The Mass of the Earth
Overview
By using a small steel ball as a “test particle” in the Earth’s gravitational field, it is
possible to determine the mass of the Earth. The main objective is to make accurate time
and distance measurements of a free falling object, (the test particle), in the Earth’s
gravitational field and to use this information to calculate the local acceleration, (of the
test particle), near the Earth’s surface.
Concept
If we assume that Galileo was correct, that is, all objects will undergo the same
acceleration when allowed to free-fall along identical (or adjacent) paths, then by
dropping any small dense object over a moderate distance, we can calculate the
acceleration experienced by any object placed in the same gravitational field.
If we assume that the acceleration is constant over the distance that we allow our test
particle to fall, (within the limits of our measurements), then simple mechanical
arguments show that for a given acceleration g, the distance fallen s, during a time
interval t, is given by the equation
s=1/2at^2
Equipment
If your equipment is not already unpacked you will need to open three boxes containing
the PASCO equipment. Carefully open the packages and neatly save the packing material
so that the equipment can be repacked for storage after you have completed your
experiment.
The equipment needed is:




The ME-8930 Smart Timer
with instruction sheets.
The Free Fall Adapter with
instruction sheets.
The support stand.
A clamp to attach the ball
release mechanism to the
support stand.
-1-
Set-up
1. Open the large box containing
the support stand. Attach the
leveling screws into the base,
insert the aluminum pole, and
level the stand on a flat stable
surface.
2. Open the Smart Time box. Set
up the timer in a location close
to the support stand. Carefully
open the box containing the 9V
AC adapter and unwind the
power cord.
3. Do not plug in the AC adapter yet.
4. Open the last box which
contains the Free Fall Adapter.
Set the steel balls aside for the
moment.
Attach the Free Fall Adapter
near the top of the support stand
as shown (using the support
clamp).
5. Centre the receptor pad directly
below the ball release
mechanism.
6. Select one of the steel balls and
insert into the ball release
mechanism.
-2-
TIP: Place the ball between the spring, (with the drilled hole centred on the ball), and the
brass contact, then holding the release mechanism as shown in the photo, depress the
sliding rod until the ball is securely “trapped” in place. Using the small screw at the side,
lock the sliding rod.
Procedure
Step 1
Connect the Free Fall Adapter to the Smart
Timer.
Step 2
Plug the 9v AC adapter into a 115v outlet and
connect the 9v cord to the Smart Timer.
-3-
Step 3
Turn on the power switch. Note: The display
may be hard to see when viewed from directly
above the LCD window. It is best viewed at an
angle of about 45 degrees.
Step 4
If you have not already done so, install the steel ball securely in the Free Fall Adapter and
align it so that it will drop onto centre of the receptor pad.
Step 5
When you are ready to make your free fall
measurement you will need to “arm” the Smart
Timer. Press the RED (Select Measurement)
button and select TIME. The display “scrolls”,
so if you miss your configuration, just keep
pressing the selection button until the word
“Time” reappears in the display window.
Step 6
Next press the BLUE (Select Gate) button and
select STOPWATCH mode. The display
“scrolls” so if you miss your configuration, just
keep pressing the selection button the word
“Stopwatch” reappears in the display window.
-4-
Step 7
Finally, “arm the Smart Timer by pressing the
Start/Stop button once
Step 8
Release the ball by carefully unscrewing the spring lock.
Step 9
Step 10
Accurately measure the height that the ball has
fallen (in metres). Record the descent time and
the distance fallen (in seconds). (Use the chart
provided).
Step 11
Repeat the experiment. Set up the steel ball in the Free Fall Adapter. You may begin at
Step 7 to repeat the experiment. Try different decent paths (heights).
Try using balls of various sizes.
-5-
Analysis
Make several independent determinations of the free-fall time. Record the distance fallen
during each of the measured time intervals. (Use the accompanying chart in which to
record your data).
Trial
Number
Descent
time
(s)
Height
(m)
1
2
3
4
Mean
value
-6-
Acceleration
2/t^2
(m/s/s)
Mass of the
Earth
gr^2/G
(kg)
Curriculum Expectations





apply Newton’s laws of motion to explain inertia, the relationship between force,
mass, and acceleration, and the interaction of forces between two objects;
identify and explain sources of error and uncertainty in measurement and express
results in a form that acknowledges the degree of uncertainty;
carry out procedures controlling the major variables and adapting or extending
procedures where required;
select and use appropriate numeric, symbolic, graphical, and linguistic modes of
representation to communicate ideas, plans, and results;
work cooperatively with team members to develop and carry out a plan, and
troubleshoot problems as they arise.
Assessment Rubric
R
significantly below
the standard
(below 50%)
produces insufficient
evidence to
demonstrate learning
demonstrates
significant
misconceptions
requires additional
learning activities
and remediation
Level 1
Level 2
approaches the standard
Level 3
the standard
(50-59%)
(60-69%)
(70-79%)
Understanding of Basic Concepts
demonstrates limited demonstrates some
demonstrates general
understanding of
understanding of
understanding of
relationships
relationships
relationships
between force, mass, between force, mass, between force, mass,
and acceleration, and and acceleration, and and acceleration, and
the interaction of
the interaction of
the interaction of
forces between
forces between
forces between
objects
objects
objects
by providing partial
explanations of the
concepts involved in
the free-fall
experiment
by providing partial
explanations of the
concepts involved in
the free-fall
experiment
by providing
complete
explanations of the
concepts involved in
the free-fall
experiment
with significant
with minor
with no significant
misconceptions /
misconceptions /
misconceptions /
inaccuracies
inaccuracies
inaccuracies
Application of Critical and Creative Thinking Skills and/or Processes
produces insufficient applies appropriate
applies appropriate
applies appropriate
evidence to
skills/strategies of
skills/strategies of
skills/strategies of
demonstrate learning scientific inquiry
scientific inquiry
scientific inquiry
with limited
with some
with considerable
requires additional
effectiveness
effectiveness
effectiveness
learning activities
and remediation
Communication of Required Knowledge
produces insufficient communicates
communicates with
communicates with
evidence to
unclearly or
some clarity and
general clarity and
demonstrate learning imprecisely
precision
precision
rarely using
sometimes using
usually using
requires additional
appropriate scientific appropriate scientific appropriate scientific
learning activities
conventions
conventions
conventions
and remediation
-7-
Level 4
exceeds the standard
(80-100%)
demonstrates
thorough
understanding of
relationships
between force, mass,
and acceleration, and
the interaction of
forces between
objects
by providing
complete
explanations of the
concepts involved in
the free-fall
experiment
with no
misconceptions /
inaccuracies
applies appropriate
skills/strategies of
scientific inquiry
with a high degree of
effectiveness
communicates
clearly and precisely
always using
appropriate scientific
conventions