Lab: Conservation of Mechanical Energy
Purpose: To verify the law of conservation of mechanical energy by analyzing the potential
energy and the kinetic energy of a marble as it moves along a rollercoaster track.
Materials:
- 1 CPO Rollercoaster track
- 1 steel marble
- 1 CPO Photogate and Timer
- Meter stick
Procedure:
1. Set up the equipment as demonstrated in class
2. Set the mode of the timer to “interval” and connect one photogate to input A.
3. Attach the photogate to the track approximately 5 cm from the starting peg at the top of
the track.
4. Measure the height at this initial position of the photogate.
5. Set the marble on the track and hold it against the starting peg.
6. Release the marble and record the time it took for the marble to travel through the
photogate.
7. Repeat steps 4-6 until you have done a sufficient number of trials for that position.
8. Move the photogate approximately 8 cm down the track.
9. Repeat steps 4-8 for positions along the entire length of the rollercoaster track. You
should have room for at least 12 positions.
10. Measure the mass and the diameter of the marble you use for this exercise.
Data Collection and analysis:
1. List the values, including uncertainty, for your marble’s diameter and the marble’s mass
in kg.
2. Create a data table to display your raw data: Gate times and heights at each position
along the track.
3. Create a second data table to display your average gate times and your marble’s
velocity at each position along the track (with uncertainties). Show a sample calculation
of the velocity and its uncertainty.
4. Create a third data table to display your calculated kinetic energy, potential energy, and
total energy at each position. Show a sample calculation for one of each of these
values.
5. Create a graph that has 3 separate lines:
a. Kinetic Energy—find the best curve fit (probably something like quintic or
something similarly odd). We don’t care about the equation…just want the curve
to look nice.
b. Potential Energy—find the best curve fit, just like for kinetic energy.
c. Total Mechanical Energy—Use a linear fit for this data set.
Note: make sure you’ve included appropriate error bars, axis labels, a legend, title, etc.
All 3 lines must go on a single graph. Add manual columns to your data set in
LoggerPro, and format the y-axis so that all three energy sets are plotted on the graph.
Analysis Questions to Answer:
6. Describe the relationship between kinetic and potential energy of your marble as it
traveled down the track. Use quantitative evidence to support your answer.
7. Did your total energy remain constant? Support your answer using quantitative
evidence. Determine the percentage energy difference between the beginning (yintercept) and the ending energy according to your best-fit line.
8. Assuming the total mechanical energy decreased as the marble traveled along the track,
what happened to it? How can we account for the difference in energy? If, instead, your
mechanical energy INCREASED as the marble traveled along the track, how could this
have happened? How can you account for the additional energy?