Exam#1
—Phys374—Spring 2006
Prof. Ted Jacobson
Wednesday, Mar. 15, 2006
Room 4115, (301)4056020
www.physics.umd.edu/grt/taj/374a/
[email protected]
1. We previously used dimensional analysis to determine the dependence
of drag force on a body moving through air. In so doing we took account
of the density of the air but neglected its viscosity. For this problem
consider the effect of viscosity: suppose a sphere of radius
R
is moving
with speed
v
through a fluid with viscosity
η
.
(a) Using dimensional analysis determine how the viscous drag force
can depend on
R
,
v
, and
η
. (
Hint
: Recall that the viscous force
in the presence of a velocity gradient perpendicular to a surface is
η
(
dv/dx
) per unit surface area.) [8
pts.
]
(b) Using “geometrical analysis”, would you expect any factors of
π
in the exact result for the force?
If so, how many, and exactly
where? [2
pts.
]
2. Consider the cubic equation
ay
3
+
y
+ 2 = 0, with
a >
0.
(a) Display the location of the real roots graphically, by sketching the
graphs of
y
+2 and

ay
3
and seeing where they intersect. Show in
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Jacobson
 Force, pts, 2 pts

Click to edit the document details