ENERGY II

DAMPED HARMONIC MOTION

Today you will use the sonic ranger and a force probe to study the energy transformations in an oscillating spring-mass 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. The position  (necessary to find GPE and PE, respectively) will be monitored by a sonic ranger. We know that the mechanical energy (ME) is defined as the sum of the kinetic (KE), the gravitational potential energy (PEg) and the spring potential energy (PEsp).   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. If you don't remember the Work-Energy theorem, you should review before coming to lab.

Part I:  Collecting data

• Carefully measure and record the mass of the pan and the mass of the spring.
• Start Logger Pro.  Open  "ENERGY2.xmbl"  in the PHY 173  or PHY 183 folder as appropriate for your class.
• Next you will need to calibrate your force probe by hanging a known weight on it and give the program that value.  Accurate calibration is very important!
• 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 wait until it is motionless.  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.  Your force probe is now calibrated.
• Next, take a set of data and verify that the average force is indeed the weight of your calibration mass. Remove the calibration mass.
• Hang the spring and pan from the force probe. Collect some data as you move the pan up and down by hand.
• Make sure that the sonic ranger is "seeing" the pan.  If not, change the position of the sonic ranger until it does.
• Normally the sonic ranger has x=0 set at the sonic ranger.  In this experiment it is more convenient if x=0 is at the position of the pan.  To do that we will use the "Zero" function in Logger.
• Hold the pan with your hands so that it is the position where the spring is unstretched but just ready to start stretching.
• Make sure your hands are above the bottom of the pan so that they don't interfere with the sonic ranger reading.
• While holding the pan in position, select "Zero" on the Experiment menu.  The sonic ranger should click just briefly.
• Let the pan hang from the spring normally and take a set of data.    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. Check that the average force is consistent with the weight of the pan and spring.
• Now add 100 grams of mass to the center of the pan, which will stretch the spring more. Wait for the pan to stop moving.  Take another set of data  and again find the average force and position.
• Use the force and position values you recorded 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 lengthy 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.
• Create a column to calculate the spring potential energy at each point.
• Create a 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 this easy for us by providing a built-in function called delta that subtracts two 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  net 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?