AN INTRODUCTION TO NEWTONIAN MECHANICS by Edward Kluk Dickinson State University, Dickinson ND |
Why and how to make a simulated experiment of free fall motion Suppose 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. |
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 t, you can write the rediscovered law of free fall as a simple mathematical relation
Evaluation
If at this point you do understand:
Last update: Jan 10, 1997 | E - mail to Edward Kluk |
Copyright (c) 1996 Edward Kluk |