Name: _____________________________________
Woodrow Wilson
Summer 2010
Inertia, Mass, and Weight
Inertia is defined as “the tendency of an object to resist any change in its motion.” Examples of changing the
motion of an object include making an object start moving when it was initially at rest, making a moving
object speed up, making a moving object slow down, and making a moving object change the direction it is
moving. Through daily experience, we all realize that it is much easier to change the motion of some objects
than it is to change the motion of other objects. It is therefore obvious that not all objects have the same
amount of inertia. The more inertia an object has, the more difficult it is to change its motion.
Mass can be defined as a quantitative (numerical) measure of inertia. The SI unit of mass is the kilogram.
The more mass an object has, the greater its resistance to changing its motion. When you compare masses,
you are actually comparing inertias. A 5.0 kg mass has twice as much inertia as a 2.5 kg mass – even if
both objects are in outer space and weightless!
Measuring Mass: The Inertial Balance
We often use spring scales and triple beam balances to measure mass. Since these measuring devices are
calibrated to make use of the Earth’s gravitational pull in order to determine mass, they would be useless for
measuring mass in the absence of gravity. Mass measured in this manner is known as gravitational mass.
Mass, however, is a quantitative measure of an object’s inertia, and is not dependent upon gravity.
Therefore, the mass of an object remains constant, regardless of the presence or strength of a gravitational
pull.
The Inertial Balance is a device that is used to measure inertial mass by comparing objects’ resistances to
changes in their motion. Unlike other mass scales and balances, an inertial balance can be used whether or
not gravity is present.
Procedure:
1.
Use a C-clamp to secure the inertial balance to the table top.
2.
Pull the free end of the balance to the side and release.
Notice how quickly it moves back and forth.
3.
Place some mass in the tray. If needed, secure it with
transparent tape.
4.
Again pull the free end of the balance to the side and release.
What do you now notice about the time it takes the
balance to swing from side to side after more mass was
added to the tray?
5.
Determine the amount of time it takes the inertial balance to make one complete oscillation (over and
back) while varying the amount of mass in the pan. In order to minimize the reaction time error in
this procedure, you will time the balance as it swings through 10-20 complete oscillations and divide
the average total time by the number of vibrations in order to determine the period of vibration (i.e.,
the time needed for one complete oscillation).
6.
Two students will time during two separate trials in order to further safeguard against timing errors.
7.
Complete the Data Table with masses shown. You may wish to begin with 800 g in the tray.
1
Name: _____________________________________
Woodrow Wilson
Summer 2010
Inertia Balance Data Table
Mass in
#
balance,
vibrations
g
0
100
200
300
400
500
600
700
800
8.
Total Time, sec
Trial 1
Trial 2
Timer 1
Timer 2
Timer 1
Timer 2
Average
Period,
sec
Use MS Excel to make a graph of “Period vs Mass” using the values determined in your trials.
Display the “best-fit” curve, equation, and r-squared value on the graph. Print your graph, making
certain you have included major and minor gridlines over a white background.
Now that you have calibrated your inertial balance,
you can use it to determine the masses of other objects.
9.
Place an object with unknown mass in your inertial balance and determine its period of vibration as
before. You should obtain better results if you choose an object whose mass is in the 500 – 800 gram
range. Use two timers and make two trials as before.
# cycles
Trial 1
timer 1
Trial 1
timer 2
Trial 2
timer 1
Trial 2
timer 2
Average
Time
“The average total time for ____ vibrations was _______ sec, so the period = ______ sec.”
10.
Use the graph to determine the best measure of this object’s inertial mass. Clearly display the
unknown period and resulting mass on your graph.
“According to my graph, an object with a period of
______ sec should have a mass of ______ grams.”
11.
Now use a spring scale, pan balance, or triple beam balance in order to determine the object’s
gravitational mass.
“According to the scale, the mass of this object is _________ grams.”
12.
Based on your results, make a statement comparing your object’s inertial and gravitational masses.
2
Name: _____________________________________
Woodrow Wilson
Summer 2010
You may be concerned that the weight of the objects influenced the period of vibration when using the
inertial balance. In order to see if/how the weight of the object affects this experimental determination of an
object’s mass, we can suspend the unknown mass cylinder though the hole in the pan using tape and a light
string. Since the pan no longer supports the mass, we can be confident that its period of vibration in the
balance is entirely due to its inertia. We can then obtain its period when the mass is secured to the pan. Do
both and compare results.
# cycles
Trial 1
timer 1
Trial 1
timer 2
Trial 2
timer 1
Trial 2
timer 2
Average
Time
Cylinder in pan
Cylinder on string
cylinder supported by pan: ______ sec for ______ cycles = period of ______ sec
cylinder suspended by thread: ______ sec for ______ cycles = period of ______ sec
 How does the period obtained when the cylinder is suspended by a thread compare with its period
when placed in the pan?
 List sources of error/uncertainty present in this activity.
 Suppose you could take the inertial balance to the moon. How might your procedure/results change if
you repeated these procedures using the same known and unknown masses?
 Suppose you could take the inertial balance to outer space where there is no net effect of gravity. How
might your procedure/results change if you repeated these procedures using the same known and
unknown masses?
Relationship between Weight and Mass
What is the scale reading (in Newtons) when these
masses are suspended by the force scale?
a) 50 g = 0.05 kg
b) 150 g = 0.15 kg
c) 300 g = 0.30 kg
d) 550 g = 0.55 kg
e) 700 g = 0.70 kg
_________ N
_________ N
_________ N
_________ N
_________ N
f) 850 g = 0.85 kg _________ N
g) 1000 g = 1.00 kg _________ N
h) 1150 g = 1.15 kg _________ N
i) 1300 g = 1.30 kg _________ N
j) 1500 g = 1.50 kg _________ N
13.
Use MS Excel to make a graph of “Weight (N) vs Mass (kg)”. Include the origin as one of your data
points. Display the “best-fit” curve, equation, and r-squared value on the graph.
14.
We know that the equation of a line that passes through the origin has the form y = mx, where m = the
slope of the line. Since y = Weight and x = Mass, our equation becomes Weight (N) = slope x Mass
(kg). This tells us that you multiply the mass of an object (in kilograms) by what value to obtain its
weight on earth (in Newtons)? __________
15.
The slope of this line should be equal to a value known as the acceleration due to gravity, or g. The
accepted value of g, with appropriate units, is approximately ___________. According to your results,
the value of g is ___________.
16.
Calculate the percent error in your value.
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