Experiment 3

I submitted a question a few days ago concerning Experiment #3 (the ball rolling experiment in assignment 3) and was wondering if you got the question so I thought I'd resubmit it.

The instructions say to use the video clips and my pendulum or timer program to time the ball rolling down the two ramps at different lengths. The only file on my computer for the experiment was just the clip of the ramp and everything being setup but not of the actual experiment, so my question is, are we supposed to build this ramp on our own?

Also, is there a way to use both the timer program and watch the video files at the same time? The instructions say that the timer is more efficient but if we're supposed to watch video files to gather the data, I don't know where the files are or how to use both programs at once." ""

The instructions at the top of the document containing the instructions tell you which CD to use:
The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.
I've just placed a copy of this instruction at the beginning of every individual experiment, as well as at the top of the entire document. However it sounds like you're using the right CD.
The instruction just below the 'red' instructions tells you
See the corresponding video files on the CD (see note in red at the top of this document) entitled Introductory Video Experiments, video clips # 3. Reference also #'s 1 and 2 for pendulum as a timer. You run the CD by running the disk_0.htm file in the root folder of the CD. Access Video Experiments by clicking on the Video Experiment Clips link in that document. Be sure you are running the CD as instructed from the disk_0.htm file, and that you have clicked on Video Experiment Clips.

You can use the TIMER while the clip is running. Just go to the Timer, then switch to the start and start it. Then use the mouse or ALT-TAB to switch back to the timer, which will appear superimposed on the clip. Move the timer out of the way if necessary. Use ALT-TAB or the mouse to quickly switch back and forth. When you switch to the video clip it will 'cover' the timer, but when you switch to the timer it's not big enough to 'cover' the clip and both will work at the same time.

Experiment 3

Good work overall, though you should order that list of velocities and send me a copy.
Second-ramp average velocities did tend to run about double those on the first ramp, though the slope of your graph did not support this. The reason for this is generally a systematic error where you tend to click a little later on some events than on others. Note that the type of error estimates you made give a good measure of your consistency in measure times, but cannot detect this sort of error.
See my notes.

Length of ramps (cm) Roll 1 Roll 2 Roll 3 Avg. Velocity (cm/s) Ramp 1 10 1.109372 1.109375 1.203125 9.014084507 Ramp 2 20 0.84375 0.796875 0.84375 25.09803922 Ramp 1 15 1.25 1.21 1.09375 12.39669421 Ramp 2 30 1.140625 1.296875 1.203125 23.13253012 Ramp 1 20 1.546875 1.4375 1.625 13.91304348 Ramp 2 40 1.53125 1.46875 1.53125 27.23404255 Ramp 1 25 1.6875 1.65625 1.59375 15.09433962 Ramp 2 40 1.25 1.40625 1.453125 28.44444444 Ramp 1 30 1.4375 1.75 1.828125 17.14285714 Ramp 2 40 1.484375 1.421875 1.265625 28.13186813 Ramp 1 35 1.875 1.765625 1.9375 19.82300885 Ramp 2 40 1.3125 1.28125 1.171875 31.2195122 Ramp 1 40 2.140625 2 2.15625 20 Ramp 2 40 1.125 1.125 1.078125 35.55555556 Ramp 1 45 2.390625 2.15625 2.1875 20.86956522 Ramp 2 40 0.96875 1.125 1.09375 35.55555556 Ramp 1 50 2.35375 2.4375 2.390625 20.51282051 Ramp 2 40 1.03125 1 1.015625 40 The slope of the line is 1.145 cm/s.

Does your straight line pass near the origin of your coordinate system? Why should it or should it not do so?

No the straight line does not pass near the origin of the coordinate system. The only reason that I should think as to why it shouldn’t is if the line is extended past the origin, then it’s assumed that the data points will be in accordance with the line. It allows for too much variation in the data, and also, the data would be in the negatives and in this case, I’m not sure that negative velocity is possible.

On which ramp does the ball have the greater average velocity? Why should this be so?

Ramp 2 has the greater average velocity of 30.49cm/s as opposed to ramp 1’s 16.53cm/s. This is because the original point of the exercise it to see if the second ramp is double the velocity of the first, and my data shows that.

