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
)
Simple Harmonic Motion
Introduction
When the net force acting on a mass is: (1) proportional to the magnitude of the displacement of the mass from its equili
ium position, and (2) in a direction opposite the direction of the displacement, then the resulting motion of the mass is simple harmonic motion. The force is a Hooke's law type force, which is given by:
F = - k x (1)
The negative sign indicates that the force, F, and the displacement, x, are in opposite directions. k is the spring constant.
The forces acting on a mass vi
ating on the end of a vertical spring are the upward force that the spring exerts on the mass and the downward force that gravity exerts on the mass. The net force is given by Equation (1).
If the spring and hanging mass are set to oscillating, the time for one complete vi
ation of the mass is called the period of the motion. The period, T, of the motion of a mass, m, suspended from the end of a vertical spring and vi
ating with simple harmonic motion is given by:
XXXXXXXXXX2)
The purpose of this exercise is to determine the spring constant and to use it to verify equation (2) for the period of the motion.
In the first part of the exercise, you will experimentally determine the spring constant, k, of the spring. Using this value of k, you will calculate values of T for several different values of m. These values of T are your theoretical predictions. Then, in the second part of the lab, you will experimentally measure the values of T for various values of m. The two sets of numbers for T can then be compared.
The magnitude of the upward force acting on the mass is kx; the magnitude of the downward force is mg. Since the mass is at rest, these forces are in balance:
The magnitude of the upward force acting on the mass is kx; the magnitude of the downward force is mg. Since the mass is at rest, these forces are in balance:
kx = mg (3)
Virtual Lab Site
Simple harmonic lab Phet link
Part I. Spring Static Extension Measurement
Procedure
1) Click the above link, you should see the site open as the figure shows
2) Select “Displacement/Natural Length”, “Mass Equili
ium”, move the meterstick and line up with the spring natural length (ready to measure to spring net extension x in meters).
3) Place the 50-gram XXXXXXXXXXkg) mass under that spring. Stop the oscillation by clicking the red stop sign in the middle of the top area.
4) Move the mass bar to have 50 g, 100 g, 150 g, 200 g, 250 g and 300 g mass on the spring, read your meterstick to have the co
esponding extension x recorded in the table1.
Data
Table1 mass and extension
Mass suspended (kilogram)
X (m)
0
0.050
0.100
0.150
0.200
0.250
0.300
Part II SHM Dynamic Time Measurement
To measure T as a function of m: suspend the 0.050 kg from the end of the spring. Measure with a stopwatch the total time for 20 complete vi
ations. Make this measurement 3 times. For each different counting, do change the oscillation range by pulling the mass down more. Compute the average of the 3 times. Compute the period of the motion T by dividing tavg by 20. Record your data in a table like that shown below. Repeat, as indicated in the table2.
(Hint: when measuring the time, use the lowest point as the reference to count turns since the natural equili
ium line would be passed two times in one turn.)
Table2 mass and time
m (kg)
(s)
(s)
(s)
tavg (s)
T (s)
0.050
0.100
0.150
0.200
0.250
0.300
Analysis
For Part I
Using table1 data, graph m (y-axis) as a function of x with Excel. According to Equation (3), the slope of the resulting straight line is equal to k/g. compute k= slope*g
For Part II
Since T versus m is not a linear function, we cannot directly use the linear graphic analysis to get k. Square both sides of Equation (2), we get
XXXXXXXXXX)
Now, versus m is linear. Based on table2, create a new table—table3
Table3 mass and time squared
m (kg)
T (s)
0.050
0.100
0.150
0.250
0.300
Now, based on table3, graph (y-axis) versus m with Excel. According to Equation (4), slope = . After getting the slope from your graph, then calculate k by using
Conclusion
Compare spring constant k from part I and part II and calculate the percent difference. % difference = |1st value- 2nd values | / average of both values * 100%