Guide

Little guide to the experimentation on
rectilinear motions

 

 
INTRODUCTION

  This is a short guide to the experimentations on rectilinear motions.

  It shows which equipment is required, the precautions that must be taken and the methodologies that must be used.

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EXPERIMENTAL APPARATUS

  Any experimental study requires a careful choice of the instrument to be used. In fact the phenomenon to study must be characterised as precisely as possible by removing or reducing to their minimum all the causes of perturbation that can affect its development.

  From a didactic point of view we ask the experiment to be:

  Besides, the collection of the experimental data must be easy and ascertained and also the processing must be fast and simple.

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RIDUCTION OF THE FRICTION

  The main cause of perturbation, in the study of a motion, is of course friction: a good experimental device must therefore eliminate or reduce the friction substantially.

  That can be obtained in different ways:

 
TROLLEY WITH WHEELS

 

  It is the easiest solution to reduce the friction force, substituting the rolling friction to the sliding friction.

  The residual friction can be compensated by a light inclination of the track on which the trolley moves.

  To obtain a guaranteed rectilinear motion we can use a rail on which the trolley moves.

  The substantial flaw is having rotating masses that can create problems (e.g. when we want to enhance the kinetic energy).

 
THE DRY ICE PUCK

 

  The dry ice puck is constituted by a puck where a container with dry ice is fixed.

  When subliming, the dry ice produces a gas of carbonate anhydride that escapes through a hole in the centre of the puck. We have, between the puck and the surface of support, (very smooth, generally a plate of crystal) an air cushion that holds the puck lightly raised over the plane of support.

  Practically we obtain a motion without friction.

  For a didactic use, the problem arises because of the necessity of producing the dry ice for each experiment.

 
AIR TABLE OR AIR TRACK

  They function on the same principle as the air cushion between bodies in reciprocal motion. They present the positive characteristics of the dry ice puck, without its flaw. The cushion that forms between the disk and the table or between the glider and the track is produced by the air, held at pressure by a compressor, thanks to a series of innumerable holes in the surface of the table or of the track.

  The air track allows to obtain easily un rectilinear motion and it can be inclined by an angle large enough (without the glider touching it) to allow the study of the motion on a inclined plane.

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COLLECTION OF THE EXPERIMENTA DATA

  The physical quantities that characterize a motion (detectable experimentally with greater facility) are position and time.

  The systems to collect the experimental data (space and time) can be:

  • the spaces are arranged and the times are measured between them (photoelectric gates),
  • the times are arranged and the spaces are measured between them (multiflash photos).

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SYSTEM WITH ARRAGED SPACES

  The system based on arranged spaces consists in settting the position in correspondence of which we will measure the times. We use a chronometer that is started and halted by the mobile with gates through a mechanical or an electrical contact or photocells.

  Flaws: for this study the knowledge of only one interval of space with the relative time is not enough; for which it is necessary to dispose of different chronometers linked to different gates ( with great experimental complication) or to repeat the motion many times, moving the gate each time, with very doubtful experimental and didactic results.

 
MULTITIMER

 

  Anyway a multiple chronometer can be used as that showed in the figure, connected as in the schema.

 
PHOTOELECTRI GATES INTERFACED WITH A COMPUTER

 

  The time intervals are measured by the computer clock

  Programs to process collected data are normally enclosed in the interface.

  Flaws: the method didactically presents some counter-indication because of the automatic data collection and process, except if we use it as comparison with the manual work of pupils.

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SYSTEM WITH ARRANGED TIMES

  The system based on arranged times consists in setting the intervals of time in correspondence of which we will measure the spaces.

 
TIME-RECORDER AND PAPER RIBBON

  The time-recorder is made of a vibrator (the first time-recorders were constituted by a modified electric bell) to which a point is fixed that leaves signs on a paper strip dragged by the mobile at constant intervals of time.

  The space covered is measured on the strip and the time is obtained as the sum of the elementary times between two contiguous points.

  Flaws: the period is always fixed (normally 1/100 s, depending on the frequency of the electric current); the strip dragged by the mobile creates practical problems when effecting the measure and can easily perturb the motion of the mobile.

 
SPARK GENERATOR AND SPARK PAPER

  The spark generator periodically produces impulses of high tension that arouse sparks between a wire linked to the mobile and a spark paper placed on the track. The spark paper blackens in correspondence of each spark.

  The detection of the data occurs, as with the time-recorder, by directly measuring the space between a point and the other and by summing the elementary time intervals.

  Advantages of the spark generator over the time-recorder:
  - the spark generator allows choosing the value of the interval of time, within quite a large range.
  - the spark paper does not disturb the motion at all, as it is not dragged.

 
MULTIFLASH PHOTOS
 

  The glider moves in the dark in front of a camera with the shutter constantly open.

  A stroboflash sends periodically a flash that exposes on the film the position taken in these moments by a flag fixed on the glider.

  If a metric scale is fixed on the track of the glider, on the film we can read the position taken by the glider moment by moment, while the times are obtained, also here, as the sum of as many periods as the number of the positions reached.

 It is necessary to have an instant camera; it is necessary to operate in the dark (even if the experimental device can be modified by illuminating the glider constantly and disposing a stroboscope in front of the objective of the camera).

  Flaws: the experimental device and the execution of the experiment are rather complex.

 
CCD CAMERA
 

  We apply to the body in motion a self-adhesive strip that reflects the luminous impulses emitted by the LEDs that the camera uses as reference to the position of the bodies.

  The camera can be directly collectable to the computer and it is provided with software for the data processing.

  The experiment does not present any problem of illumination.

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PROCESS OF EXPERIMENTAL DATA

  Whatever method is adopted, at the end of the experiment we have the values of space and of time and the relative experimental errors depending on the instruments used.

  The process of the experimental data consists in:

  • calculating speed and acceleration,
  • drawing space - time, speed -time and, eventually, acceleration - time graphs ,
  • finding out the type of motion from the calculated values and from the graphs,
  • writing, if possible, the equation of the motion.

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