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course Phy 202
3/11 7pm
Raising Water in a Vertical TubeCopy this document, from this point to the end, into a word processor or text editor.
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Equipment:
If you don't have one you will need to obtain a 2-liter soft drink bottle.
The experiment was originally written for a rubber cork-shaped object called a stopper, with three this tubes protruding from both sides, and a 3-liter container.
There are also several miscellaneous pieces of tubing in your kit, and none should be discarded.
The stopper looked like this, and most of the pictures in these instructions show the stopper in a 3-liter tea container.
The bottlecap looks like this, and includes a short, a medium-length and a long tube.
The lab materials package, as of Spring 2010, actually consists of two such bottlecaps, one bottle cap at each end of the longest tube. Each cap has a short tube and a medium-length tube, inserted in the same manner as in the above picture. NOTE: It is possible that each cap has a single tube 'looped' through two of its holes. If this is the case, you can cut the tube about a centimeter above the top of the cap to form a short tube, leaving the rest to form a longer tube. After the cut you would have a short tube a few inches long extending through the cap (this will be the so-called 'pressure release' tube), a longer tube a couple of feet long (this will be the so-called 'pressure measuring tube'), and of course the tube connecting the two caps. Wait to make the cut until you need to do so; once you've seen the setup below you should understand.
The picture below shows the stopper in a tea container, with the tubes protruding. The short tube is 'capped' with a piece of 1/4-inch tubing, which is closed at one end by a plug of glue. The smaller tubing fits tightly into this 'cap', which seals off the end.
The picture below shows the system set up with a 3-liter bottle.
Initial Experiment
Notes about the tubing:
If necessary you can pull the tubing in one direction or the other, through the holes in the bottlecap. However the tubing should be at a usable length.
The apparatus has been pressure-tested against leakage.
It isn't recommended that you pull the tubing all the way out of the bottlecaps; it can be difficult to reinsert. Should it happen that the tubing does get pulled out (the tubing fits fairly tightly so it's unlikely to be pulled out by accident), it will probably require a little ingenuity and a pair of pliers to pull the end back through.
Short pieces of thin tubing, filled with glue, are included in your materials. These tubes do a good job of sealing the ends of the thicker tubes inserted through the cap. They are usually packed in the cylinder you used for the flow experiment. There are also pieces of thicker tubing, sealed at one end with glue, which can if the situation arises be used to seal the ends of the thinner tubing. Short unsealed tubing pieces of one diameter can be used to connect tubing of the other diameter (i.e., thin tubing can be used to connect two pieces of thicker tubing, or thicker tubing to connect two pieces of thinner tubing).
A 20-penny nail will also for a tight seal in a tube. Some packages may include some cut-off 20-penny nails. However nails tend to rust--no problem for the experiments, but who wants rusty nails around--so their use has probably been discontinued.
For an initial experiment, we are going see how to set up the system and apply force to raise water in a vertical tube.
The longest piece of tubing will be supported vertically above the bottle to make a 'vertical tube':
This 'vertical tube' should either be a few centimeters above, or should just reach, the bottom of the bottle when the cap is screwed on. The other tubes should extend just an inch or two into the container.
You will place about a liter of water in the bottom of the container. Then screw on the cap so that the low end of the vertical tube is submerged in the water.
The 'vertical tube' should be supported so that it is more or less vertical. A little sag or tilt away from vertical won't hurt, but get the tube as nearly vertical as possible without taking a lot of time to do so. The second cap will be near the top of this tube, and will not get in the way of anything (in fact the second cap should make it easier to find a way to support the tube in the vertical position).
The picture below shows the bottle with the vertical tube extending out the top. The tube is actually not all that vertical--you should try to do a little better, but if you can't it should be OK.
Mark heights on the tube and give the bottle a squeeze
Mark the tube or attach small pieces of tape to indicate the points that lie 30 above the level of water in the container, then 40 cm, then 50 cm, 60 cm, etc. to a height of at least 100 cm.
Be sure the caps are still attached to the ends of the other two tubes coming out of the stopper, so that air cannot enter or leave the container through these tubes.
You are going to squeeze the container and make water rise in the vertical tube. If you have reason to believe your hands aren't up to a hard squeeze, you should use a different means of compressing the container. Sitting on the floor and squeezing it between your feet and the wall is one possible alternative.
