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Purpose

Purpose. Gain experience in analyzing relationships between variables by graphical methods. For Q  0: T. The Pendulum. Period (T): Time for a complete swing (from A to B and back to A again). L. Q. B. A. Finding the Relationship Between T, m, A, and L Experimentally.

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Purpose

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Presentation Transcript

  1. Purpose • Gain experience in analyzing relationships between variables by graphical methods.

  2. For Q 0: T The Pendulum Period (T): Time for a complete swing (from A to B and back to A again). L Q B A

  3. Finding the Relationship Between T, m, A, and LExperimentally Without prior knowledge we assume: (T is some function of A, m, and L: The measured value of T may or may not depend in some way on the amplitude of the swing, the mass on the pendulum, and the length of the pendulum.) One possible functional relationship may be: where k, I, J, N are constants to be determined.

  4. T A Varying One of the Parameters Vary only one of the parameters at a time. Example: Vary the amplitude A, but leave the mass of the ball and the length of the string the same. Measure T for several different amplitudes. T A use averaging as shown in manual 5°± 1° 1.4 s ± 0.1s 10°± 1° 1.5 s ± 0.1s …. Make graphs of the data. ….

  5. Evaluating the Data • From the theoretical relationship of the period T we anticipate: - T   N = 0.5 ? - T is independent of the mass  J = 0 ? - T may depend on A (Q)  I = 0 or not ???

  6. T A Is T Independent of a Amplitude? If linear plot of T versus A can be fit by a horizontal line (slope=0).  I=0 and T is independent of A

  7. Is T Proportional to a Variable? T If linear plot of T versus A can be fit by a straight line.  I=1 (T is proportional to A) A

  8. Is T  ? T If T versus L cannot be fit by straight line:  N is neither 1 nor 0 L T If plot of T versus can be fit by straight line.  N=1/2 is verified

  9. Hints • Is it better to average the period by measuring 10 times a single period and averaging the result: • Or is it better to measure the time of 10 periods and dividing the result by 10: • To understand why the second method is better: • Assume the uncertainty in a time measurement is • Use error propagation to find out what is in the two cases. • Which of the two methods gives a lower ?

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