The core of any physics simulator is, of course, the
emulation of the theoretical description of the phenomena of interest.
This means implementing the relevant equations with numerical techniques.
However, even this is not as straightforward as it first seems.
Say, for example, that we want to measure the gravitational
Newton, unfortunately, did not have access to a desktop
computer with Java installed to do simulations of experiments to
Nevertheless, we can look at how he might have used a simulator
to design and analyze such an experiment. The procedure will be
general to any type of physics experiment simulation.
Before we begin we must first deal with some basic
questions and options for this experimental simulation:
- What aspects of the phenomena will we simulate?
In what environment or context will the experiment be done?
- We could look at the torsion on a thread holding a mass that
is attracted to a nearby large mass.
- We could look at the acceleration of a mass m
due to the FG
from another mass M.
How detailed is the simulation of the physics?
- We could simulate the FG
between planet and moon, or even between binary stars, over
very large distances.
- We could look at the force on a small body over a short distance
near the surface of the earth.
The experimental apparatus and its operation must also be simulated.
This involves several questions:
- At what scale should we simulate the the interactions? For
example, FG occurs between every pair of atoms in the bodies
of mass m and M.
- What are the effects of other masses such as other planets
on an orbital simuation or of other nearby masses in a torsion
- Should we include tidal effects in an orbital simulation,
friction in the torsion case, or drag in mass drop?
- To what detail should the experimental apparatus be simulated?
- What are the uncertainties in the measurements made by the
- Should there be an option of including systematic errors,
such as misalignments in the apparatus?
Regardless of what type of physics or other scientific and engineering
simulations you are doing, these types of questions must be answered
first before the you can start to create a useful simulation.
To illustrate a physics experiment simulation we will
return to the falling body example discussed in Chapter
2: Physics and simulate an experiment common to introductory
physics courses in which a student determines the gravitational
by measuring the acceleration of a body in free fall. Since the
measurements occur over a short range at the surface of the earth,
the force can be treated as a constant:
= FG = GMm/r2 = mg
where g = GM/Re2 and Re = earth's radius
Thus if we know Re
and M, we
can obtain a value for G by measuring the
Equations of interest:
FG = ma = md2y/d2t
v = v0 + gt
y = y0 + v0t + 1/2gt2
is the initial velocity at time t=0
and y0 is
the initial position.
Our detector will provide an estimate of the acceleration by measuring
the times that the object passes given points along its fall. This
would simulate a photodiode setup or a spark chart system.
Latest update: Jan.27.2004