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phy 201
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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rubber band calibration
#$&*
phy 201
Your 'rubber band calibration' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Rubber Band Calibration_labelMessages **
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an hour
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length 70 cm
Using paperclips bent into the shape of hooks, form a 'chain' of all six of your marked rubber bands (a chain of two rubber bands is shown below). Be sure you observe which is which, and when you record data make sure that the individual rubber bands are clearly identified by the number of marks.
Hang the plastic bag from the chain.
Place one domino in the bag.
Measure as accurately as possible the length of the topmost of your rubber bands. Be sure you keep track of which is which.
Measure from one end of each rubber band to the other. You will therefore be recording the positions of both ends of each rubber band. Be sure you measure the end-to-end distance, from the point where one end of the rubber band ceases and the air beyond the end begins, to the similar point at the other end.
You should not attempt to align the end of your measuring device with either of the positions you are recording. Rather align one of the markings (e.g., the 10.0 cm marking) on your measuring device with one end of the rubber band, see what marking corresponds to the other end, and record both markings.
To get the most precise measurement possible you should use a reduced copy of a ruler. To make sure the measurement is also accurate, you should take into account any tendency toward distortion in the corresponding part of that copy. You can choose whichever level of reduction you think will give you the most accurate and precise measurement.
In the box below, indicate in the first line the ruler markings of both ends of the first rubber band, entering two numbers in comma-delimited format.
In the second line indicate the distance in actual centimeters between the ends, to an estimated precision of .01 cm..
In the third line explain how you obtained the numbers in the second line, and what the meaning of those numbers is. Also indicate how this rubber band is marked, and the limits within which you think your measurement is accurate (e.g., +- .03 cm, indicating that you believe the actual measurement to be between .03 cm less and .03 cm greater than the reported result).
Your answer (start in the next line):
length of first rubber band 5.5 cm
Im not sure whats being truly asked
within .15 cm
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Explain the basis for your estimate of the uncertainty of the length of the first rubber band.
Your answer (start in the next line):
Well there can be some error in judgement of length
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Measure as accurately as possible the lengths of the remaining rubber bands. Be sure you keep track of which is which. You may move your measuring device from one rubber band to the next.
In the space below enter the ruler markings of the ends of the first rubber band, delimited by commas, in the first line (this will be the same information you entered in the first line of the last space ), the ruler markings of the ends of the second rubber band on the second line, etc., until you have a comma-delimited line for each rubber band.
Then put the word 'End' in the very next line.
Follow this in the very next line by a comma-delimited line containing the numerical distances in cm, each estimated to within .01 cm, of the rubber bands in your chain.
Follow this by a line indicating the markings on the rubber bands.
Finally indicate the uncertainty in your measurements, which should probably be the same as the uncertainty as that given in the preceding space .
Your answer (start in the next line):
5.5 cm
5.5 cm
6 cm
6 cm
5.5 cm
5 cm
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Add another domino to the bag and repeat your measurements. The positions of the ends should be recorded in your lab book, and should be backed up electronically in a way you can easily interpret at any future date (a comma-delimited text file or a spreadsheet file would be good; a tab-delimited file would also work but tabs can be variable and invisible so if you are going to use a text file, a comma-delimited is probably the better choice).
You won't enter the endpoint information here, but as cautioned above be sure you have it so if the information reported here has any anomalies, you can go back to your raw data and correct them.
Determine the distances in centimeters between the ends of each rubber band, and enter them in the space below, in the same order you entered them in the preceding space . Use one line and use comma-delimited format.
In the second line indicate that these results were from the weight of two dominoes.
Your answer (start in the next line):
5.75 cm
5.5 cm
6.25 cm
6.25 cm
5.75 cm
5.25 cm
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Continue adding dominoes and measuring until one of the rubber bands exceeds its original length by 30%, or until you run out of dominoes, then stop. To keep the time demands of this experiment within reason, you should beginning at this point adding two dominoes at a time. So you will take measurements for 4, 6, 8, ... dominoes until the 'weakest' of your rubber bands is about to stretch by more than 30% of its original length, or until you run out of dominoes.
If one rubber band reaches its limit while the rest are not all that close to theirs, remove this rubber band from the experiment and modify your previous responses to eliminate reference to the data from this band. However, keep the band and keep your copy of its behavior to this point.
In the space below, enter on the first line the actual lengths in cm of your rubber bands when supporting four dominoes, in comma-delimited format. Enter in the same order you used previously.
On the second line enter the number 4 to indicate that this result is for four dominoes.
On the third line enter in comma-delimited format the lengths in cm when supporting 6 dominoes.
On the fourth line enter the number 6 to indicate the six dominoes being supported.
