The computer timer isn't very accurate at these short time intervals; the pendulum timer would be more accurate.
In any case, you have correctly done most of the steps in your analysis but one step is inappropriate.
Again I've inserted several notes and hope they help clarify the 'missing pieces' in your understanding of these ideas. You've got 90% of the pieces in the right place, and hopefully this will help you sort out the last 10%.
Please send me a revision of your calculation and explanation for the very first timing, on the 10 cm ramp, before you revise the rest. You may of course ask questions as well.
Video Experiment #4
Acceleration is constant for an object rolling down a uniform incline.
Distance (cm) Time (s) Velocity (cm/s) Final Vel. (cm/s) vAve (cm/s) change in vel ('dv) aAve
10 0.53123 18.82423809 37.64847618 28.23635713 18.82423809 35.43519396
15 0.7265525 20.64544544 41.29089089 30.96816816 20.64544544 28.41562784
20 0.921875 21.69491525 43.38983051 32.54237288 21.69491525 23.53346739
25 1.0625 23.52941176 47.05882353 35.29411765 23.52941176 22.14532872
30 1.203125 24.93506494 49.87012987 37.4025974 24.93506494 20.72524878
35 1.310547 26.7064058 53.4128116 40.0596087 26.7064058 20.3780603
40 1.417969 28.20936142 56.41872284 42.31404213 28.20936142 19.89420179
I used the video file and the computer timer to gather this data instead of using the previous experiment’s data. I chose to do this because I felt I could run the timer more accurately this time since there was only one ramp to worry about timing. Since the video only used the distances of 10cm, 20cm, 30cm, and 40cm, I averaged those times to come up with data for the 15cm, 25cm, and 35cm time slots.
CALCULATIONS:
For velocity, I divided Distance / Time.
For final velocity, I multiplied velocity *2.
I averaged the two velocities to get vAve, then subtracted vf-v0 to get ‘dv.
By the time you averaged you had three velocities available to you: the initial velocity (which was 0), the average velocity (which is `ds / `dt and which you called simply 'velocity'; the word 'velocity' always has to be modified as in 'initial', 'average', 'final' or 'change in') and the final velocity (which since the init vel was zero and the accel presumably uniform is double the average vel).
You don't say which two you averaged. It's important to be very specific in describing how you calculate your results, both for the sake of your own understanding and to make things very clear for the general reader.
In any case, by the time you averaged two velocities you already had the average velocity, and the result you got was not the average velocity. It looks like the average of your average velocity and your final velocity.
And for the aAve, I divided ‘dv / ‘dt.
`dv would be final velocity - initial velocity; initial velocity is zero.
I think that the acceleration changes are more than likely caused by systematic error, like the anticipation of the cart beginning or ending because of the way the line curves. Experimental uncertainties such as the slope of the table or a slight inaccuracy with the computer timer may also play a role but I don’t think they are as prevalent.
I didn’t really use my results from the previous experiment at all to justify my calculations. I did, however, use notes from the “synopsis” and the “memorize this” to make sure that my calculations were right. My notes from the previous experiment don’t have calculations for aAve.
I feel that my variations in the acceleration are within the range of variations that are expected with the equipment we are using.
My results for acceleration do not support the hypothesis that the acceleration of the ball down the uniform incline is independent of how fast the ball rolls and where it is on the ramp. Looking at the aAve numbers, the aAve slowed down with each increase in distance on the ramp. It did start to even out on the last 3 distances, so the hypothesis may still hold and my data simply decreases due to systematic and unknown errors. But in looking only at the numbers I’ve calculated, we cannot say it fully supports the hypothesis.
I estimated the uncertainty to be around .08.
No I don’t think it is possible to draw a straight horizontal line that passes between the error bars for every graph point.
If the horizontal line could pass through the error bars for all of the graph points, then it would be good support for the hypothesis. Since my data does not show that as being possible, I don’t think the graph or the horizontal line supports the hypothesis very well. I still feel that it doesn’t support the hypothesis because of systematic error and uncertainties, not because the hypothesis isn’t true.
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