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ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 1
Assignment Due: 06/09/2010
Q1.
Problem 11: Forces
P
and
Q
are applied to a particle of mass
m
.
The magnitudes of these
forces, P and Q, are constant but the angle
between their lines of action can be varied, thereby
changing the total force, and hence the acceleration of the particle.
Suppose that the magnitudes
of these forces are such that the maximum possible acceleration is three times as large as the
minimum possible acceleration.
Now, the forces are arranged at an angle such that the
acceleration attained by the particle is the mean of the maximum and minimum accelerations.
Find the angle
between the forces.
Q2.
Problem 13:
Consider a triad of vectors (not necessarily unit vectors)
e
1
, e
2
,
and
e
3
.
Let
them be represented in terms of the Cartesian basis
i
,
j
, and
k
as:
1
1
2
3
2
1
2
3
3
1
2
3
,
,
.
e
l i
l j
l k
e
m i
m j
m k
e
n i
n j
n k
(a)
Find
the
three
equations
that
must
be
satisfied
by
the
coefficients
1
2
3
1
2
3
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 Fall '10
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