Continue in this manner until you have entered all your lengths and numbers of dominoes.
Then on the next line enter 'End'.
You may then enter any brief identifying information or commentary you wish. However since the nature of the information has been defined by previous spaces, this is optional.
If you have reason to believe the uncertainty in your measurements has changed, indicate this also. Otherwise it will be assumed that your previous uncertainty estimates apply.
Your answer (start in the next line):
6.5 cm , 6 cm , 6.75 cm , 7 cm , 6 cm , 5.75 cm
4
6.75 cm , 6.2 cm , 7 cm , 7.5 cm , 6.5 cm , 6 cm
6
End
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Compiling and Graphing your Data
Each domino is pulled downward by the Earth's gravitational field. Each rubber band resists this force by stretching out, which creates a tension equal and opposite to the force exerted by the Earth (each rubber band also supports the rubber bands below it, but the rubber bands don't weigh much so we neglect that weight). The force exerted by the Earth on each domino is about .19 Newtons.
Make a table of the force exerted by each of the first four rubber bands vs. the length of the rubber band. You do not need to do this with all six, but you should retain the last two rubber bands and your data for those two, in case you have need of them in later experiments.
Make a force vs. length table for each of these four bands. The length will go in the first column, the force in the second. Your graph will be of the type shown below, but you probably won't have quite as many data points; your forces will also differ from the forces indicated by this graph.
There is a tendency for students at the beginning of a physics course to connect graphs point-to-point. This is a usually a very bad idea in physics, since there are experimental uncertainties in our data and we learn nothing by following those uncertainties around. The graph below is an example of this Bad Idea.
Note also the REALLY bad idea, which is to treat the 'origin' as if it is a data point. In this example, we never measured the force at the 8 cm length, and there is no justification at all for using the 'origin' as a data point (actually the point where the axes come together in this graph is not the origin, it's the point (8 cm, 0); the origin would be (0 cm, 0) and is well off the scale of this graph ).
It is a good idea to add a smooth curve to the data. This is because we expect that force will change smoothly with rubber band length. However we acknowledge that errors might occur in our data, so we never attempt to make the smooth curve pass through the actual data points, though we don't try to avoid them either.
In the example below the curve wobbles around from point to point instead of smoothly following the trend of the points.
In the next example the curve doesn't try to 'hit' each data point, but rather to follow the pattern of the actual force vs. length. It passes among the data points, remaining as smooth as possible and coming as close as possible to the data points without making unsightly 'wobbles' in an attempt to pass through specific data points.
In the space below give your table in a series of lines.
The first line will contain, in the previous order, the lengths the rubber bands supporting 1 domino, separated by commas, followed by the downward force exerted by gravity on 1 domino ( i.e., the number, indicating .19 Newtons). You can copy most of this information (all except the .19) from a previous space .
The second line will contain, in the previous order, the lengths the rubber bands supporting 2 dominoes, separated by commas, followed by the downward force exerted by gravity on 2 dominoes. Again you can copy most of this from a previous space .
Continue in this manner until you have all the lengths and downward forces, in the same comma-delimited syntax described above.
Follow your data with a line containing the word 'End'.
In subsequent lines specify the meaning of each column of your table, the units and the quantity measured in each.
Your answer (start in the next line):
5.5 cm , 5.5 cm , 6 cm , 6 cm , 5.5 cm , 5 cm , .19
5.75 cm , 5.5 cm , 6.25 cm , 6.25 cm , 5.75 cm , 5.25 cm , .38
6.5 cm , 6 cm , 6.75 cm , 7 cm , 6 cm , 5.75 cm , .76
6.75 cm , 6.2 cm , 7 cm , 7.5 cm , 6.5 cm , 6 cm , 1.14
End
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If you haven't already done so, construct a graph for each rubber band and fit a smooth curve that you think best depicts the actual behavior of that rubber band.
In the space below describe the shape of the curve you drew to approximate the force vs. length behavior of first rubber band. The curve in the last figure above could be described as 'increasing at a decreasing rate, then increasing at an increasing rate'. Other possible descriptions might be 'increasing at an increasing rate throughout', 'increasing at a decreasing rate throughout', 'increasing at an increasing rate then increasing at a decreasing rate', etc.).
Then describe the shapes of all six rubber bands. Follow your last description by a line containing the word 'End'. You may if you wish add comments starting on the next line.
Your answer (start in the next line):
As the rubber bands length increases the force increases so as x goes up y also goes up end
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Do the forces all go up in the same manner (e.g., all linearly, or all increasing at an increasing rate, etc..)?
If so what is your description?
If different graphs go up in different manners, then give a description of each.
