AN INTRODUCTION TO
NEWTONIAN MECHANICSby Edward KlukDickinson State University,
Dickinson ND |

**FREE FALL
MOTION**

Why and how to make a simulated
experiment of free fall motionSuppose you have never study any Physics before. Your first assignment is to investigate and describe a free fall motion. Such motion occures if a body is lifted up, stopped, and let to fall down with no significant air resistance. In 16th
century Galilei Galileo investigated free fall
motion and concluded that all bodies fall down
identically. Good examples of it are falls of metal or
glass solid balls, as opposed to a sheet of paper which
is initially in a horizontal position. Even taking a
styrofoam ball you may notice an air resistance comparing
its fall with a fall of solid metal ball. An obvious
qualitative observation for motion of all mentioned above
balls and many other compact objects is a gradual
increase in their speed in the initial phase of the
motion. Taking quantitative data, like covered distances
for different times, is more difficult. Photogates,
ultrasonic rangers or other suitable technologies are
needed. Human beings have too slow reflex for that kind
of measurements on the surface of our planet. This is
only real obstacle because nowadays almost every wrist
watch with digital display has a stopwatch of accuracy of
0.01 s. Our reflex, however, has accuracy of about 0.1 -
0.2 s, and this is not good enough to make meaninfull
measurements. Now you should comprehend why ancient and
medival scientists had difficulties with understanding
even simple motions. They were deprived of reliable
experimental data.If you have not enough money to buy one of the mentioned above technologies, but you still have good enough computer, imagine yourself a different planet with much lower gravitational pull. On such planet a free fall would be much slower and our reflex would not be an obstacle in taking reliable experimental data. This applet provides you with simulation of the planet. When you click on Start button the red object blinks and falls freely 10 m down. Do not try to stop it. When the object reaches the bottom, you can reset the applet and start all over again. Now measure with a stopwatch and record times the object needs to reach the levels 1 m, 2 m, ... , 10 m from the level 0 m. Remember to record your data in a neat fashon, and whatever you will be doing with them, do it rather precisely. Too much of precision (precision beyond of exerimental errors) if you are aware of such possibility is usually not as dangerous in science as not enough of it. |

**Interpretation
of the experimental data**

If you are a math wizard and you have
any curve fitting programs try to fit simple curves to the
collected distance versus time data. This way you will rediscover
the law of free fall. If you do not feel too comfortable with
math, do not worry. Neither **Isaac Newton** nor **Albert
Einstein** knew enough math for their purposes. Newton created
math he needed (calculus) and Einstein learned it (Riemann
geometry) in "on a job training". Make a neat distance
versus time graph and have a good look at it. Well, it looks like
a curve. But what kind of curve? Here is a hint. Graph the
distance versus square of time and you should be able to fit to
your data a straight line running through the origin (0,0) of the
graph. If so, then you have rediscovered **the free fall law
stating that the covered distance is proportional to the square
of time**. It means that the graph distance versus time must be
a simple parabola with vertex at the origin.

**Math helps to reach more conclusions**

Making the measurements you have not
had any problems with ideas of time and distance. You have
learned how to measure them very early, and most probably with no
reference to any science. But be aware, knowing how to measure
something is not equivalent with full understanding of what this
someething really is. To measure something we need an operational
definition which is an instruction how to measure it. To
understand it much more is needed. You may have heard that the
Big Bang or begining of our Universe (according to the Big Bang
model of the Universe) was a begining of time and space. It
sounds simple, but it is not simple at all. in other words we are
not quite sure what time and space are.

At least intuitively you understand
what is a speed. In this country we deal with it practically
every day driving our cars. If you drive your car with the steady
speed 70 mph along a long streach of Interstate it means that in
1 hour it covers 70 miles, in 1/2 of an hour 35 miles, in 6
minutes just 7 miles, and so on. What can we say about the speed
of our freely falling object? You know from our experiment that
the distance it covers is proportional to the square of elapsed
time. Moreover, you know the proportionality coefficient because
it is equal to the slope on the graph of distance versus square
of time. Calculating the slope, find a "distance" along
the distance axis in meters (rise) as they are marked there and a
related to it "distance" along square of time axis in
seconds squared (run). Find rise/run ratio. Marking this ratio as
*a/2*** **, covered distance by ** d**
and elapsed time by

Now we need a definition of speed. If we take two distances

This definition is valid for any dependence of

Here for final simplification well known algebraic identity

If the time interval (

You should notice that starting with experimental dependence of covered distance on time and doing some elementary algebra, we have proven a linear dependency of a free falling body speed on time. The constant

Moreover, introducing the idea of instand speed we have applied a method which is used in mathematics to introduce a function derivative. As a matter of fact if you take derivative of

**
Evaluation**

If at this point you do understand:

- why ancient and medival scientists were not able to discover the law of free fall
- how the law of free fall can be deduced from experimental data
- definition of speed
- how the speed of a free falling body can be mathematically deduced from the law of free fall

the objectives of this lesson are fully achieved. If you have doubts try to read it once more concentrating on them, but do not try to memorize this text. physics is not about memorizing, it is about understanding.

**Since February 1997
you are visitor**

Last
update: Jan 10, 1997 |
E
- mail to Edward Kluk |

Copyright (c) 1996 Edward Kluk |