Lab13_-_Hooke's Law

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PHY 202/PHY 241 Hooke’s Law and Oscillations Name: ______Gabrielle Thompson__________________________ Purpose: Investigate the Hooke’s law and simple harmonic motion. Procedure Go to PHET Masses & Springs (https://phet.colorado.edu/en/simulation/mass-spring-lab) simulation. You should be able to click on the arrow in the middle of the display to run it, or, if you want, you can download it onto your computer. This simulation requires Flash to be installed on your computer. Part I: Hooke’s Law NOTE: It may be necessary to move the ruler used for measuring different lengths in this lab either left or right of a spring for best measurement. 1. You will see two springs, some labeled masses and some unknown masses. 2. Make sure that “Earth” is set. 3. Slide the ruler so that its zero point is at the base of Spring 1. 4. Check the two check boxes, one marked “Natural Length” and one marked “Movable length. Two dashed lines will appear. Use the Natural length to check the placement of your ruler at the base of Spring 1. 5. Place the 50-gram mass on Spring 1. Allow it to stretch the spring. If the spring oscillates, there is a red button near the top of the spring that should stop it. 6. Drag the movable dashed line so that it lines up with the point on the spring that the 50- g mass is attached. Record the mass and the stretch of the spring in the table. 7. Remove the 50-g mass and replace it with one of the 100-g masses. Repeat step 6. It may be necessary to use the orange reset button in the right corner to remove masses for the inclusion of a different mass. 8. Remove the 100-g mass and replace it with the 250-g mass. Repeat step 6. 9. Remove the 250-g mass and replace it with the one of the three unknown masses. Record the stretch of the spring in the table. 10. Change the Softness Spring 2 indicator to a point to the right of the middle. 11. Repeat steps 3 through 9 for Spring 2. Part II: Effects of gravity 1. Reset the simulation. 2. Set object indicator to “Moon”. 3. Repeat steps 3 through 9 above for Spring 1.

Part III: Simple Harmonic Motion 1. Reset the simulation. 2. Set object indicator to “Earth”. 3. Click on “Stopwatch”. You can try this first in real time by clicking on “Normal”, but if you need to slow things down, you can click on “Slow”. You will still get the same time on the stopwatch, much like watching the whole thing in slow motion. 4. Check the Natural Length and Movable Line check boxes. 5. Place the 100-g mass on Spring 1 and stop the oscillation as before. 6. Line the ruler up as before and check the Equilibrium Position check box. 7. Now move the Movable Line down to the 30 cm mark. Record the difference between the position of the Equilibrium Position line and the Movable Line as the amplitude. 8. Pull the mass down so that the bottom of the spring is now on the Movable Line, and then let go – the spring will begin to oscillate. 9. When you are comfortable with the rhythm of the spring, start the timer when the bottom of the spring reaches the dashed line and count ten (10) oscillations. Stop the timer, record the time, and reset the timer, without stopping the spring. 10. Repeat step 8 three more times.

Part I Mass (g) Position (cm) Spring 1 Position (cm) Spring 2 50 8.00 5.00 100 16.00 11.00 250 40.00 27.00 Unknown 12.00 8.00 Part II Mass (g) Position (cm) Spring 1 50 1.00 100 2.50 250 7.00 Unknown 1.75 Part III Amplitude: _______6.00 cm_____________ Mass: ______100 g______________ Trial 1 Trial 2 Trial 3 Trial 4 Total time (s) 8.10 8.11 8.12 8.09

Analysis 1. For the tables from parts I and II, construct separate graphs. Plot the displacements on the horizontal axis (make sure to extend your graph to include the displacement of the unknown object) and the weight on the vertical axis. Find the line of best fit, and from that, determine the slope. Compare the line of best fit to Hooke’s law and determine the spring constant. 2. Use each graph to determine the mass of the unknown object you chose, based on its displacement. 3. From the average of the four trials in Part III, determine the period of oscillation. Use this and the given mass to determine the spring constant of Spring 1. 4. Calculate the percent differences (not the percent errors) between the spring constant gotten by the method in part III and each of those for Spring 1 gotten from the graphs of the data for Parts I and II. 5. From the information gathered in part 3, write expressions for the displacement of the mass attached to Spring 1, its velocity and its acceleration versus time (the textbook could be useful here). On the same piece of graph paper, one under the other, plot the displacement versus time, velocity versus time, and acceleration versus time (our text shows examples of this) for at least two periods. Include relevant data in the expressions. Questions 1. Based on your two separate graphs from part I, what values for the unknown object did you get? If different what is the percent difference between them (calculations would be shown on calculation page with results here as appropriate)? Based on the two separate graphs from part I, the values for the unknown object that I got was 77g and 73g. 77g is what I received for Spring 1 and 73g is what I received for Spring 2. The percent difference between the two values is 5.33%. However, when the average of the two values is taken, the amount is 75g.

2. Based on your graph in part II, how did the mass of the red object compare to your values from Part I? What does this say about the effects of moving an object from one location to another in terms of changes (if any) of its mass value? Based on my graph from part II, the mass of the unknown value (pink) compared directly to my values from part I. This is because mass is a scientific measurement, so no matter where the mass is, it will always stay the same. However, the weight of the object does change. This is because based on the location, the acceleration due to gravity chances. Therefore, the weight is different in the moon than on earth, but the mass does not change. 3. Based on your percent difference calculations from step 4 of the analysis section, how well do these two different processes determine the spring constant? Based on my percent difference calculations from step 4 of the analysis section, the two different processes determine the spring constant well. This is because all of the percent values were under 10%, so they are all pretty close in relation. However, I do think that the process done in part III is slightly more accurate. This is because there are less variables, meaning that there are less opportunities for things to go wrong. 4. Based on your graphs of displacement, velocity, and acceleration versus time from Part III, at what location would the mass have had its greatest kinetic energy? At what position would it have experienced its greatest acceleration?

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