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BE 110
An Introduction to Biomechanics
Fall 2005
Homework Assignment #4
Due Tuesday 10/25/05, 8AM before class
1. Reading assignment
:
Examine the equations of motion in Section 3.4 in terms of the stress
tensor
τ
ij
.
Study both linear motion and rotations.
2. Practice Problems
(a) Find the stress distribution of a rope with density
ρ
and length L hanging from the ceiling
with a weight W at the bottom.
Under what conditions would the stress distribution be uniform ?
For a way to find the solution see problem 3.26.
(b) Derive the atmospheric formula for the pressure in the air as an ideal gas.
See Problem 3.27.
(c) If the temperature is not uniform in the atmosphere but falls off in a known fashion towards
the outer atmosphere, what will be the pressure distribution.
(d) Consider a twodimensional stress state without body forces, i.e.
τ
xx
,
τ
xy
and
τ
yy
are nonzero
all others are zero.
Find a stress field (in the xy plane) that is
in equilibrium and one that is not
in equilibrium.
3. *Analysis Problem
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 Spring '08
 SCHMIDSCHOENBEIN

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