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