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Estimating Forces
We can now use our curve to estimate the force at a given length, or to estimate the length that will give us a specified force.
In the figure below we estimate the force for the 9.5 cm length.
From the data point it might appear that the force corresponding to 9.5 cm is about 1.5 Newtons. However we're going to put our trust in the curve.
We project a line from the L = 9.5 point on the horizontal axis, straight up to the curve, then straight over to the F axis.
Reading the point on the y axis as F = 2.6 or maybe F = 2.7 we see that the curve gives us a force between 2.6 and 2.7 Newtons.
If our curve has been drawn carefully and if it appears to make good sense then we believe that the curve is more reliable than our data points, and we will tend to believe this estimate more than our data point.
Similarly we use the curve to estimate the length that gives us a force of 2 Newtons.
We project a horizontal line from the F = 2 point on the vertical axis to the curve, then from this point we project vertically downward to the horizontal axis.
We read a length of about 10.4 cm. Again we use the curve, which 'averages out' the characteristics of several data points, to estimate the required length.
If you haven't already done so, include in your report a table of your data for force vs. length for each of the four selected rubber bands.
Now for the first rubber band, sketch your best smooth curve, the one you believe best shows the real force vs. length behavior of a rubber band. Describe your curve and describe your thinking about how to construct the curve.
Use your curve for the first rubber band (the one with 1 mark) to do the following:
Estimate the force in Newtons corresponding to a length of 9.8 cm and report the number in the first line of the space below.
Your answer (start in the next line):
17 newtons (I used the graph on the main page)
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Estimate the length in cm of a rubber band that gives a force of 1.4 Newtons and report the number in the second line.
Your answer (start in the next line):
9.3 cm (using same graph)
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From the curve estimate the force in Newtons corresponding to each of the lengths you actually observed. For example, if you observed lengths of 8.7, 8.9, 9.3, 9.8, 10.1 cm with 1, 2, 4, 6 and 8 dominoes, what forces would be predicted by the curve for each of these lengths? Give your estimates in the first line, using comma-delimited format. In the second line indicate by how much the estimate of the curve differs from the actual weight supported.
Your answer (start in the next line):
I'm not sure
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This question needs to be answered. What is it you are unsure of?
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From the curve estimate, using or your first graph, report in comma-delimited format, in the first line, the length corresponding to each of the forces .19 N, .38 N, .76 N, 1.14 N, etc.. In the second line indicate in comma-delimited format by how much each of these lengths differs from the length you actually observed when the rubber band was resisting this force.
Your answer (start in the next line):
5.35 , 5.7 , 6.4 , 6.6
.15 , .05 , .1 , .15
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Which do you have more faith in, the values from the curve you just created or the values you reported in your table, and why?
If you were to estimate a force for a given length using one of your graphs, what do you think would be the uncertainty in that force (e.g., +- .12 N, or +- .03 N, etc.) and what is your evidence for this estimate?
Your answer (start in the next line):
The values in the curve My values are based on estimates by eye which could end up being horribly innaccurate
+- .12 N no real basis it is what I feel I would most reasonably be innacurate from I just don't feel I would be within .03 N
and the proportions of the graph make it hard to be very close
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If you were to estimate a length for a given force using one of your graphs, what do you think would be the uncertainty in that length (e.g., +- .05 cm, or +- .13 cm, etc.) and what is your evidence for this estimate?
Your answer (start in the next line):
Yet again it would be as above the +- .13 I would err on the side of being less than more
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Rubber bands
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Within the context of rubber bands, we use the following terminology:
The product of the average tension exerted by a rubber band as it is stretched from one length to another, multiplied by the distance through it is stretched, is the work-energy associated with that stretch.
The term 'work-energy' indicates that 'work' and 'energy' are equivalent and pretty much interchangeable terms (but to avoid possible confusion we do have to learn to be careful how we use those terms).
Most of the energy associated with the stretching of the rubber band can be recovered when the rubber band is allowed to 'snap back'. However as a rubber band stretches or snaps back, there are complex effects involving thermal energy (heating and cooling) and a significant amount of the energy ends up being converted to thermal energy and dissipated.
An 'ideal rubber band' is one in which thermal energy losses are negligible. There is no such thing as an ideal rubber band, and while real rubber bands are not all that far from the ideal, they aren't all that close either. The more common terminology used in physics is that of an 'ideal spring'; this is because metal springs are more often used in experiments and applications and typically have much smaller thermal losses than rubber bands. Ideal springs also have linear force vs. length graphs, and though no actual spring results in perfect linearity, metal springs typically come much closer to this ideal than rubber bands.
Rubber bands are used here for several reasons:
They are cheaper.
