Page 423 - Dynamics of Mechanical Systems

0593_C11_fm Page 404 Monday, May 6, 2002 2:59 PM

404 Dynamics of Mechanical Systems

B
R
P11.4.4: See Problem P11.4.3. Express ωω ωω in terms of the unit vectors N , N , and N .
Z
Y
X
P11.4.5: See Problems 11.4.3 and P11.4.4. Find the partial angular velocities of B in R for
α, β, and γ. (Express the results in terms of both n , n , and n and N , N , and N .
z
y
x
X
Z
Y
P11.4.6: See Problems P11.4.3, P11.4.4, and P11.4.5. Let O be the origin of a Cartesian axis
system X, Y, Z fixed in R, and let Q be a vertex of B as in Figure P11.4.6. Let the velocity
of Q in R be expressed alternatively as:
V = XN + YN + ZN
R Q ˙ ˙ ˙
X Y Z
and
R Q
V = ˙ xn + ˙ yn + ˙ zn
x y z
˙
˙
˙ z
˙ x ˙ y
X Y
a. Express , , and in terms of , , and . Z ˙
˙
˙
˙
˙ x ˙ y
Z
X Y
b. Express , , and in terms of , , and . ˙ z
a
c P
b
N n y
Z
n z
B
O Q
n
N x
FIGURE P11.4.6 N Y
A box B moving in a reference frame R. X X
P11.4.7: See Problem P11.4.6. Find the partial velocities of Q in R for the coordinates x, y,
z, X, Y, and Z. Express the results in terms of both n , n , and n and N , N , and N .
x y z X Y Z
P11.4.8: See Problem 11.4.6. Let the sides of the box B have lengths a, b, and c, as represented
in Figure P11.4.6, and let P be a vertex of B as shown. Find the velocity of P in R. Express
the results in terms of both n , n , and n and N , N , and N . Use either , , and or
˙ z
˙ x ˙ y
Z
y
x
X
z
Y
˙
X Y ˙ Z ˙
, , and for convenience.
P11.4.9: See Problems P11.4.3 to P11.4.8. Find the partial velocities of P in R for the
coordinates x, y, z, X, Y, Z, α, β, and γ. Express the results in terms of both n , n , and n
x y z
and N , N , and N .
X Y Z
Section 11.5 Generalized Forces: Applied (Active) Forces
P11.5.1: A simple pendulum with length of 0.5 m and bob P mass of 2 kg is subjected
to a constant horizontal force F of 5 N as represented in Figure P11.5.1. Determine the
generalized active force F on P for the orientation angle θ. (Include the contributions of
θ
F, gravity, and the cable tension.)