1. Problem 11.186 In the position shown, collar B moves A
to the left with a velocity of 150 mm/s.
Determine (a) the velocity of collar A,
(b) the velocity of portion C of the
cable, (c) the relative velocity of portion
C of the cable with respect to collar B. A B C

2. Solving Problems on Your Own
In the position shown, collar B moves
to the left with a velocity of 150 mm/s.
Determine (a) the velocity of collar A,
(b) the velocity of portion C of the
cable, (c) the relative velocity of portion
C of the cable with respect to collar B. A B C
1. Dependent motion of two or more particles:
1a. Draw a sketch of the system: Select a coordinate system,
indicating clearly a positive sense for each of the coordinate axes.
The displacements, velocities, and accelerations have positive
values in the direction of the coordinate axes.
1b. Write the equation describing the constraint: When particles
are connected with a cable, its length which remains constant is
the constraint.

3. Solving Problems on Your Own
In the position shown, collar B moves
to the left with a velocity of 150 mm/s.
Determine (a) the velocity of collar A,
(b) the velocity of portion C of the
cable, (c) the relative velocity of portion
C of the cable with respect to collar B. A B C
1c. Differentiate the equation describing the constraint: This
gives the the corresponding relations among velocities and
accelerations of the various particles.

4. constant = 2xA + xB + (xB - xA)
Draw a sketch of the system.
Problem Solution A B C xA xC xB
Write the equation describing
the constraint.
The total length of the cable:
(a)
constant = 2xA + xB + (xB - xA)
vB = 150 mm/s
Differentiate the equation describing the constraint.
0 = vA + 2vB
vB = 150 mm/s
vA = - 2 vB
vA = -300 mm/s vA = 300 mm/s

5. constant = 2xA + xC 0 = 2vA + vC vC = - 2vA vC = 600 mm/s
Problem Solution xA A
(b) The length of the cable from
the right end to an arbitrary
point on portion C of the cable: C B xC
constant = 2xA + xC xB
vB = 150 mm/s
0 = 2vA + vC
vC = - 2vA
vC = 600 mm/s
(c) Relative velocity of
portion C:
vC = vB + vC/B
600 = vC/B
vC/B = 450 mm/s