PHY108
Lab # 1 Introduction
When you need to determine the volume of an object, the way that you go about
it will often vary depending upon the size and shape of the object you are working
with. If the object has a “regular” shape that is easy to work with (like a cylinder or
a rectangular shaped object) you can measure the physical dimensions and
calculate the volume based upon those dimensions. When the object has a shape
that is difficult to calculate, it may be found using what is called the displacement
method.
Displacement is one of those words that have more than one meaning. In the
lectures we often use the term displacement to refer to the vector quantity that
indicates the net change in location of an object. (In this sense it is the straight line
distance measured between the location an object starts at and its final location…
with the direction included.) But the term displacement can also be used to refer to
the volume of material pushed out of the way by an object that is submerged in a
fluid.
Any time that a solid object (one that will not dissolve) is submerged in a fluid it
will push a volume of that fluid out of the way that is equal to the volume of the
object itself. This fact is used with a device called an overflow tank to determine
the volume of small irregularly shaped objects.
In the picture shown to the right there
is an overflow tank and a “capture
bucket”. The overflow tank itself is
nothing more than a cup that has a hole
in the side. If you try to fill a container
that has a hole in the side with a liquid,
as soon as the liquid tries to go above
the location of the hole, it will leak out
of the hole.
Note: The tube on the side of the overflow tank allows you to “capture” the water
that comes out of the tube in a separate container. In the physics lab, the little cup
shown to the right of the overflow tank is this “capture bucket”.
The picture to the right shows the
overflow tank that I put together. It uses
an old Tupperware cup and a tube that
came from an old drafting eraser.
When using an overflow tank, you simply add water to the overflow tank until it
comes out of the tube attached to the side of the overflow tank. Once the water
level stabilizes, if you lower a solid into the overflow tank, the water level will try
to rise. Since it can’t stay above the level where the hole (tube) is attached to the
side of the overflow tank, some of the water inside the overflow tank will come out
of the tube and fall into the capture bucket. When you are careful about doing this,
what you should find is that the volume of the object lowered into the overflow
tank is equal to the volume of the water that comes out of the tube on the side of
the overflow tank and is captured in the little container.
Due to random errors in the operation of the equipment, best results for the
volume are taken by repeating the above operation a number of times and finding
the average (arithmetic mean) of the measurements. The amount of the variation in
the obtained measurements will also indicate the reliability of your device.
I suggest that you repeat your measurements at least five times and then find the
average (mean) of your readings to obtain the measured volume of the object
placed inside the overflow tank.
Having said that, depending upon the volume of the object you are working on
and the capacity of your balance… you have two ways of doing this.
Method 1 – measure the mass of your capture container before you start using it to
capture water from the overflow tank and after it catches the water from the
overflow tank to get the mass of the water captured each time. Once the overflow
tank has been reset, empty out the capture bucket and repeat the steps above four
more times. Then find the arithmetic mean (average) of the five volumes based
upon the mass of the captured water. The volume of the captured water tells you
the volume of the object lowered into the overflow tank.
Method 2 – measure the mass of your capture container before you start using it to
capture water from the overflow tank. Use a separate container when “resetting”
the overflow tank, so that the “capture bucket” is only used to capture water that
comes out of the overflow tank when the object is being lowered into the water.
After you have captured the water from the overflow tank 5 times into your
overflow tank, then measure the mass/volume of the water in your overflow tank.
The volume of water that you have should be five times the volume of the object
lowered into the overflow tank. Simply dividing the calculated volume of water
inside the capture bucket by 5 should give you the same average value calculated
in method # 1 above.
The real difference between these two methods is that if your overflow tank is
not giving a consistent volume when the object is lowered into the tank, the first
method will clearly indicate the amount of variation. Some variation should be
expected. Large amounts of variation indicate a problem with either your
equipment or your technique. Again, the second method is faster (because you only
need to take 2 mass measurements instead of 10) but the first method will tell you
if there are any problems with your measurements.
When building your overflow tank… please
remember to follow safe
shop practices and wear safety glasses any time that you are drilling or
cutting materials. Your eyesight is more important that your grade for this course.
Construction Notes:
- It is important that the tube that is used is not too small in diameter. In my
first attempt, I used a plastic straw for the tube. The inside diameter of the
straw, however, seemed to be too small for the job. When the inside
diameter of the tube was less than ¼ inch, the measurements obtain in use
were unreliable. The device as shown above, however, gave more consistent
readings that were closer to the calculated values than those obtained using
the standard overflow tank bought by the school and shown on the previous
page.
- You should make sure that the tube is angled down so that any water that
flows down into the tube goes all the way down and out the bottom end of
the tube.
- Best results have been obtained when the tube used for the overflow tank has
a thin wall with a relatively sharp edge to it. This tends to help reduce the
effects of surface tension and keeps the maximum water level in the tank
more consistent.
- The smaller the inside diameter of the container used for the overflow tank,
the more reliable/precise your measurements should be. Just remember, you
have to be able to fit the object down inside the overflow tank.
IMPORTANT: If you watch the water level as you are using your overflow tank,
what you will often see is that the height of the water in the overflow tank at the
point when the water first starts flowing out of the tube is not always the same.
Furthermore there will be some variation in the water level at the point where the
water level stops when the water stops flowing out of the tube. This variation in the
height of the surface of the water, multiplied by the cross-sectional area of your
overflow tank, will set the margin of error for your overflow tank. The smaller the
cross-sectional area (diameter) of your overflow tank, the smaller the margin of
error. The tank does, however, need to be large enough in size to allow the object
to be measured to fit inside. The overall results are best when the size of the
overflow tank is relatively close to (but obviously still larger than) the object being
measured.