#$&*
course PHY 231
10/23 11:07 pm
In lab you timed the Atwood machine (paperclips on pulley) using your bracket pendulum.`qx001. What was the length of your pendulum? What would be the period of a pendulum of this length, based on T = .2 sqrt(L)?
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I was quick to start this and didn't think to measure the length of my pendulum.
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`qx002. Give the time from release to first, second, third and fourth 'strikes' of the pendulum.
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I did not time these strikes as such but worked out that, based on the rhythm of strikes, that I had 4 counts per second or, more usefully, 1/4 seconds per count.
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`qx003. In your first set of trials there were 3 large clips on each side.
• In the first line give your counts for the first set of trials, separated by commas.
• In the second line give the mean of your counts.
• In the third line give the time interval in seconds which is equivalent to the mean of your counts.
• In the fourth line give the acceleration corresponding to the time interval just reported.
• Starting in the fifth line give an explanation of the results you gave in the third and fourth lines.
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13, 12, 13, 14
13
3.25
9.47
The third line is the number of seconds obtained from the mean count times the seconds/count conversion factor from above. The fourth line is the a obtained by using [( `dx/ `dt)* 2]/ `dt with `dx = 50 cm.
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`qx004. In your second set of trials there were still 3 large clips on each side, but there was a small clip on the side which ascended in the first set.
• In the first line give your counts for this set of trials, separated by commas.
• In the second line give the mean of your counts.
• In the third line give the time interval in seconds which is equivalent to the mean of your counts.
• In the fourth line give the acceleration corresponding to the time interval just reported.
• You don't need to include an explanation, since the procedure is identical to that of the preceding questions, which you explained in answering that question. Just make sure your results make sense.
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4, 4, 4, 5
4.8
1.2
69.4
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`qx005. In the third set of trials a second small clip was added to each side.
• In the first line give your counts for this set of trials, separated by commas.
• In the second line give the mean of your counts.
• In the third line give the time interval in seconds which is equivalent to the mean of your counts.
• In the fourth line give the acceleration corresponding to the time interval just reported.
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My notes here indicate that only one clip was added to the side with a small clip on it already. Here's the results I have:
3,3,3,3
3
0.75
178
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`qx006. If there was a fourth set of trials, report as before:
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No other trials.
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`qx007. For the trial with the greatest acceleration, sketch a force diagram showing, to scale, the tension and gravitational forces acting on the clips on the descending side of the system.
• Which vector was longer?
• By what percent was it longer?
• What is the net force on these clips as a percent of the gravitational force?
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The weight vector was longer and it was by 18%, which is what I think would also the percent of the Fgrav since the a is 178/980 = 0.18.
That would be correct. Good.
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`qx008. For the trial with the greatest acceleration, sketch a force diagram showing, to scale, the tension and gravitational forces acting on the clips on the ascending side of the system.
• Which vector was longer?
• By what percent was it longer?
• What is the net force on these clips as a percent of the gravitational force?
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The longer vector is the tension vector, T and I think it will also be 0.18% longer as well, but the % Fgrav is greater since the clips have a different mass but same acceleration as the other side so it would be > 18%, probably about 27%
Good.
quick note: it would be 18% longer, not .18%. 18% is .18, a bit less than 1/5. .18% would be .0018.
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`q009. At what average rate does the acceleration of the system change with respect to the number of small paperclips?
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I'm not sure about this. The %gain for 0small to 1small is 69/9.5 = 7.26 and the 1sm to 2sm is 178/69 = 2.58. The average of these is clear to be 4.92 but I'm not certain this is what's being asked for as the gain was so much more for the first clip than the second. This number may make more sense though if we had added more clips and then averaged those gains. So with more data it may 'even out' more.
Think about the definition of average rate of change. It tells you exactly how to interpret the question.
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`q010. How much acceleration do we tend to be gaining, per added paperclip?
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As I mentioned above: with only two clips added it seems hard to make a broad a generalization as this and since the %gains were so different from one clip to two so I may be missing something here.
about 60 cm/s^2 change, then 100 cm/s^2 change; given uncertainties in measurements that's not a huge difference
an estimate of 80 cm/s^2 per added clip wouldn't be unreasonable
However your pendulum strikes were likely about .35 sec apart. 1/4 second would correspond to a pretty short pendulum.
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`q011. The unbalance in the gravitational forces with each new paperclip is of course significant. It is this unbalance that causes the differences in the system's acceleration.
The total mass of the system does increase slightly with each added small paperclip, but for the moment let's assume that the resulting change in the total mass of the system isn't significant.
• What percent of the acceleration of gravity do we get from each added small clip?
• How is this related to the mass of a single clip as a percent of the system's total mass
• What is your conclusion about the ratio of the mass of a large clip to the mass of a small clip?
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For the first clip we had a 6% increase in acceleration vs g. Well the clip should reasonably be 6% of the total mass and the mass of the small clip would be about 18% that of a large clip since mS=0.06(3mL)
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`q012. This question can be challenging. Don't let yourself get too bogged down on it:
In the preceding you drew conclusions based on the assumption that the changes in the system's total mass due to adding up to a few small paperclips was insignificant. It is perfectly possible that uncertainties in measuring the time intervals were large enough to obscure the effect of the changes in the total mass.
However refine your answers to the preceding question to take account of the change in total system mass.
(One possible approach: assume that the requested ratio is r and symbolically solve for the acceleration a in terms of the number N of added small clips, sketch a graph showing the predicted shape of your a vs. N curve, and see what value of r best matches this graph with a graph of your observed a vs. N).
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It's late now and I'll have to give this some more thought than what I can put into it right now. Instinctively I want to say the graph would have a very large increase from 0 to 1 and then still increasing but at a decreasing rate and very possibly approaching a limit. I think about a natural log function.
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Good intuition. The graph might well be increasing and concave down, but it won't actually turn out to be the log function.