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course PHY 201
10/23 4:30pm
Lab-related Questions for 101013Note: Before doing the lab questions you should run through the Sketching Exercise below. That exercise starts with questions about masses pulled upward by tension and downward by gravity, much along the lines discussed in class. It continues with questions related to masses on inclines.
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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Length of pendulum was 12cm
T=.2sqrt(12)=.69s
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`qx002. Give the time from release to first, second, third and fourth 'strikes' of the pendulum.
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.69s, 1.38s, 2.07s, 2.76s
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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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12, 15, 15, 12, 14
13.6
2.04s
24cm/s^2
In the 3rd line, I took the mean of the counts and multiplied that by .15s which is the per count in seconds.
In the 4th line, to find acceleration, I did the following:
`ds=50cm
`dt=2.04s
vAVE=24.5cm/s
v0=0
vF=49cm/s
a=`dv/`dt=(49cm/s)/2.04s=24cm/s^2
According to the .69 period of that pendulum, and your answer to question 2, 13.6 strikes would correspond to around 8 or 9 seconds. Strikes don't occur at .15 second intervals.
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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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4,5,5,5
4.75
.71s
197cm/s^2
The acceleration seems off to me so I want to show my work below:
`ds=50cm
`dt=.71s
v0=0
vAVE=70cm/s
vF=140cm/s
a=(140cm/s)/.71s=197cm/s^2
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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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3,3,3,3
3
.45s
493cm/s
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`qx006. If there was a fourth set of trials, report as before:
· 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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No 4th trial
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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?
`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?
`q009. At what average rate does the acceleration of the system change with respect to the number of small paperclips?
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234.5cm/s^2 per added paperclip
I took the mean of the change in accelerations for the paperclips 173cm/s^2, which was the difference with 0 small paperclips and 1 paperclip, and 296cm/s^2, which was the difference between 1 small paperclip and 2 small paperclips.
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`q010. How much acceleration do we tend to be gaining, per added paperclip?
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For the 1st added paperclip we gained 173cm/s^2 in acceleration. For the 2nd added paperclip, we gained 296cm/s^2 in acceleration.
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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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24%
Acceleration of gravity is 980cm/s^2. Taking the mean of each added small paperclip, the percentage can be expressed as (234.5cm/s^2)/(980cm/s^2) which results in 24%.
The mass of the small clip would correspond to 24% of the system’s total mass according to the acceleration change.
If there are 6 big clips and 1 small clip and 1 small clip represents a 24% change in acceleration, then the ratio of the mass of a small clip to that of the large clip would be .24 to 1.
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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).
Your thinking is good. However your accelerations are based on .15 seconds per 'strike' of the pendulum, which is not consistent with the reported length. Probably closer to .35 seconds per 'strike', which will systematically change your values for the acceleration of the system.
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