PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion

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1 PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion NAME: DATE: SECTION: PARTNERS: OBJECTIVES 1. Verify Hooke s Law and use it to measure the force constant of a spring. 2. Investigate the relationship between mass and period for a mass oscillating on a spring and use it to measure the force constant of the spring. EQUIPMENT Spring support on vertical rod Spring Mass hanger Set of masses Timer Meter sick and meter stick clamp on stand Mass balance PRE-LAB EXERCISE (Complete 1-10 BEFORE Lab) HOOKE S LAW 1. Write the equation for Hooke s Law. Eqn In this experiment the applied force is produced by the weight, mg, of the mass, m, hung on the spring. If you plot a graph of the amount of stretch versus the weight, how is the slope of the resulting straight line related to the spring constant? Write an equation using the word slope to represent the slope in the equation. Eqn If the amount of stretch is measured in meters and the weight is measured in Newtons, what are the units for the slope in step 2? 4. Solve the equation in step 2 for the spring constant, k (i.e. write k in terms of the slope). Eqn What do you expect the units of k to be based on the equation in step 4 and the units for the slope in step 3?

2 SIMPLE HARMONIC MOTION 6. Write the equation that relates the period, mass, and spring constant for simple harmonic motion. Eqn In this experiment you will measure the period of oscillation for different masses suspended from a spring. If you plot a graph of the period versus the square root of the mass, how is the slope of the resulting straight line related to the spring constant? Write an equation; you may use the word slope to represent the slope in the equation. Eqn If the period is measured in seconds and the mass is measured in kilograms, what are the units for the slope found in step 7? 9. Solve the equation in step 7 for the spring constant, k. Eqn What do you expect the units of k to be based on the equation in step 9 and the units for the slope in step 8? Notice that these units may not be the same as in your answer to step 5, but they should be equivalent. Show that they are equivalent. PROCEDURE HOOKE S LAW 1. Measure the position (in meters) of the bottom of the spring with no weight attached. Position of bottom of spring with no weight: = 2. Add mass to the spring in increments of 100 grams from 150 to 550 grams of mass (including the mass hanger). Record, in Table 1, the position (in meters) of the bottom of the spring for each mass. Table 1 Mass (kg) Weight (in N) Position (m) Stretch (m) SIMPLE HARMONIC MOTION

3 3. For each of the masses used in step 2, gently set the spring into vertical oscillation with a small amplitude of oscillation. Measure and record the time (in seconds) required for 10 complete oscillations ( round trip ) in Table 2 Mass (kg) Square Root of Corrected Mass (kg 1/2 ) Table 2 Time of 10 Oscillations (s) Average Period (s) 4. Measure and record the mass of your spring. Mass of spring ANALYSIS OF DATA HOOKE S LAW 1. Calculate the weight in Newtons for each mass in Table 1. Record the results in the second column of Table Subtract the zero reading from Step 1 of the Procedure form each of the positions in Table 1 to obtain the amount of stretch. Record the results in Table Plot a graph of the amount of stretch versus the weight (applied force) from the data in Table 1. The origin (0, 0) may not be a good data point. Draw the best straight line that comes closest the five data points. 4. Determine the slope of the line of the graph in step 3. Include the correct units. Slope of straight line: 5. Calculate the spring constant with the help of Eqn from the Pre-Lab section. Spring constant, k = SIMPLE HARMONIC MOTION 6. The equation that you were expected to write for Eqn.11.4 of the Pre-Lab was for an ideal spring with zero mass. For real spring with a finite mass, a portion of the spring mass (one-third) must be included along with the mass hanging from the spring. To find the corrected mass add one-third of the spring mass to each of the hanging masses. Record the square root of this corrected mass in the second column of Table 2. (NOTE: You must convert to kg before taking the square root). 7. Using the data in Table 2, calculate the average period of oscillation for each mass and record the values in the last column of Table 2.

4 8. Plot a graph of the average period versus the square root of the corrected mass from the data in Table 2. Draw the best straight line that comes closest to the five data points. 9. Determine the slope of the line from the graph in step 8. Include the proper units. Slope of straight line 10. Calculate the spring constant with the help of Eqn from the Pre-Lab section. COMPARISON OF TWO VALUES OF THE SPRING CONSTATN 11. Compare the two values of the spring constant obtained above by calculating the percent difference between them. Use the smaller value in the denominator. Value from Step 5 Value from Step 10 Percent Difference 12. When you read the slopes of the lines on your graphs, how many significant digits were in the rise and the run? Slope of graph of stretch versus applied force: No. of significant digits in rise No. of significant digits in run Slope of graph of average period versus square root of the corrected mass: No. of significant digits in rise No. of significant digits in run 13. The precision of the slopes of the graphs will determine the precision of your values for the spring constant. If you have not done so already, round off your values for k to the number of significant indicated in Step 12. If the number of digits in the rise and the number of digits in the run are not the same, use the smaller number. Value from Step 5 Value from Step 10 We will say that these two values agree if they differ by no more than two in the last significant digit. Do your two values for k agree? Way No way 14. If No way is checked above, attempt to give some possible explanations for this. BE SPECIFICexperimental error is not an acceptable answer.

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