Experiment Analysis
Analysis - a strange result
-
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?
-
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
with the initial condition
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
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
- Let us start with eqn. (3.1) which involves inertia, gravitation
and drag forces:
with the initial condition
the solution is
- 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
- Take the limit of the velocity in eqn. (9.3) as
. Since
we see that
Thus
is the terminal velocity of the bob.
- Clearly
and
must be dimensionless. Satisfy yourself that this is indeed the case.
- We write eqn. (9.3) in dimensionless form, that is, in terms of a
dimensionless velocity. Thus
where Vtb = terminal velocity of the bob(m/s).
- Let us calculate the quantity
- 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.
- Let us rewrite eqn. (3.1) as
and normalize
with
. Thus
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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1998-1999
Rensselaer Polytechnic Institute. All Rights Reserved.