Which is the greatest and which is the least of the following: the average velocity of the ball on the first ramp, the initial velocity of the ball on the first ramp, or the final velocity of the ball on the first ramp?

The initial velocity is the least, and the final velocity is the greatest.

Place in order, from the smallest to the largest, indicating any 'ties': the initial velocity of the ball on the first ramp, the initial velocity of the ball on the second ramp, the average velocity of the ball on the first ramp, the final velocity of the ball on the first ramp, the average velocity of the ball on the second ramp, the final velocity of the ball on the second ramp

This appears to be the original order. Can you place these statements in the correct order?

Sketch a graph of the velocity of the ball vs. clock time from the instant it is released until the instant timing stops on the second ramp. Indicate the instant at which you think the ball reaches its average velocity on the first ramp. I’m not sure that my sketch is correct, but I think the ball reaches its average velocity on the first ramp right in the center of the graph or the velocity v/s clock time of the second ramp.

Why might we suspect that the average velocity on the second ramp should be double that on the first, and how well does this experiment validate that hypothesis?

Since the ball is starting from rest, then it is said that the final velocity will be double the average velocity. We used this ramp experiment to prove that that’s true and by looking at the average velocities from my data of the two ramps, the hypothesis holds.

For the 30-cm distance, what do you think is the uncertainty in your measurement of the time interval on the first ramp (e.g., +-.01 sec, +-.05 sec, +-35 hours)? Why do you think that this is an appropriate value for the uncertainty? I used a formula from when I took statistics:

(1.4375+1.75+1.828125) / 2 = 1.672875

I took the difference of each time and the average, squared the difference and divided it again by the average:

[ (1.67284-1.4375)^2 + (1.67185–1.75)^2 + (1.671875–1.828125)^2 ] / 1.671875 = .047s

I think it’s an appropriate value for the uncertainty since I used an equation to figure it out as opposed to just guessing what the margin of error could be.

Your formula gives a good and valid measure of the consistency of your observations, but would not take account of systematic errors in observation (e.g., if you have a tendency to always start the clock .1 second late that wouldn't appear in this calculation, but would have a significant effect on your conclusions).
Another consideration is that the computer timer itself is incapable of resolving differences of less that .055 seconds. .047 seconds is consistent with the best results possible for the computer timer.

Based on your observed time and your expected uncertainty, what are the minimum and maximum values between which the actual time should lie?

1.671875-0.047 = 1.62 and 1.671875 + .047 = 1.72 so the actual time should lie between 1.62s < ‘dt < 1.72 Had the actual time `dt been equal to the minimum expected value, then what would have been the average velocity on the first ramp?

• I’m guessing that if they were equal, then the average velocity would be ‘ds / ‘dt, 30cm/1.62s = 18.52cm/s. Had the actual time been equal to the maximum value, what would have been the average velocity on this ramp? ‘ds / ‘dt = 30cm / 1.72s = 17.44cm/s What therefore do you expect is the minimum value that the actual average velocity might have had on this ramp? What is the maximum? • I think the minimum value would be 17.44cm/s and the max value would be 18.52cm/s. On your last graph, near the point corresponding to the 30-cm distance, indicate this range of velocities as explained under Q & A on the homepage, under topic Error Bars, Rectangles and Linearity. For ramp 2, my calculation for the margin of error gave me 0.0183, and I think that may be kind of small so I put the corresponding range of velocities on the graph at 0.025.

Your accuracy with the timer won't vary from trial to trial. The deviations of three timings from their mean will be subject to statistical fluctuations. It would take a very large number of timings of the a number of different events to establish your consistency.
In the case of this experiment your consistency is probably within +-.05 sec, but this will be pretty much the same for all trials.

I don’t think it’s possible for the straight line to pass through all the data points at once. If the uncertainty was increased to something like 0.05, they may be large enough to where the line will pass through all of them but as is, it is not possible.

I would think that the distance errors would be more significant because it is the independent variable that affects the time.

The distance can be measured with a meter stick, with a resolution of +- 1 millimeter. Distances in this experiment can be measured much more accurately than time intervals.

patcon ******************