If you squeeze the container a bit you should see water rising in the tube.
Squeeze the container hard enough so that the water rises to the 30 cm level.
Now squeeze a little harder so that water rises to the 40 cm level.
This requires a significant amount of force. Most people can manage 40 cm, depending on hand size and strength and the shape of the container being used. Most people can't manage much over a meter, maybe two, though of course some people are much stronger than average and can do quite a bit more.
This isn't a test of strength, so stop before your face gets red, and well before you risk a hand or arm injury.
However, continue squeezing to achieve additional 10 cm increments of height in the tube, until water either reaches the top of the tube or you reach the reasonable limits of your ability to raise the water.
In the space below:
Indicate how you perceived the force necessary to raise the water to change with the height of the water column.
Do you think it takes twice the force to raise water twice as high?
Do you think it takes more, less, or the same additional force to raise water from 40 to 50 cm compared to the additional force required to raise it from 30 to 40 cm.
You are answering based on your perception rather than on measurements, and the perceptions of our senses are not generally linear.
Would it be possible to somehow measure the forces required?
If so, how might we do this?
Your answer (start in the next line):
Yes, I think it takes twice as much force to raise water twice as high
it takes more force to raise from 40 to 50 cm than 30 to 40 cm
it would be possible, force=mass/acceleration so you take the mass of the water and divide by the time it takes to get to the distance
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Answer the following in the space below:
At the highest level you achieved, how much do you think the water in the tube weighed?
Do you think the weight of the water in the tube is greater, less than or equal to than the force you had to exert?
Do you think the comparison you make here is obvious? If so what makes you think so?
How might we measure the weight of the water and the force you exerted to make the comparison?
Your answer (start in the next line):
an oz. or so
equal too
Yes , because the more force you exert the more water in the tube
Measure the weight of the bottle without water and the the bottle with the water and then again when the water is in the tubes. The force exerted would be approximated and given a scale on for oneself
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If you think the force you exerted is different from the weight of the water, how could this be so? If you think they are the same, then why do you think it is so?
Your answer (start in the next line):
I think it is the same because if you exert no force you have no water in the tubes
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Now set the system so that the tube comes out of the top of the stopper, makes a quick but smooth bend, runs horizontally a foot or so before making a quick but smooth bend to vertical. The tube in the picture below pretty much does this, but the horizontal run is a little curvy, not perfectly horizontal. The tube is hooked around the edge of the monitor and then runs more or less vertically, running out of the picture near the upper right.
You can set up the system, improvising with whatever resources you have handy. Supporting the horizontal run with a board or on a book or a coffee table shelf is one possibility.
The horizontal run doesn't have to be as long as the one shown here. 10 cm or so would be sufficient. The subsequent vertical run can also be as short as about 10 cm.
Once the system is set up, squeeze the container so water rises to the horizontal bend. Let the water stop before reaching the bend, then try to notice how much additional force seems to be required to move the water through the horizontal section, just up to the point where the tube again begins rising toward vertical.
Then continue squeezing as water once more begins rising vertically.
Compare the additional force required to run the water through the horizontal section with the additional force required when water starts rising vertically.
Once it's up to the horizontal section, is significant additional force required in order to move the water through the horizontal section?
Does it require significant additional force to then move the water through the subsequent vertical section?
Enter your answers in the space below:
Your answer (start in the next line):
No, significant additional force is needed to move through the horizontal section
Yes, more force is needed for the vertical section
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Repeat. Adjust your squeeze so that water moves at a constant speed in the tube, moving through a few centimeters every second.
If you were to graph your force against time, which of the graphs below do you think would most accurately depict your actions?
Enter your answers in the space below. Include a description of the graph, the reasons you chose the graph you did and the reasons you rejected each of the others
Your answer (start in the next line):
the graph would be linear, which has a constant slope, if the water was moving at a constant speed
you wouldn't choose the other graphs because they don't depict this, they are non-linear and shows this with the patterns
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What do you think happens to the pressure of the gas in the bottle as you gradually raise the water?
Your answer (start in the next line):
the pressure increases as you raise the water
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Do you think it would take more pressure, less pressure, or about the same pressure in the bottle to raise water to a height of 50 cm in the first setup, where the tube was pretty much vertical, or in the second, where the tube had a horizontal 'run' before returning to vertical?
