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Ph101: Fundamentals of Physics Laboratory
Instructor: Tony Zable
1
Laboratory: Conservation of Energy for a Simple Pendulum (Video)
Purpose: (1) To investigate the properties of energy conservation (i.e. the relationship
between potential and kinetic energy) associated with the motion of a simple pendulum. (2) To
calculate the potential and kinetic energy associated with a simple pendulum. (3) To use video
analysis to study the energy PE to KE transfer for a simple pendulum.
Part A: Calculation of Kinetic and Potential Energy
a)
An Olympic high diver (mass = 70 kg) stands on a platform 20 m above the surface of
the water, what is the diver’s potential energy?
b)
The athlete in (a) then dives off the platform. If it assumed that all of the diver’s
potential energy is conserved, what is the diver’s potential energy at the moment when
the diver is halfway to the water? What is the diver’s kinetic energy at this moment?
c)
The athlete then reaches the water. What is the diver’s kinetic energy at the moment
just before entering the water? What is the diver’s potential energy?
d)
What is the diver’s speed just before entering the water? Solve the problem based on
your answers above.
e)
Determine the average power expended by the gravitational force to pull the diver to
the earth.
File Name: \ph101\lab6_simp-pendulum-video.doc
Ph101: Fundamentals of Physics Laboratory
Instructor: Tony Zable
2
Part B: Investigating a Simple Pendulum
A pendulum consists of a mass attached to a string
that is fastened so that the assembly can swing in a
plane. For a simple or ideal pendulum, all of the mass
is considered to be concentrated at a point at the
center of the mass.
R
When the mass is pulled in one direction, the height of
the mass (H) is elevated relative to its height when the
mass is freely hanging. Since the mass has been
raised it has acquired potential energy relative to when
it is freely hanging (i.e. at its lowest point!). When the H
mass is released, it swings during which time it loses
potential energy but gains kinetic energy (since the
m
mass gains speed during the downward phase of the
swing). At its lowest point, the kinetic energy of the mass should be the same as potential
energy the mass had at its highest point. This is because the energy of the mass is conserved,
as long as there are negligible frictional forces, which might “suck” energy from the system.
Using a hanging mass or plumb bob, some string, and a ringstand we will construct a simple
pendulum and test this hypothesis.
1. Weigh the mass/plumb bob using a triple scale.
2. Construct a simple pendulum using the plumb bob according to the directions of the
instructor.
3. Using a digital camera, record the motion of several swings of the pendulum. Be sure to
include a “reference object” such as a meter stick in the field of view for scaling the movie.
4. Review the movie in the camera. If it is acceptable then upload the movie file to a computer,
place it on the “desktop” for easy access
5. Start the Graphical Analysis software and open the “PHY101-VideoEnergyAnalysis.xmbl”
experiment file.
Note: Two graphs should be displayed in the main window: KE & PE vs Time and Total E vs
Time
6. You will need to put movie into the the experiment by right clicking on the movie window and
selecting “Movie Options”. Browse to locate your movie file.
7. Resize and move the movie field (if necessary) for viewability and convenience
8. Use the QuickTime buttons to review the movie
9. Use the Data Browser feature to change the mass in the KE and PE columns to the measured
value for YOUR pendulum (in kg)
10. Select pendulum position in each frame (for 2 or more swings)
11. Scale movie (using “reference” object) & set origin to the bottom of the pendulum swing
File Name: \ph101\lab6_simp-pendulum-video.doc
Ph101: Fundamentals of Physics Laboratory
Instructor: Tony Zable
3
12. Use the “Examine” tool to determine the maximum KE & PE during 1st swing.
KEmax=
PEmax=
13. Calculate % error between these values (use the smallest value as the denominator). Do
they appear to obey Law of Conservation of Energy? What is the basis for your answer?
% Error 
KEmax  PEmax
100%
 smallest _ value 
14. Describe the transfer of energy between PE and KE during the pendulum swings. What is
the shape of the PE and KE graphs?
15. Describe the general “shape” of the Total Energy graph? As the swings progress, does the
Total Energy remain constant? Does it increase? Decrease? Why?
16. Using the Line tool, fit the Total Energy graph to a “line” and calculate the slope and yintercept.
Slope:
Y-Intercept:
Note: If the slope is zero then the graph (the total energy) is not changing. If the slope is
negative the total energy is decreasing with time, whereas a positive slope will indicate the total
energy is increasing with time.
17. What are the units of the slope of the line in 16? What are the significance of these units?
18. Can you relate your pendulum data to the Law of Conservation of Energy?
File Name: \ph101\lab6_simp-pendulum-video.doc