initial timing experiment

Your 'initial timing experiment' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.

Initial Timing Experiment

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In this experiment you will use the TIMER program, a hardcover book, a cylinder or some other object that will roll along the book in a relatively straight line, and a ruler or the equivalent (if you don't have one, note the RULERS link on the Assignments page).

• The book's cover should be straight and unbent.
• The object should roll fairly smoothly.

Place the book on a flat level tabletop.  You will prop one end of the book up a little bit, so that when it is released the object will roll without your assistance, gradually speeding up, from the propped-up end to the lower end.  However don't prop the end up too much.  It should take at least two seconds for the ball to roll down the length of the book when it is released from rest.

• Using the TIMER program determine how long it takes the ball to roll from one end of the ramp to the other, when released from rest.  Time the object's motion at least five times.
• Determine how far the object actually travels as it rolls from one end to the other.
• Determine how much higher one end of the book was than the other, and how far it is from one end to the other.

Then reverse the direction of the book on the tabletop, rotating the book and its prop 180 degrees so that the ball will roll in exactly the opposite direction.  Repeat your measurements.

In the box below describe your setup, being as specific as possible about the book used (title, ISBN) and the object being used (e.g., a solid glass marble, a small can of tomato paste (full or empty?), a ball-point pen), and what you used to prop the object up (be as specific as possible).   Also describe how well the object rolled--did it roll smoothly, did it speed up and slow down, did it roll in a straight line or did its direction change somewhat?

Note:  Don't trust this form.  Compose your answer in Notepad or a word processor, saving it every few minutes, then copy and paste it into the box.  Power could surge, your computer could malfunction, in any of a number of ways the work you put into this form could be lost.  Compose it elsewhere and keep a copy.

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In the box below report your data.  State exactly what was measured, how it was measured, how accurately you believe it was measured and of course what the measurements were.  Try to organize your report so the reader can easily scan your data and see any patterns that might occur.

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Using your data determine how fast the object was moving, on the average, as it rolled down the incline.  Estimate how accurately you believe you were able to determine the object's average speed, and give the best reasons you can for your estimate of the accuracy.

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Your calculation divides the change in position (length of the roll) by the change in the clock time, ans is consistent with the definition vAve = `ds / `dt in the following discussion.

A common definition reads v = d / t. Many students use this definition to calculate the average velocity here, and it works fine for this example. However this formula has some shortcomings and won't be used in this course. Read on:

In this course t will generally stand for clock time and `dt for time interval. The symbol `d represents the capital Greek delta (the triangle symbol) and denotes 'change in ...', so `dt stands for 'change in t'.

Since d is used in `d to stand for 'change in', we generally won't use d to stand for any actual quantity (it would be confusing if we wanted to represent 'change in d' by '`dd').

We will use s or x to stand for position, so that `dx or `ds stands for the change in position.

What the equation v = d / t would calculate is actually the average speed or average velocity. We'll worry later about the difference between speed and velocity. Using `d for 'change in', t for clock time and s for position we use here the definition

vAve = `ds / `dt.

So for example if the ball travels 24 cm while the clock time changes from, say, 28.1 sec to 32.9 sec, we would observe the following:

`ds is the change in the position of the ball, which in this example is 24 cm.

`dt is the change in the clock time; if the TIMER program is triggered at clock times 28.1 sec and 31.7 sec, then the corresponding time interval will be the difference 31.7 sec - 28.1 sec = 3.6 sec.

So here we would have

vAve = `ds / `dt = 24 cm / 3.6 sec = 6.7 cm / sec.

Use the units in your calculations, and actually do the symbolic unit calculations. The calculation should read 29 cm / (2.625 sec) = 11 cm / s. The unit m/s^2 below does not follow at all from your calculation.

Note that your distance is probably accurate only to the nearest cm; your time interval is indicated to a much higher precision, but as you saw in the TIMER program, the precision of the program itself is limited to around .01 sec. So even if your own triggering of the mouse was flawless, the TIMER couldn't give you as much precision as used in this calculation.

As a rule of thumb, when the precision of one of your observed quantities is limited to 2 significant figures (as is the case here), the precision of the result cannot exceed two significant figures. In this experiment the limits of precision of the distance measurement usually dictates that the velocity is good to only two significant figures.

So for example if the distance is 24 cm and the TIMER reports an interval of 1.8071 seconds, we wouldn't report an average velocity of 24 cm / (1.8071 sec) = 13.28094737 cm / sec. The ... 071 in the time interval is pretty meaningless, since the TIMER itself, and also the user, do not have that sort of precision. So most of the figures in that result are meaningless. The best we can report is probably that the average velocity is 13 cm/s. If we think the measurements are really close we might report 13.3 cm/s, but we would probably mention that the .3 part is very questionable.

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Devise and concuct an experiment to determine whether or not the object is speeding up as it rolls down the incline.  If you have set the experiment up as indicated, it should seem pretty obvious that the object is in fact speeding up.  But figure out a way to use actual measurements to support your belief.

Explain how you designed and conducted your experiment, give your data and explain how your data support your conclusions.

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You haven't explained how you conducted this part of the experiment. Please do so.

Please respond with a copy of this question, a copy of any other part of this document you wish to include, and your response to the question. Indicate your response using the symbols *&##. As your title use the 'response title' suggested above (just copy and paste that title into the Title box of the Submit Work form).

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Your instructor is trying to gauge the typical time spent by students on these experiments.  Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades: 

• Approximately how long did it take you to complete this experiment?

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You may add optional comments and/or questions in the box below.

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************* This note is added to each submission to ensure that the instructor has reviewed your work. The instructor must manually remove this note. If it hasn't been removed, and if the instructor has not made specific responses, then it is possible that your work hasn't been properly reviewed and you should notify the instructor to be sure.

Your responses have been reviewed and everything looks good.

Please let me know if you have any questions related to this orientation assignment.