Goals: 1) To investigate the determination of the spring constant, and 2) to investigate how mass and the spring constant relate to the period of oscillation.
Equipment:
TI-82 calculator spring mass hanger meter stick
SPRING TI program CBL ac adapter masking tape C-clamp
TI link cable 50g and 100g masses index card flag short rod
TI-CBL stopwatch right angle clamp ring stand
sonic ranger with CBL adapter
Journal formatting: In addition to all previous journal formatting instructions, carefully incorporate the following into your report.
* Items in brackets in the instructions must be included in your lab form. Those that are also in italics must appear word-for-word. Leave plenty of space to show your work.
* Bold-face section titles and the goals of the experiment must appear word-for-word, and parts and steps of the experiment must be numbered as given.
* Except for percentage error, all calculations must be shown, beginning with formulas.
* Consistent symbols must be used, with subscripts as needed.
* All your work must proceed in a step-by-step form that is easy to read. If you make mistakes in a calculation or derivation, simply cross out and start again on the next line.
Part I. Determining the spring constant
prelab: a) Read sections 6-4 and 11-1 Giancoli 3rd edition. b) Read through numbers 1-4 below. Note that y0 would represent the position with no stretch in the spring. While you will need to refer to y0, you will not actually measure this position. Side-by-side on a clean journal page, sketch three figures depicting the placement of the ranger and hanging mass for each of the three situations m=0, m=m1, and m=m2 (m2>m1). Be sure to clearly and correctly label y0, y1, and y2. c) Just below each of the latter two figures, construct the force diagram for the hanging mass and write the corresponding Fnet equation. Invoke Hooke's Law where appropriate.
1) Write the identifying number of the spring you are using. Be sure to use the same spring throughout all parts of the experiment. If you change springs, you will have to redetermine the spring constant for the new spring and redo all calculations!
[Spring number = ]
2) The spring should be hung from the short rod clamped to the ring stand. The ring stand should be clamped securely to the tabletop. Position the apparatus so that the spring hangs at least 0.10 m beyond the edge of the table. Tape the index card to the bottom of the mass hanger. Suspend the mass hanger (0.050 kg) from the spring and put the sonic ranger on the floor directly below the mass hanger. Position the rod that supports the spring so that the bottom of the weight hanger is 0.65 to 0.70 m above the ranger. Attach the sonic ranger to the CBL sonic port using the provided adapter. Plug the CBL into a wall outlet using the ac adapter.
3) Turn on the CBL. Hit the [MODE] button until the screen displays the word MULTIMETER in the lower left corner. Now press the [CH VIEW] button several times until the display says it is reading SONIC in M. This means the CBL will take a reading from the sonic ranger once per second and will display the results in meters. At this point you should hear one click per second coming from the ranger. Make sure the ranger is "locked on" to the 0.050 kg mass hanger and not the table edge or some other object. When the mass hanger is motionless and you are satisfied that the displayed reading is correct, record the position reading.
[Equilibrium position for m1 = 0.050 kg is y1 = ]
4) Now load the 0.050 kg mass hanger with 0.150 kg (for a total of 0.200 kg) and read the position again. Turn off the CBL when you are finished gathering the position data.
[Equilibrium position for m2 = 0.200 kg is y2 = ]
5) Using the equations you wrote in the prelab, calculate the spring constant of your spring in units of N/m. (Hint: you should use all the data you have taken so far.)
[Calculated spring constant = ]
6) Using the spring constant, predict what the measured position of the spring would be if 0.250 kg were placed on the mass hanger. Then measure the position with the sonic ranger. Expect agreement to better than 5%.
[Calculated position for m3 = 0.300 kg is y2 = ]
[Measured position = ]
[Percentage error = ]
Part II. Determining the period
7) To set the system into oscillation, gently lift the 0.300 kg mass and let go. Measure the period of oscillation to 3 significant figures using a stopwatch.
[Number of cycles measured = ]
[Total time measured = ]
[Measured period of 0.300 kg = ]
8) Assuming that the period, T, of an oscillating spring depends only the spring constant, k, and the mass, m, determine the mathematical combination of k and m that gives the right units for period. This result should be correct to within a constant numerical factor (call it "C"), to be determined in step #9 by experiment.
[Units analysis]
9) Using the spring constant, mass, measured period, and the result of #8, calculate a value for the numerical constant in the formula for period. What familiar number is it close to? What does the text (Giancoli 11-3) say it should be? Compare the two values.
[Calculated constant = ]
[Expected constant = ]