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Physics--Chapter 12: Vibrations and Waves Springs Lab Title: Springs, Spring Constants, and Changes in Potential Energy Date: Partner(s): Background Information: The law of conservation of energy states that the total energy in an isolated system remains constant at all times. If there is no friction, this energy will remain mechanical energy. That is it can be exchanged between one form of potential energy and another, or it can be exchanged between kinetic and potential energy. Suppose a spring is hung vertically with a mass attached to its lower end. The force exerted on the spring by the mass will cause the spring to stretch and the mass will come to rest at its equilibrium position. If the mass is lifted a few centimeters above its equilibrium position and dropped, it will oscillate with simple harmonic motion. At the top and bottom of its motion the mass will be momentarily at rest and thus have zero kinetic energy. Choosing the lowest point in the oscillation as the reference level for gravitational potential energy, the total mechanical energy at this point will all be in the form of elastic potential energy of the spring. Similarly, at the top of the oscillation, the total mechanical energy will again be all in the form of gravitational potential energy. Objectives: In this lab you will study the conservation of energy in a mass hanging from a spring. You will compare the change in gravitational potential energy of the system with the change in elastic potential energy as the mass oscillates between its two extreme positions. You will determine a spring constant for the spring, and verify this by timing oscillations of the spring-mass system. Procedure: Needed Materials: long spring hanging from ceiling, short spring supported by ring stand, clamp, and cross bar at the lab tables, meterstick, various masses, 50-g mass holder, stopwatch To Do for each spring: Spring Constant Determination Data: 1. Use a meter stick to measure the height of the bottom of the vertically hanging spring and record it in the data table. This is the zero displacement. Note that no masses or the holder are attached to the spring at this point. 2. Add the mass holder to the spring, measure the height and record it in the data table. Determine displacement and enter this in the data table. 3. Experiment with the amount of mass that can be added to achieve a noticeable stretch, result in good oscillation, not touch the table or floor, and not overstretch the spring. 4. Add even-increment masses (i.e. 100 g per trial) to the holder based on your experimenting in #3, measuring the height after each. Record total mass on the spring for each trial and the corresponding height. Note that the mass value is increasing and the height value is decreasing. 5. Continue to add masses, measure the heights and record until you have collected 10 data points. Fill in displacement data as well. Conservation of Energy and Period Data: 1. Leave the final mass from the previous section attached to the spring. 2. Lift the mass so that the spring is in its unextended position. This needs to be verified from your height data so that your oscillation time can be accurate. Physics--Chapter 12: Vibrations and Waves Springs Lab 3. Drop the mass, measure its lowest height with the meter stick and record the data in the table. Repeat three times to verify this measurement. 4. Time one period of oscillation and note in data summary. 5. Repeat this procedure three times. * If you started with the long spring, repeat both procedures with the short spring. If you started with the short spring, repeat with the long spring. Data Summary: Determination of Spring Constant Data height (m) displacement (m) long short long short mass (kg) long short Trial mass (kg) long short Conservation of Energy Data unextended height lowest height (m) (m) long short long short force (N) long short Δh (m) long short 1 2 3 Average Δh: Trial Oscillation Data time (s) long short 1 2 3 Average: Results: Spring Constant Determination: 1. Calculate the force on the spring for each mass and record in the data table. 2. Make a graph of force vs. displacement using your graphing calculator for each spring. Record the linear equation and the correlation values of your graphs in your notebook. Also, sketch each of these graphs in your notebook. Physics--Chapter 12: Vibrations and Waves Springs Lab 3. What is the experimentally determined spring constant for the long spring? For the short spring? Conservation of Energy and Period Determination: 1. Calculate the difference between the unextended height and the lowest height for each of the three trials and record the data. 2. Calculate the average difference between the unextended height and the lowest height and record on the value in the data table. 3. Calculate the gravitational potential energy of the spring when the mass is at the highest spring position for the long spring. Repeat for the short spring. 4. What would be the elastic potential energy of both springs in this position? 5. What would be the kinetic energy of both springs in this position? 6. What would be the total mechanical energy of both springs in this position? 7. Calculate the elastic potential energy of the spring when the mass is at the lowest spring position for the long spring. Repeat for the short spring. 8. What would be the gravitational potential energy of both springs at this position? 9. What would be the kinetic energy of both springs in this position? 10. What would be the total mechanical energy of both springs in this position? 11. Using the time for one period of oscillation, verify the spring constant value for each spring by calculation. Conclusion: (what did you learn? from what in the lab did you learn this? real world example?) Discussion of Error: 1. According to the law of conservation of energy, the total mechanical energy at the highest and lowest points should be the same. Determine the percent difference between your values for both the long and short spring. How can you account for any difference between the values? 2. Calculate a percent difference for the two values obtained for the spring constant for each spring. Which method do you think is more accurate? Why? Suggestions for Improvement: (always make reasonable suggestions!)