1. Problem 2.137 y x Collars A and B are connected P
20 in A B O z P Q
Collars A and B are connected
by a 25-in.-long wire and can
slide freely on frictionless rods.
If a 60-lb force Q is applied to
collar B as shown, Determine
(a) the tension in the wire when
x = 9 in., (b) the corresponding
magnitude of the force P required
to maintain the equilibrium of
the system.

2. Solving Problems on Your Ownx
20 in A B O z P Q
Solving Problems on Your Own
Collars A and B are connected
by a 25-in.-long wire and can
slide freely on frictionless rods.
If a 60-lb force Q is applied to
collar B as shown, Determine
(a) the tension in the wire when
x = 9 in., (b) the corresponding
magnitude of the force P required
to maintain the equilibrium of
the system.
Problem
1. Draw a free-body diagram of the particle. This diagram shows
the particle and all the forces acting on it.

3. Solving Problems on Your Ownx
20 in A B O z P Q
Solving Problems on Your Own
Collars A and B are connected
by a 25-in.-long wire and can
slide freely on frictionless rods.
If a 60-lb force Q is applied to
collar B as shown, Determine
(a) the tension in the wire when
x = 9 in., (b) the corresponding
magnitude of the force P required
to maintain the equilibrium of
the system.
Problem
2. Set the resultant, or sum, of the forces exerted on the particle
equal to zero. You will obtain a vectorial equation consisting
of terms containing the unit vectors i, j, and k. Three scalar
equations result, which can be solved for the unknowns.

4. S F = 0: P i + Ny j + Nz k + TAB lAB = 0
Problem Solution x P
_ x i _ (20 in) j + z k AB
lAB = = AB
25 in A
Draw a free-body diagram of the particle. O
20 in Q z B x z
Free Body: Collar A
Ny j
Nz k
TAB lAB
P i
S F = 0: P i + Ny j + Nz k + TAB lAB = 0 A
Substitute for lAB and set coefficients
of i equal to zero:
P _
TAB x 25
= (1)

5. S F = 0: (60 lb) k + Nx i + Ny j _ TAB lAB = 0
Problem Solution
Ny j
Nx i
_ TAB lAB
Q = (60 lb) k
Free Body: Collar B
S F = 0: (60 lb) k + Nx i + Ny j _ TAB lAB = 0 B
Substitute for lAB and set coefficients
of k equal to zero:
60 _
TAB z 25
= (2)
(a) Since x = 9 in.: (9 in)2 + (20 in) 2 + z 2 = (25 in) z = 12 in
From eq. (2):
60 _
TAB (12) 25
= TAB = lb
(b) From eq. (1): P =
(125.0 lb)(9 in)
25 in
P = 45.0 lb