Gravitational Force
Purpose: To obtain the gravitational constant G through examining the force that two objects exert on each other at certain distance.
Theory:
The tendency of bodies to move toward one another is called gravitation. According to the Newton’s law of gravity, the magnitude of the gravitational force acting on each due to the presence of the other is given by
Where G is the gravitational constant:
Sketch:
Procedures
(1) Go to https:
phet.colorado.edu/en/simulation/gravity-force-la
(2) Click the a
ow on the Gravitational La
(3) Fix distance and change the values of the two masses according to data table 1 below.
(4) Plot as a function of , find the slope of the graph, and thus the gravitation constant .
(5) Fix change the value of according to data table 2 below.
(6) Plot as a function of , find the slope of the graph, and thus the gravitational constant
(7) Find the percent e
or for G in both cases.
Data Recording
Part I--- fix , change masses, and record F value.
No. of trial
1
100
200
5.34*10-8
2
200
200
3
200
300
4
200
400
5
200
500
Part II--- fix masses, change distance, and record F value
No. of trial
(
1
2.00
0.250
8.34*10-7
2
4.00
3
6.00
4
8.00
5
10.00
Data Analysis
(1) Part I, plot as a function of , find the slope. , compare with
G value given above and find percent e
or.
(2) Part II, plot as a function of, and find the slope. G, compare with G values given above and find percent e
or.
% e
or =
Conclusion
General Structure of the Lab Report
1. Title Page: A single page that includes the title of the experiment, the date the
experiment was performed, your name, and the names of any other lab partners.
2. Purpose: A
ief statement of the purpose of the experiment.
3. Theory: Relevant physics concepts and background knowledge should be stated;
equations used in calculations should be included here.
4. Sketch: A simple sketch of the experimental set-up. Note, this may be different
than the sketch given in the lab manual. Clearly label appropriate parts
5. Data: All raw data (and sometimes derived data) should be put in tables in a clear
and logical order. Physical quantities have units, which must always be included.
Table column-headings should label the type of data and the units.
6. Analysis: All calculations and graphs should be presented here in a logical order.
In the case of repetitive calculations – repeated use of the same equation – show
only one sample calculation, but be sure to put the results of your calculations in
a table. All e
or calculations go here as well.
7. Results: A statement of the result(s) of the experiment with reference to the
purpose of the experiment. Present all numerical results (and only the results)
with the co
ect number of significant figures and the proper units including a
percent difference or percent e
or, if any. Include a
ief discussion citing
possible sources of e
or in the experiment and any other relevant observations.
Percent E
or vs. Percent Difference
Percent e
or calculations are performed when you are comparing your experimental
esult with an accepted or “true” value for the quantity.
For example, if you experimentally measure the acceleration of gravity, you would
compare it to the known value, 9.8 m/s2, using a percent e
or calculation.
100% x
valuetrue
valueexp - valuetrue
E
or %
Percent difference calculations are performed when you are comparing your
experimental result with a second experimental determination of the same quantity.
In this case, neither value can be considered more official or more “true” than the
other. As such, the comparison is made with the average of the two values, as shown
in the following equation.
For example, in the Ballistic Pendulum experiment you will measure the speed at
which a projectile is fired by a spring-gun in two ways: using a projectile motion
analysis and a conservation of momentum analysis. In this case, you compare the
two values using a percent difference calculation.
100% x
two theof average
value2 - value1
Difference %
ndst
Graphing
Often, you will be asked to graph your data. There is a conventional order to this -
the first quantity is plotted on the y-axis and the second quantity on the x-axis. For
example, when asked to plot log (T) as a function of log(L), you plot log (T) on the
y, or vertical axis, and log (L) on the x, or horizontal, axis. An example graph is
shown on the following page as a guide.
1. Title your graph.
2. Make your graph big. Fill as much of the page as is convenient.
3. Label the axes, including units.
4. Carefully plot the points as large dots.
5. Draw a smooth curve, or the best-fit straight line, through the points.
6. If the graph is a straight line, calculation of its slope will generally be part of
your analysis. Choose two points that lie on the line, avoiding the plotted
points, and circle them to identify them. Calculate the slope in the analysis
section of your report.
Example 1
Graph for determining spring constant bkxy
Example 2
General Form that should be used in curve plotting
XXXXXXXXXX 100
Displacement of the spring (cm)
R
es
to
i
n
g
f
o
c
e
(N
)
150
125
100
75
50
25
K=1.88 N/cm
XXXXXXXXXX
Time (s)
250
200
150
100
50
0
D
is
ta
n
ce
(
cm
)