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ENERGY II
DAMPED HARMONIC MOTION
Today you will use the sonic ranger and a force probe to study the
energy transformations in an oscillating mass-spring system quantitatively. A force probe
will be used to support the spring and mass, thereby, we can find the force acting on the
mass at any time. We know that the mechanical energy (ME) is defined as the sum of the
kinetic (KE), the gravitational potential energy (GPE) and the spring potential energy (PEsp).
The position (necessary to find GPE and PE, respectively) will be monitored by a
sonic ranger. The data will be analyzed using Logger Pro. Logger
Pro will provide you with position and velocity data as usual. You will then
create new columns to calculate the various energies from the position and velocity
data. Finally, an experimental check will be made of the Work-Energy theorem.
Part I: Collecting data
- Carefully measure and record the mass of the pan and the mass of the
spring.
- Start Logger Pro by double clicking on "ENERGY2.xmbl"
in the PHY 183 folder on the desktop. The needed experimental data collection rates have
been preset at 20 readings per second and no averaging of the data.
- Next you will need to calibrate your force probe. The entire
experiment depends on an accurate calibration!
- Under the Experiment menu choose Calibrate,
then Ch 1, then Perform now.
- Make sure that no force is applied to the force probe and then click Keep.
- Add the 200g mass to the hook and allow it to stop swinging. Enter
the weight of the 200g mass in the box for the known calibration force. Watch
the lower window. When its value is stable, click Keep.
- Next, take a set of data and verify that the average force is indeed the
weight of your calibration mass. Remove the calibration mass.
- Add the spring and pan to the force probe hook and adjust the location of
the sonic ranger. Take a set of data and check that the average force is consistent
with the weight of the pan and spring. Use the "statistics" function
(under "ANALYZE" or a button on the toolbar) to find the average value of
the position of the pan and the average force measured by the force probe. Record both
values.
- Now add 100 grams of mass to the center of the pan, which will stretch
the spring more. Take another set of data (once the motion has ceased) and again find the
average force and position.
- Use the force and position measurements to find the spring constant of
the spring. (If you don't remember how, look back to the Hooke's law experiment in
your lab notebook.)
- Gently pull straight down on the pan (with both hands) and then try to
release it without any sideways motion. The pan should oscillate smoothly, without
jerkiness. If this is the case, acquire a set of data. Look at the force and position
graphs. If they are relatively smooth and mostly free from ‘glitches’ you can
save your data under a new filename. (This just makes sure you don't accidentally lose
your data during the analysis process.)
- Remove the spring and pan from the force probe. The springs are
fragile and will fatigue if left supporting the pan and mass for a length period.
- Print a graph of your data and include it in your report.
Part II: Analysis of Data
- Create a new column that uses your velocity data to calculate kinetic
energy. The mass you should use is the pan plus the 100g plus half the mass of the
spring. This is because effectively only half of the mass of the spring is moving.
- Next we need to calculate a column for spring potential energy.
Since this involves the amount the spring is stretched, we need to know the
position of the spring when it is unstretched. You can find this using your spring
constant and force and position measurements when their was no extra weight in the
pan. First, find how much the weight of the pan stretched the spring. Then use the
final position of the pan to determine where the pan would be if the spring wasn't
stretched. Now you can set up a column to calculate the spring potential energy at
each point.
- In order to calculate the gravitational potential energy, we need to
decide where we want the zero of GPE to be. We could just use the x=0 of the
position data, but it is more convenient to have it be at the same place that the spring
potential energy is zero. Thus the h in mgh will be position - unstretched position.
Put in a new column to calculate gravitational potential energy for each point.
- Lastly, you need a column for mechanical energy, which is just the sum of
the other three energies.
- Set up graphs for each of the four energies. Compare the two
potential energy graphs. Why does KE have a different period than the potential
energy graphs. Would you conclude that mechanical energy is constant for this
system? If not, where does the lost energy go? Either print all four graphs or
set up a single graph with all four functions plotted on it and print that composite
graph.
- Now we want to verify the work-energy theorem by calculating the change
in KE and the work done for each time interval. Logger Pro makes the easy for us by
providing a built-in function called delta that subtracts to adjacent data points.
So, for instance, if you wanted to calculate the change in velocity you would put
in delta("velocity") for the equation that defines that column. Create new
columns for change in kinetic energy and work done. Remember work is force * change
in position.
- Create a graph that has work and change in kinetic energy on the same
graph. Are they equal? In what way are they different? Add KE to your
graph. Are the differences between work and change in kinetic energy small compared
to the size of the KE?
last modified on Tuesday, October 21, 2003
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