Experiment Analysis

Analysis - a strange result

  1. Examine the graph of velocity vs. time given by the data in Table 1 and describe the shape of the plot. Extrapolation of the curve to zero velocity shows that the velocity is zero when t is about -0.1s.
    The graphs of equations. (1.4) and (3.4) are curves of different types. Which of these graphs is of the same geometric character as the plot of the data in Table 1?

  2. Since equation. (1.4) seems a better representation of the data, model the fall of the bob assuming that only inertia and gravitation are important. Thus
        (1.1)
    with the initial condition
      m/s   (9.1)
    One might expect the initial condition would be v(t=0)=0, but this is not the case experimentally due to the way in which the equipment is built and operated.

    The solution is
        (9.2)
    Is eqn. (9.2) a good fit of the data? Assume g = 9.81 m/s2 for this test. Extrapolate the data to evaluate .

    s.

Go on to the collaborate section and discuss the first question with your classmates, then come back to this page.

Analysis - inclusion of drag forces in model

  1. Let us start with eqn. (3.1) which involves inertia, gravitation and drag forces:
        (3.1)
    with the initial condition
      m/s   (9.1)
    the solution is
      Derivation DERIVE! (9.3)
  2. Compare representations of the data in Table 1 based on eqns. (9.2) and (9.3) by plotting v(t) and vs.

Go on to the collaborate section and discuss the second question with your classmates, then come back to this page.

Analysis - unraveling the quandary

  1. Take the limit of the velocity in eqn. (9.3) as . Since we see that

    Thus is the terminal velocity of the bob.

  2. Clearly and must be dimensionless. Satisfy yourself that this is indeed the case.

  3. We write eqn. (9.3) in dimensionless form, that is, in terms of a dimensionless velocity. Thus

        (9.4)
    where Vtb = terminal velocity of the bob(m/s).

  4. Let us calculate the quantity


  5. Using the data in Table 1, calculate the maximum value of in the experiment:
    We see now that during the experiment the velocity of the bob is nowhere close to its terminal velocity.

  6. Let us rewrite eqn. (3.1) as and normalize with . Thus
        (9.5)
    Since the maximum value of in the experiment is 0.0577 we see that
    In other words, the acceleration during the experiment is very close to g, so that the drag force does not influence the acceleration of the bob. That is why we can measure g in this experiment.

    Go on to the practice section to test your knowledge.


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