Conservation of Energy on a Roller Coaster
Introduction
Topics in lab report should include but are not limited to – work-energy theorem, energy
in general, potential energy, kinetic energy, gravitational potential energy vs. other types
of potential energy, kinetic mechanical energy vs. other forms of kinetic energy,
discussion of the different formulas for gravitational potential energy and mechanical
kinetic energy, the impact of variables like mass, height, velocity, etc., law of
conservation of energy – with regards to gravitational potential and kinetic energy and
free fall, transfer of energy from one form to another, role of friction/heat with respect to
mechanical energy transformation. Don’t forget to organize into MANY different
logical paragraphs and to cite and least once if not more per paragraph in proper APA intext parenthetical format.
Objectives and Hypothesis (Last paragraph of introduction – properly formatted in past
tense, passive voice)
 To determine if mechanical energy will be conserved on a toy roller coaster.
 To determine the relationship between velocity and height on a roller coaster.
At which position(s) will the marble have its greatest velocity given the experimental
positions for today’s roller coaster lab? Why?
**Introduction should probably be a MINIMUM of 2 pages.
Methods and Materials
1 – Set up the roller coaster ramp by attaching it to the 5th hole of the CPO stand.
Practice rolling the marble down the ramp so that it doesn’t fall off the track.
1B – Measure the mass of the marble and convert to kilograms. Record this mass right
here:
g
kg
2 – Position 1 is at the very beginning/top of the roller coaster track. Measure the height
of the bottom of the marble at position 1. This is from the lab table up to the bottom of
the marble. Be sure to measure to nearest mm (.1 cm) and it must be converted to m.
3 - Set up a photogate and timer at position 2 as shown in Figure 1 below. Be sure that
the timer is set to A and that it is in interval mode.
Figure 1 – Labeled Marble Positions
4 - Measure the height of the marble at position 2.
5 –Release the marble from position 1 each time. Assume that the marble has 0.0 m/s
velocity at this starting position.
6 – Record the time for the marble to cross position 2 as measured by the photogate. The
velocity of the marble is its diameter (0.019 m) / time (s). These calculations DO NOT
need to be explicitly shown in the calcs section.
7 – Repeat steps 3 – 6 for positions 3 through 7.
(8 – When done, carefully put back all materials as they were found. Keep your marble.
Someone will come and collect it from you. )
(9 – Work on calculations!)
** Don’t include methods noted in parentheses. DO include additional methods
paragraph(s) where you explain how you did all the calculations, where the variables all
came from, and then what variables were graphed and what kind of graph was made.
Results
Table #1 – Marble Data
Position #
1
2
3
4
5
6
7
d
0.019 m
0.019 m
0.019 m
0.019 m
0.019 m
0.019 m
0.019 m
t
N/A
exp. vf
0.0 m/s
height
theo. vf
0.0 m/s
% error
N/A
Include the above table – Position # 1 – 7, distance traveled (which is actually
consistently just the marble diameter), time for travel from photogate A timer,
experimental velocityf of the marble (calculated from photogate data of marble diameter
distance / photogate time – DO NOT SHOW THESE CALCS SINCE THEY ARE JUST
SIMPLE d/t calcs but do round to sig figs), height of the marble in m, theoretical vf
calculated as noted below in calcs section, and calculated % error.
Include also 1 Double Line Graph (HAND DRAWN) with 2 y axes
You should graph Position # (0 through 7) on the x axis and then make a scale on the left
y axis for experimental velocity and a different scale on the right y axis for height. They
should both have a 0 origin. Plot one line for changing experimental v and one line for
changing height, making sure to use the appropriate y scale. (Position # really doesn’t
have a unit – no need to get actual measurements for our purposes but they should be
evenly space apart from each other).
Take a photo of this graph, make sure it is clear and that NOTHING has been cut off and
include it as a photo in your digital lab. There should be no appendix this lab.
Calculations
Epi + Eki = Epf + Ekf
(mghi) + (½ mvi2) = (mghf) + (½ mvf2)
Substitute in for all of the above values, leaving vf as your unknown. After that
substitution, you can do all of the other math in your calculators and just give the final
answer for vf (calculator and sig fig rounded). As mentioned in class, you should
probably do these on BLANK white paper and hold the paper landscape so that
everything can fit on one line across.
For lab reports, you should write the above equations out only once to show where the
rest of the work is coming from.
You are keeping the left side of the equation a constant based on Eki assumed to be 0 J at
the beginning and Epi measured/calculated for Position 1. The right side of the equation
is what changes for each of the positions 2-7.
You are solving for the theoretical vf on the right side of the equation for each of the 6
other positions. You may sub-in the measured heights for the h in each Epf. There should
be 6 of these for positions 2-7. Position 1 = the left side of the equations always. You
must show the entire giant equation each of the 6 times. These calculated vf’s are your
theoretical vf’s and you will compare them to the experimental vf’s gotten from the
photogate data. Once calculated, fill in these theoretical vf’s in your Table 1.
We’ll be doing work on these calculations during class time also.
Perform 6 % error calculations for the vf theoretical vs. the vf experimental. You should
write the equation every time and do the entire 3 step method for calcs complete with sig
figs.
Percent error = theoretical – experimental x 100
theoretical
Calculations can still be done by hand, but they MUST then be included in their entirety
as photographs inserted into the report into a properly labeled Calculations subsection.
They must appear in the digital file on turnitin and they should NOT be at the end in an
appendix.
Discussion – should be a big one!! There are lots of inferences to make.
Here are some questions to help guide you but your discussion SHOULD NOT read like
a list of answer to these questions. They must be organized and developed into
discussion paragraph format.
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What kind of energy was present at the beginning of the lab before the marble
was released? Discuss in terms of mechanical and also potential vs. kinetic.
What happened to the energy as the marble traveled? Use graph/figure 1 to
explain. Talk about each position specifically and also group similar positions to
make inferences about different parts of the roller coaster.
Discuss how the variables of height and velocity were related to the marble’s
travel? Again, use the graph/fig 1 as evidence to explain and note specific
positions.
Was mechanical energy conserved? Use your calculations and percent errors to
discuss and explain. A 0 % error would mean mechanical energy was conserved.
If energy is supposed to be conserved, why does the energy total actually decrease
a bit experimentally? – What other form of energy might the mechanical energy
have been converted into? (This is related to an error source).
Discuss other error sources.
Make sure that at some point in your above discussion, you noted if and how the
objectives were met. Don’t wait until the end to do this or it gets repetitive.
Be sure that you have several different well organized paragraphs and that the
discussion is at least 1 full page long or more depending on how concisely you
write.
References APA format as usual – as usual at least 2 reputable sources required.
****** ALSO – you MUST attach a digital image of the first page of your last graded
full lab report – the one on velocity of cars. It must have the grade and any comments
that I left on that first page. Failure to include this will result in an automatic -5.