Physics Experiment #1
Measurement of Length and Mass
Part A---Measurement of Length
Problem:
How can a meterstick be used to measure:
(a) the dimensions and volume of a rectangular block and a textbook.
(b) the average thickness of a single page.
It is easy to use a meterstick to make measurements of lengths such as the dimensions of
book. However, a meterstick seems too crude an instrument to obtain a good
measurement of a length as small as the thickness of a sheet of paper. Nevertheless, with
a little ingenuity, such a measurement can be made.
Apparatus:
Meterstick, wooden block, balance, nails, textbook.
Discussion:
Note that there is a special technique used to measure the length of an object.
Because the end of the meterstick may be chipped or worn with use, it is not used in
making a measurement. Instead, some mark like the 1-cm, or 10-cm mark is lined up
with one end of the object. Then the mark at which the other end lines up is read. The
desired length is obtained by subtracting the reading of the meterstick at one end from the
reading at the other end.
To measure the thickness of a single sheet of the textbook, you might begin by
holding the meterstick over the edge of one sheet and attempting to make a reading. Can
a good measurement be made this direct way? In measurements of this kind, you can
often do better by using an indirect method of measurement. If you assume that every
sheet of the textbook has the same thickness, you can measure the thickness of 50 or
more sheets instead of one. You can then divide by 50 to get the thickness of one sheet.
Procedures:
1. Measure the length, width, and height of the block and of the laboratory manual to the
nearest tenth of a millimeter. Enter the values in table 1-1.
Table 1-1
Length (cm)
Width (cm)
Height (cm)
Volume (cm3)
Block
Textbook
2. Count off 50 sheets (HINT: not 50 pages) of the textbook and measure the combined
thickness. Do the same for two other numbers of sheets from 100 and above. Enter
the values in table 1-2.
Table 1-2
Number of Sheets
Total Thickness (cm)
Average Thickness of one
sheet (cm)
3. Calculate the volumes of the block and of the textbook and enter them in table 1-1.
Retain only the significant figures in your answers.
4. Calculate the average thickness of one sheet of the textbook, from each of the three
batches of sheets, and enter it in table 1-2.
Questions:
1. Do your three calculations tend to support the assumption that all the sheets of the
textbook are equally thick? Explain.
2.
You have assumed that the sheets of the text are equally thick. Design a procedure to
test the accuracy of this assumption.
3. Referring to your three trials in table 1-2, which one will give you the most accurate
value for the thickness of a single sheet? Explain.
4. As a home experiment, determine whether there is a measurable difference between
the thickness of the sheets of two different books. Describe your procedures.
Part B---Measurement of Mass
Problem:
What is the mass of a small nail? A triple beam balance is too insensitive an instrument
to make a good direct measurement of a small mass like a nail. However if you assume
that all of the nails of the same kind are alike, you can solve the problem by measuring
the mass of a group of nails and dividing the total mass by the number of nails in the
group. In this experiment you will begin by assuming that the nails are alike. You will
later examine your data to see to what extent this assumption is true.
Apparatus:
Platform balance, set of metric masses, wooden block, small nails.
Discussion:
Make sure the triple beam balance is placed on a level surface, and the needle is
‘balanced’. Adjust as needed. When measuring the mass of an object, the needle must
return to this ‘balanced’ position. The mass of the object is the combination of the
readings on all three beams.
Procedures:
1. Measure the mass of the wooden block to the nearest hundredth of a gram. Repeat
the measurement two more times. Be sure to slide all of the riders back to the zero
positions before re-measuring the mass of the block. Record your values in table 1-3.
2. Calculate the average value of the mass of the object. This is likely the ‘true’ mass of
the block.
Table 1-3
Trial #
Mass (g)
1
2
3
Average Mass
3. Select any three nails. Measure and write down the mass of each nail separately.
Nail #1: __________
Nail #2: __________
Nail #3: __________
4. Now measure the mass of a group of 10 nails to the nearest hundredth of a gram.
Increase the number of nails to 20, then 30, 40, and finally 50 nails. For each group
of nails, record the data in table 1-4.
Table 1-4
Average mass of a single
Number of Nails
Total Mass (g)
nail (g)
10
20
30
40
50
5. For each group of nails in table 1-4 compute the average mass of a single nail, and
record it in the third column of the table.
Questions:
1. If all of the nails actually have equal masses, which of the values in the third column
is probably closest to the true mass of a single nail? Explain.
2. If all of the nails have equal masses, what should be the ratios of the masses of 10, 20,
30, 40, and 50 nails to each other?
3. Do the ratios of the masses in the second column of table 1-4 support the assumption
that all the nails have nearly equal masses? Explain.
4. Make a graph of the data in table 1-4, plotting the number of nails on the horizontal
axis against the mass of the nails on the vertical axis. What should be the shape of
this graph if every nail has nearly the same mass? Use the graph to predict the mass
of 35 nails, and 65 nails.
5. From your experience gained in this experiment, describe how a balance may be used
to determine how many nails are in a box without actually counting them.
6. The Earth’s gravitational field is weaker on the top of a mountain than at sea level.
Will a triple beam balance give the same value for a mass measured on top of a high
mountain as it does at sea level?
Calculations:
Show one example of each calculation.
Conclusions:
Discuss the:
a) Point(s)of the lab.
b) results of the lab.
c) sources of error and ways to correct them.