They are typically lighter and interfere with certain other physical properties of a system (e.g., mass and weight) less than do metal springs.
They clearly exhibit non-ideal behavior at a directly observable level.
All this leads up to a couple of very important statements:
When a rubber band is stretched the energy associated with the process is equal to the average force of tension multiplied by the distance of the stretch.
This quantity is equal to the area beneath a graph of force vs. length.
Most of this energy can be recovered when the rubber band snaps back.
The recoverable energy is called the potential energy of the rubber band.
So increasing the length of a rubber band increases its potential energy by an amount which is approximately equal to (but a bit less than) the corresponding area beneath its tension vs. length graph.
Using the new terminology, answer the following, assuming that the rubber band of the original graph does not lose any energy to thermal effects:
By how much does its potential energy increase as it is stretched from a length of 100 mm to a length of 150 mm?
By how much does its potential energy increase as it is stretched from a length of 150 mm to a length of 200 mm?
By how much does its potential energy increase as it is stretched from a length of 100 mm to a length of 200 mm?
How much energy would we expect to get back if the rubber band 'snapped back' from its 200 mm length to a length of 150 mm?
How would this last result be obtained from your answers to the first and third questions in this series?
Answer with four numbers in comma-delimited format in the first line, followed by an explanation starting at the second line.
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Iv elooked and looked but trying to find out how to find the force exerted by a rubber band , According to this i need tension but i dont know how to find it either. Ive looked at all the experiments and ive looked online i cant seem to find a way i can find force.
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How to find the force of a rubber band
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The experiment points you to your rubber band calibration results, and I believe I've previously referred you to these results.
Go to your rubber band calibration experiment, and find the lines that read
5.5 cm , 5.5 cm , 6 cm , 6 cm , 5.5 cm , 5 cm , .19
5.75 cm , 5.5 cm , 6.25 cm , 6.25 cm , 5.75 cm , 5.25 cm , .38
6.5 cm , 6 cm , 6.75 cm , 7 cm , 6 cm , 5.75 cm , .76
6.75 cm , 6.2 cm , 7 cm , 7.5 cm , 6.5 cm , 6 cm , 1.14
You should have also graphed this data, so you should have force vs. length graphs for all of your rubber bands.
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Here is the entire thing for the rubber band calibarations but i still dont see how we get the tension from this to be relative to the other question? which is also on the form
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How do i get the tension for the rubber bands
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Your data line reads
5.5 cm , 5.5 cm , 6 cm , 6 cm , 5.5 cm , 5 cm , .19
5.75 cm , 5.5 cm , 6.25 cm , 6.25 cm , 5.75 cm , 5.25 cm , .38
6.5 cm , 6 cm , 6.75 cm , 7 cm , 6 cm , 5.75 cm , .76
6.75 cm , 6.2 cm , 7 cm , 7.5 cm , 6.5 cm , 6 cm , 1.14
The bottom line is that the tension in the rubber band chain is the only thing supporting the dominoes, so for any trial the tension is equal to the weight of the dominoes.
However it's important to understand this within a more general context. So check out the following:
For the first rubber band the lengths 5.5 cm, 5.75 cm, 6.5 cm, 6.75 cm appear to be associated with weights of .19, .38, .75 and 1.14 Newtons.
Every rubber band supports the dominoes, as well as any rubber bands that lie below it. The weight of the rubber bands is much less than that of the dominoes, so at the level of uncertainty in this experiment the weight of the rubber bands can be neglected.
If we ignore the weight of the rubber bands, which is more or less insignificant compared to the weights of the dominoes, the tension in the rubber band chain is the same at all points.
Since the dominoes are in equilibrium, the net force on them is zero. The forces on the dominoes are the weight and the tension. So
tension + weight = 0.
It follows that
tension = - weight.
That is, the tension in the rubber band chain is equal and opposite to the weight being supported.
So when the weight is .19 Newtons downward, the tension exerted on the weight is .19 Newtons upward.
The tension throughout the chain is therefore .19 Newtons.
Now back to the first rubber band.
At lengths lengths 5.5 cm, 5.75 cm, 6.5 cm, 6.75 cm the respective tensions would be .19, .38, .75 and 1.14 Newtons.
You can graph these tensions, then sketch the trendline you think best reveals the actual behavior of the rubber band. The behavior of the tension is very continuous, so the actual curve representing the behavior will be very smooth. It won't wobble around in order to 'hit' every point, each of which has an inherent uncertainty in both the tension (the dominoes aren't completely uniform) and length (you probably have an uncertainty of at least half a millimeter in your measurements of length).
From this graph you can with reasonable accuracy determine the tension in the first rubber band associated with any given length.
You can construct a graph for each rubber band.
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