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course phy 201
9/15 930
120912Do the exercise Fitting a Straight Line.
Read through Chapter 2 of your text.
`gGeneral College Physics
Giancoli: Do Text Chapter 1 Problems 16-24
Openstax: Do Text Chapter 1 Problems 29-35
Submit query_04.
In the Introductory_Problem_Sets be sure you can solve any of the problems posed in these sections, using any of the techniques demonstrated in the given solutions.
`q001. The system with two weights suspended from a pulley is called an Atwood machine.
When one domino was suspended from each side the machine was observed to accelerated from rest through 30 cm in about 3 seconds. When one paper clip was added it accelerated through the same 30 cm in about 2 seconds. With another added paper clip the time interval was about 1.7 seconds.
Find the acceleration for each trial.
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30cm/3sec = velocity 10cm/sec...20cm/sec / 3sec = acceleration 6.67cm/sec^2 30cm/2sec = velocity 15cm/sec.......30cm/sec / 2sec = acceleration 15cm/sec^2 30cm/1.7sec = velocity 17.65cm/sec ............35.3cm/sec / 1.7 = acceleration 20.76
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Graph acceleration vs. number of paper clips and sketch the straight line that you think best fits the trend of your results.
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y=mx+b line would look like y=x7
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According to your results, what is the average rate of change of acceleration with respect to the number of clips?
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around 7cm/sec^2/ clip
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If the trend is in fact linear, how many clips would it take to result in an acceleration of 980 cm/s^2?
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About 140 clips
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When two dominoes were suspended from each side, data similar to that obtained for the previous system indicated accelerations of 1, 7, 10 and 15 cm/s^2 for 1, 2, 3 and 4 added clips.
At what average rate was acceleration changing with respect to the number of clips?
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Arond 3.37cm/sec
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For this system, what is the slope of a linear trendline for a graph of acceleration vs. number of clips?
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Would be a slope of about 3.5 cm/sec^2
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Which graph had the lesser slope?
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The second one, with 2 dominoes
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What was it that was different about the two systems that resulted in different slopes?
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The weight of 2 dominos in the second system
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Good, but note that it's the mass of the 2 dominoes, not their weight, that resists being accelerated.
On the other hand it's the changing weight of the changing number of paper clips that causes changes in the acceleration.
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If we conducted the same experiment for a system consisting of four dominoes, what do you think would be the slope of the graph of acceleration vs. number of clips?
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Slope near 1.75 cm/sec^2
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If we conducted the same experiment for a system consisting of four dominoes, what do you think would be the average rate of change of acceleration with respect to the number of added clips?
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Around 1.87cm/sec
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`q002. Assume that at a length of 60 cm, a rubber band chain exerts no significant force, but that for every centimeter stretched beyond that length it exerts an addition 0.1 Newton of force. You don't need to know what a Newton is, but if you want something to relate to, a Newton is about the weight of a typical small-to-medium-sized apple grown on a typical backyard tree. I weigh about 800 Newtons. A liter of water weighs about 10 Newtons. A 20-ounce soft drink weighs about 6 newtons. A pound is about 4.4 newtons.
Now, if a given constant force was exerted on a ramp rotating on a domino, then the greater the distance through which the force is exerted, the further we would expect the ramp to coast after the force is removed. If the force was exerted through twice the distance, we might expect the ramp to rotate twice as far.
If we exerted a greater force through the same distance we would expect the ramp to coast further. If twice as much force was exerted through the same distance, we might expect the ramp to rotate twice as far.
Using these assumptions, reason out the following:
Suppose we extend the chain to a length of 68 cm, use it to set the rotating ramp in motion and find that the ramp coasts through 3600 degrees before coming to rest. If we had an additional chain identical to the first, and extended both to 68 cm, how far would we expect the same system to coast?
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Around 7200 degrees
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How much force does the chain exert at the 68 cm length?
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.8 newtons
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As the chain returns from the 68 cm length to its 60 cm length, does it exert a constant force, an increasing force or a decreasing force?
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A decreasing force
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What average force does the chain exert as its length decreases from 68 cm to 60 cm?
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-.1cm/sec
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The force decreases from .8 N to 0 N, and the decrease is linear. So we expect the average force to be .4 N, halfway between the initial and final values, and equal to the midpoint value (which you estimate correctly in the next question).
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It looks like you've calculated the average rate at which force changes. You've pretty much done that correctly, except that the change in force is -.8 N and the change in position is -8 cm so the rate would be -.8 N / (-8 cm) = +0.1 N / cm. Note also that the units are not cm / sec.
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Now if the chain is extended to 64 cm, how much force does it exert?
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.4 newtons
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What average force does it exert as its length decreases from 64 cm to 60 cm?
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-.1cm/sec
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You'll want to rethink this. Force decreases from .4 N to 0 N. So what's the average force?
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If the chain produces 3600 degrees of rotation when extended to 68 cm, how much rotation does it produce when extended to 64 cm, assuming that in each case it returns to its 60 cm length before releasing the ramp?
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1800
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How does the average force between 68 cm and 60 cm compare with the average force between 64 cm and 60 cm?
How does the distance through which the force is exerted compare?
How would the two comparisons combine?
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If we had two identical ramps, one on top of the other, through how many degrees do you think they would rotate if the rotation was produced by a single chain extended to a 68 cm length?
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If the weights of the ramps where indentical
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It's not clear what your estimate is.
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If the original ramp was 2 feet long, then how far would we expect a ramp 1 foot long to coast, when the rotation is produced by a single 68 cm chain?
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7200 degrees
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Would you expect the 1-foot ramp to have a greater or lesser coasting acceleration than the 2-foot ramp?
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Would expect it to have a greater acceleration
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`q003. University Physics
Give your data for rubber band chain length vs. proximity of magnets.
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Assuming that the force exerted by your rubber band chain is a linear function of its length, sketch a graph of force vs. proximity to the magnets. You don't know at what exact length the chain begins to exert a force, so your force axis might be subject to relabeling, but the shape of that graph will not be affected by your assumption of the zero-force length of the chain. So go ahead and make a reasonable assumption of the zero-force length and proceed accordingly.
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How does the shape of your graph compare to the shape of the 'slope graph' constructed from your previous graph of coasting distance vs. proximity of magnets?
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&#Your work looks good. See my notes. Let me know if you have any questions. &#