ie-Physics

Experiment I-1

Of course change is a part of reality!  Without change life could not exist.  We observe a multitude of changes with our senses.  We take change for granted!  But when people stopped taking change (such as motion where an object changes its location) for granted, much was learned about our world.

1. It takes a finite time to cover any non-zero distance.  With an infinite number of points between any two locations, it is mathematically impossible to transverse an infinite number of points in a finite time.
   
   
2. The second argument is the famous Achilles paradox:  In a race between the fast Achilles and a slow tortoise, the tortoise is allowed to start some distance ahead of Achilles.  Achilles must first reach the location where the tortoise started.  But in the time Achilles is transversing that distance, the tortoise will have progressed a little further.  This reoccurs in each successive time interval.  Achilles must now transverse that newly added distance.  But as Achilles does so, the tortoise continues to move still further, beyond where it was at the start of the time interval.  In each successive time interval Achilles gets nearer, but having first to get to the tortoise's previous position, never can catch the tortoise.  No one can ever win a race if starting behind!
   
   
3. Consider that the tip of an arrow in flight in a space made of points must, at any given moment, be stopped AT some particular point in space.
   
   
4. Consider three parallel rows of points in space.  One set of points (B) remains fixed while A and C move in opposite directions at equal speeds.  But compared to C, A will have passed twice as many points as compared to B.  Therefore an instant of time can NOT correspond to the passage from one point to the next point.
   

But we observe the reality of motion through space.  So either our notion of space made up of points is in error, or the notion of motion is in error.  Motion which originally seemed obvious and natural to everyone, needing no explanation, now seemed to contain some kind or logical flaw which needed to be understood and explained away.  Trying to unravel these arguments led to new understanding that we call physics.  And in the process of developing the physics, we developed a civilization based on that physics far advanced from the world of the ancient Greeks.

Experiment

Because observing is the basis of all science, it is appropriate to start the study of physics with practice observing things that change.  We have all been observing since before birth!  So observation is not new to anyone.  But scientists have developed some habits that they believe optimize learning using observations.  These habits will be valuable whether you become the owner of your own business, a physicist, or just about any other vocation.

Get a notebook, perhaps a traditional bound notebook with pages sewn together or maybe an iPad, that can become your personal science journal.  Don't use loose scraps of paper which can get discarded or lost.  The purpose of your journal is to keep information forever.  Each page should be numbered.  Each entry should be dated and initialed or signed.  (Journals take on legal significance if you ever have to prove when you did something!)  Ink lasts much better than pencil, so use an ink that will be easy to read years in the future.  If you decide to use a computer based journal, set up routine backups.  If you are not familiar with what information you should record in your journal, use this (colored, underlined) link→ to look at suggestions for writing a technical report.  Those suggestions are relevant since much of the information needed for a technical report should be recorded initially in your journal.

There are many methods of recording and studying motion and other things that change.  The author cannot know what equipment is available to you.  So you should consider the following as flexible suggestions that you can modify depending upon equipment, facilities and technology available.  You may have access to a digital camera, a cellphone or iPad with video capabilities, as well as more traditional ruler and watch.  Use whatever technology is available to gather data.

traditional tools

A ruler and clock maybe the least expensive technology!  And as you will find in Experiment I-2, with a little creativity you can often modify existing equipment to serve your needs.  Measure out distance intervals along the expected path of motion.  (For example, for studying someone walking along a path, make a number of successive marks separated by equal distances, perhaps a couple meters apart.)  Then record the time the subject reaches (or alternatively passes) each mark.  After your first attempts, you may have to modify the chosen distance intervals or your timing procedure to best fit the motion you choose to study.  A useful analysis might start by graphing each distance from the origin verses the elapsed time for each marked location.  Don't be too quick to pass up traditional tools.  When you are trying to learn new ideas, sometimes fancy technology is more confusing than helpful.  You need to judge which technology is best for you and the chosen task.

computerized digital tools

A small portable digital video cameras (such is in a cell phone or iPad) often works for recording motion in well lighted situations.  It is simplest to keep the camera in a fixed position (fastening or sitting it on a stationary object) and allow the moving object to pass in front of the lens.  When capturing video, the camera will provide a uniform time interval between successive images.  Something of known length should be visible in at least one image to allow you to establish a scale between the real size and the apparent size in the images.  (For example, if one were photographing an airplane passing overhead, the wingspan or length of the craft may be a published measurement.)

Photographing an object carrying a strobe light is a technique which works in the dark.  (For example, there are inexpensive lights for bicycles and joggers which flash at regular time intervals.)  Time how long it takes perhaps 101 flashes (i.e., 100 intervals between flashes) and then move the decimal place to calculate the time between successive flashes.

You may need to find a computer application which allows viewing successive image frames when requested.  Standard digital video captures images 30 frames per second, i.e., 1/30 second apart.  But a particular video may not use that standard.  ( On a Macintosh computer, QuickTime Player can show the frames of a paused video sequentially using the ← and → keys.  Use the Movie Inspector to see the frame rate.)

You'll need to establish the rough path of the subject across the screen where you choose to do the measurements.  Decide what convenient part of the subject you wish to measure (such as leading edge, estimated center of its mass, or trailing edge).  Starting with the first image, measure the subject's location (along the motions path; that might be a diagonal or curve across the screen) compared to an arbitrary reference spot on the screen or the screen edge.  Move to each successive image recording the distance from that same reference spot on the screen edge.  Also measure the length of the known object on screen and establish the ratio between its real size and the size measured on screen.  All the other screen measurements will need to be multiplied by this ratio.  

analyzing your data

1. Measure and compare speeds of
   1. a moving person (your choice:  walking, running, crawling, rolling???),
   2. several vehicles driving by,
   3. other moving objects.
2. To do so, measure distances for a number of marked locations.  (Distances could be measured and marked in the real world.  Alternately they can be measured on a monitor or photograph using image size then multiplying by the scale ratio comparing a photographed object of known size with its image size.)
3. Record times passing each location.  (Time, perhaps in seconds, could be real elapsed time using a clock or stopwatch or by calculating time using that between successive video frames.)
4. Construct several line graphs for each motion:
   1. displacement verses time.  The value for displacement at each time is the distance from the selected original location.
   2. speed verses time.
      Average speed (or velocity) is defined by v_av ≡ Δd / Δt
      where Δ, the Greek letter Delta, is used to represent the change in... ,
      Δd is the change in location called displacement, Δt is elapsed time.
      So the speed at each time is the distance covered in the previous time interval divided the the length of the time interval.
   3. acceleration verses time.
      According to the definition Galileo Galilei chose, acceleration is a ≡ Δv / Δt
      So the value of the acceleration at each time is the change of speed between successive time intervals divided by the length of the time intervals.
5. Consider the possible extent of error in locations and times, and the effects of possible errors on displacement, speed, and acceleration.
6. Ponder the limitations of your methods.  (e.g., What are the most outrageous measurements you might make?  What makes them outrageous?)

Finally, scientists often construct technical reports for others to read.  Communicating technical information such as observations and findings is another skill used by scientists but useful for most others.  If you need course credit, use your observations recorded in your journal to construct a technical report.  If unsure what details should be included, read the screen describing a technical report.  Make sure your report is based on YOUR personal observations and not copied from someone else.  If you are working with a partner or team, give them credit in your report.

Reference

• George Sarton, A History of Science: Ancient Science Through the Golden Age of Greece, Wiley, 1952.