Download 1. Understand and use the Conservation of Mechanical Energy

SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
Physics
Lab 5
SP211
Conservation of Mechanical Energy
I. Introduction
A. In the absence of dissipative forces (i.e. non-conservative forces that do work,
such as kinetic friction), the mechanical energy of an isolated system is
conserved. This can be written in the form: Kf + Uf = Ki + Ui. Thus the sum of the
kinetic energy and potential energy is constant and K + U = 0.
B. Consequently any change in kinetic energy is compensated for by an equal and
opposite change in potential energy. For example, if the potential energy
decreases, the kinetic energy increases by the same amount.
C. An easy experiment to test this theory is to let the cart run freely down the
inclined plane and measure the change in height and change in speed of the cart.
It would then be straightforward to calculate the decrease in potential energy
and increase in kinetic energy and show that their sum is zero.
Let us carry out that experiment.
II. Objectives
At the end of this activity, you should:
1. Understand and use the Conservation of Mechanical Energy equation
(Kf + Uf = Ki + Ui) while seeing its limitations.
2. Understand that the Work-Energy Principle (WEP) always applies:
Wnet, external + Wnonconservastive, internal = K + U = Emech
3. Understand that a plot Emech vs x will find the effective frictional force.
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SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
III.Needed Equipment
Your instructor will show you the experimental setups, which consists of a motion
sensor (MS), an inclined plane, and a dynamics cart. Use of an Excel Spreadsheet to
graph the energies is helpful.
Our experimental setup is shown in the diagram below. The angle is shown as 6o
because it gave good results in a trial run. However any angle between 5o and 10o
should also yield good results.
IV. Procedure
A.
Discussion:
In the Homework Problem, we found that if the ramp-cart system is
conservative, then the total mechanical energy should be constant. How can
we take data to test whether the system is conservative? How shall we
analyze this data?
If you plot KE, PE and E, all vs t, what should the graph look like? Let’s sketch
it on the blackboard.
Which of the constants xi, vi, and a = g sin can we determine a priori? Which
can be determined only after we do the experiment?
B.
Preliminary Data:
B.1. Set your track at a ramp angle of about 6˚ (5˚ <  < 10˚ works well.), and then
measure the angle carefully by making a graph of the ramp’s height as a
function of distance along its edge. Use the function in Excel called “Linest” to
find sin and its uncertainty.
B.2. Measure and record the mass of the cart along with its uncertainty.
B.3. Remember that g = +9.810 +/- 0.005 m/s2
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SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
C.
Connect the MS to the Lab-Pro and set up Logger-Pro
Check that everything is plugged in correctly: the MS into DIG/SONIC2
Recurring steps:
Using Logger Pro to program the LabPro: Known as the “Three Steps”
D.

Experiment -> Set Up Sensors -> Show all Interfaces: Make sure all the right
sensors show up in all the right holes.

Experiment -> Data Collection: Set the length of time data is to be taken and
the rate at which data is to be taken.

File -> Settings for...: Check the checkbox to Show Zero on Toolbar, and make
sure number of points for Derivative and Smoothing are both 7.
Experiment: Potential Energy transferring to Kinetic Energy
D.1. Follow the Three Steps in Logger Pro to program the LabPro to take data
for position (x) as a function of time (t ) appropriately for this experiment.
D.2. Collect data of the cart as you allow it to run down the ramp; use the data
to calculate v and h, and then K, U, and E. Use Excel or Logger Pro.
D.3. Note that since this is uniformly accelerated motion, the exact velocity at
the mid-point of any time interval is equal to the average velocity over the
entire interval.
D.4. Once you know v, calculating K is easy.
D.5. If you take h to be zero where x is zero, then you can calculate U = mgh,
where h = -x sin. Note the minus sign! As always, g = +9.810 +/- 0.005 m/s2.
E.
Use Excel or Logger Pro to plot K, U, and E on a single graph as
functions of t.
F.
Discussion Questions:
F1. Does the system pass the test for a conservative system? Explain.
F2. How much energy was lost to friction during your experiment?
How does that compare (what %) with the kinetic energy at the end of your
experiment?
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SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
G.
Since our ramp-cart system did not pass the test for a conservative
system, Conservation of Mechanical Energy does not apply, but the
Work-Energy Principle (WEP) always applies:
Wnet, external + Wnonconservastive, internal = K + U = Emech,
so that the slope of a graph of Emech vs x will be the effective frictional
force.
G.1. Plot Emech vs x and find the effective frictional force.
G.2. In a few sentences, explain whether today’s exercise supports, or fails to
support, conservation of mechanical energy and the Work-Energy Principle.
H.
Lab Report

Measurement of mass of cart and sine of ramp angle.

Spreadsheet from part D in support of the graph from part E.

Graph from part E, properly annotated and labeled.

Answers to discussion questions from part F on back of graph H.3.

Graph from part G1 with conclusion G2.
V. Clean-Up
A. End of Lab Checkout: Before leaving the laboratory, please tidy up the equipment at
the workstation and quit all running software.
B. The lab station should be in better condition than when you arrived and more
importantly, should be of an appearance that you would be PROUD to show to your
legal guardians during a “Parents Weekend.”
C. Have your instructor inspect your lab station and receive their permission to leave
the Lab Room.
D. You SHALL follow this procedure doing every lab for BOTH SP211 and SP212!
Many thanks to Dr. Huddle for his assistance in producing this Laboratory procedure; specific references
can be supplied on request. LCDR Timothy Shivok
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