Your answer (start in the next line):
more pressure in the first setup to raise to 50 cm
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How much difference do you think there would be in the pressure required to raise water to the 50 cm level in a perfectly vertical tube, and the pressure required in a tube which runs upward but, say, a 10 or 20 degree angle with vertical? What difference would it make if the tube ran at 45 degrees from the vertical?
Your answer (start in the next line):
I think it would be 10 to 20 percent more pressure in the straight vertical than the tube at the angle, roughly half the pressure for the 45 degree angle
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What other means might you use to raise the pressure in the bottle?
Your answer (start in the next line):
heat and forcing air into the bottle
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Now we're going to use the system to raise some water from its level in the container, to a higher position, thereby increasing the potential energy of the system. As you have already experienced, you're going to have to do some work to accomplish this.
Set up the system so that after a graceful bend the (formerly) vertical tube runs horizontally to the end. Place a container underneath the open end of the tube so that water runs into the container. The picture below shows the tube running out of the stopper, then running in a very nearly horizontal direction to the top of a graduated cylinder. It is not necessary to use the graduated cylinder to catch the water--you may use any container.
Increase the force of your squeeze (and hence the pressure of the gas) gradually and notice that once the water reaches the horizontal segment of the tube, very little extra force is required to move the water through the horizontal segment and maintain the flow.
Continue squeezing steadily until one or two cupfuls of water have been transferred to the container. Try to keep the flow of water slow and steady. Try to remember what the system feels like during the process, so you can answer the following questions:
Once the water begins flowing out, you will notice that you have the squeeze the bottle further and further to displace more and more water. The question is, do you have to exert more and more force to do this, or will a steady force accomplish the purpose?
You might have to repeat the process a couple of times before you are confident in your answer to this question. When you do, insert your answer in the space below:
Your answer (start in the next line):
steady force could accomplish this
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Now repeat, but this time try to make the water flow faster and faster into the container. Does it take more and more force to increase the speed of the flow?
Your answer (start in the next line):
yes
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To what average height was the water raised, relative to the level in the bottle? This will be the difference between the average vertical position height of the water surface in the bottle and the vertical position of the end of the tube. It doesn't matter that the water fell back down after exiting the tube; if we had placed a container at the level of the tube, we could have caught it at that level.
Your answer (start in the next line):
30.5 cm
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How much potential energy gain was therefore accomplished, per cm^3 of water raised?
Your answer (start in the next line):
PE=mgh=(1kg)(9.8m/s^2)(30.5cm)=298.9J
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1 cm^3 of water has a mass of 1 gram, not 1 kg.
The units of the calculation as you give it would be kg * m/s^2 * cm, which is not Joules.
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A cupful of water has a volume of about 250 cm^3 (very roughly). By how much would the potential energy of the system therefore be increased if you raised a cupful of water to the height of the outflow position?
Your answer (start in the next line):
m=rho*V=(1000kg)(250cm^3)
PE=mgh=(250*10^3)(9.8m/s^2)(30.5cm)=74.725e6J
would increase 100%
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right ideas but there aren't 1000 kg of water in a cubic centimeter.
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How much force would you have to exert to raise the water to this position, using a slow steady flow? Simply estimate the force in pounds, then convert to Newtons.
Through how much distance would your hands have to move, from the instant they touch the sides of the bottle?
Estimate the work they would therefore do, and compare to the potential energy increase. Which do you think would be greater, based on your experience with this system, and why?
Your answer (start in the next line):
A=V/y=250cm^3/30.5cm=8.2cm^2
P=rho g y=(1000kg)(9.8m/s^2)(30.5cm)=298.9e3N/m^2
F=P x A=298.9e3 x 8.2= 2.45e6
W=F x d=2.45e6 x 30.5= 74.75e6
the work would be greater because of the pressure
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Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
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Copyright © 1999 [OrganizationName]. All rights reserved.
Revised: 07/26/10
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You're doing pretty well, but your units are off in some of your calculations (which otherwise follow the correct line of reasoning).
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you.
Spend a reasonable amount of time on your revision, but don't let yourself get too bogged down. After a reasonable amount of time, if you don't have at least a reasonable attempt at a solution, insert the best questions you can showing me what you do and do not understand, and I'll attempt to clarify further. &#
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