching logic, I would first check the location of the cart. If it is not near the center, then a full Newton of force could be used.

• Next, if it is near the center, I would test to see if the full Newton of force would be more than enough to stop the cart

The Solution to the Problem

• If it is, then I would determine the portion of the Newton that would be necessary to stop the cart on the center.

• The last part of the loop would be to update the variables being used with the new applied force.

• Using the a = (F[friction]+F[applied])/m equation and the v = v + a equation, I would be able to find the new velocity

The Solution to the Problem

• From there, I would be able to update the location variable by using the equation x = v*t + ½ * a * t. Since one loop would simulate one second, this could be shortened to deltax = v + ½ * a. Thus x = x + deltax.

• This would give us a new position and velocity for the next loop to observe.

• If the cart is at the center ( or |x| > 50), I would now end the loop.

The Sources of the Solution

• http://www.acm.org/ubiquity/interviews/j_hayes_1.html?searchterm=physics+relationship+computer

• http://siggraph.org/~rhyne/com97/com97-tut.html?searchterm=physics+of+motion

• http://en.wikipedia.org/wiki/Computer_science

• http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html