Comparison
Question 1
Expand in a Taylor series about the point
t=0
retaining the first two terms of the series. Show that eqn. (
3.4) reduces to eqn (
6.2) when
k/m << 1.
Question 2
Plot eqns. (
2.5) and
(
4.1) for the distances between 0 and 3500
m with
k = 0.2 Ns
2/m
2 and
m = 80
kg and note how badly eqn. (2.5) correlates with eqn (4.1) for the
skydiver as the distance increases.
Question 3
a. Make a plot of [
v(t) -
vf(t)]] for the skydiver (
k = 0.2
Ns
2/m
2 and
m = 80 kg) as a function of
time for times from 0 to 10 s.
b. What does this plot tell you about the difference between Falling
in a Fluid vs. Falling in a Vacuum? How do you explain the shape of
the plot for small t? for large t?
Question 4
The plot of (v - vf)
vs. t shows that vf becomes constant for
large t. Determine the time required for vf
to be equal to
:. (k =
0.2 Ns2/m2 and m = 80 kg)
Copyright
1998-1999
Rensselaer Polytechnic Institute. All Rights Reserved.