The Inertial Balance
Carl
E. Martikean |
Lew
Wallace High School |
10937
Sheephead Court |
415
W. 45th Ave. |
DEMOTTE
IN 46310-9352 |
GARY
IN 46408 |
cmartikean@yahoo.com |
(219)
980-6305 |
Objective(s):
At
the end of this lesson, the student will be able to:
1. Explain how either a single
pan or double pan balance operates;
2. Explain the physics
principle of the balance using Newton’s First and Second Laws;
3. Differentiate between mass
and weight;
4. Explain how mass and weights
are related using Newton’s First and Second Laws;
5. Explain the difference
between gravitational and inertial mass.
Materials:
Triple
beam balance |
Centigram
balance |
Various
masses |
Two
c-clamps |
Metal
meter stick or 1m of thin metal flat |
Wooden
blocks formed into an L shape to hold the meter stick in a horizontal
position. |
35mm
film container to be attached to the end of the meter stick |
Masking
tape, stop watch |
Strategy:
Many
students confuse the concepts of mass and weight. Our purpose here is to clarify for the student, through
self-discovery, the difference between mass and weight. Further, the student will be challenged to
discover how to “weigh” objects in outer space with an inertial balance.
Performance Assessment:
Briefly
describe the performance assessment that you would use and the expected results
that should be obtained. A grading
rubric would also be nice.
Background
Weighing,
really massing on the surface of a planet or planetoid is easily demonstrated
with either a two-pan balance or a centigram balance. Ask students what the balance is measuring (mass or weight). Then start a discussion of how the balance operates. What we ultimately are looking for are the
physics principles of the balance.
Among these are the fact that gravity is used and that no matter what
body we were standing on the balance would operate exactly the same. But what would be different? So just what is the balance measuring- mass
or weight? How do we know? So, in order to successfully use either a
beam balance or a spring balance we need a gravitational force. These balances are a simple (?)
demonstration of Newton's second law.
So does the balance measure mass or weight? Why?
What
if you were in the orbiting Space Shuttle or space station? Would this balance work? What problems would be present? The measurement of mass presents a unique
problem. How do we measure mass in a
microgravity environment?
In
space, because of the free fall conditions neither a beam or spring balance
will operate. So there must be a third
method of measuring a mass of an object.
This brings us back to Newton's first law. This law is the principle of inertia, the property of matter that
resists acceleration. The amount of
resistance (laziness) is directly proportional to the mass of the object.
To
measure mass in space, scientists use an inertial balance. An inertial balance is a spring device that
vibrates the sample being measured. The
frequency of the vibration will vary with the mass of the object and the
stiffness of the spring. In this case
we are using a metal meter stick. For a
given spring, an object with greater mass will vibrate more slowly than an
object of lesser mass. The object to be
measured is placed in the balance, and a spring mechanism starts the
vibration. The time needed to complete
a given number of cycles is measured, and the mass of the object is calculated.
Procedure:
1.
Using
a drill and bit to make the necessary holes, bolt two blocks of wood to the
opposite sides of one end of the metal meter stick.
2.
Tape
an empty plastic film canister to the free end of the meter stick. Insert a piece of foam into the canister.
3.
Anchor
the wood block to the table top with C-clamps.
The opposite end should swing freely from side to side.
4.
Calibrate the inertial
balance by placing objects of known mass (pennies) in the sample bucket
(canister with foam plug). Begin with
just the bucket. Push the end of the
meter stick to one side and release it.
Using a stopwatch or clock with a second hand, time how long it takes
the stick to complete 25 cycles.
5.
Make
a plot of the data. (See the sample
graph.)
6.
Place
a single penny in the bucket. Use the
foam to anchor the penny so that it does not move inside the bucket. Any movement will result in an error
(oscillations of the mass can cause a damping effect). Measure the time needed to complete 25
cycles. Plot this data.
7.
Repeat
this procedure for different number up to 10 pennies.
8.
Draw
a curve on the graph through the plotted points.
9.
Place
a nickel in the bucket and measure the time for 25 cycles. Use the pennies plot to determine the mass
of the nickel in "penny" units.
Conclusions:
25 cycles
(s) |
Number of
Pennies |
19.99 |
0 |
20.31 |
1 |
20.94 |
2 |
21.4 |
3 |
21.97 |
4 |
22.47 |
5 |
23.03 |
6 |
23.57 |
7 |
23.94 |
8 |
24.5 |
9 |
24.9 |
10 |
|
|
|
|
|
|
Quarters |
|
20.81 |
1 |
22.06 |
2 |
Questions
1.
Does
the length of the meter stick make a difference in the results?
2.
What
are some of the possible sources of error in measuring the cycles?
3.
Why
is it important to use foam to anchor the pennies in the bucket?
4.
Is
there a difference between the nickel's inertial mass and its gravitational
mass?
References:
Experiment
III-3 Inertial and Gravitational Mass
Physics: Laboratory Guide, Physical
Science Study Committee, D.C. Heath and Company, copyright 1965.
Activity 4 : Inertial Balance Part 1 Microgravity:
a Teacher’s Guide with Activities
(Secondary Level) National
Aeronautics and Space Administration, July, 1992