# 3DEquilibrium of particles SampleProblems

```“Ball-andsocket
joint”
1. The pole is subjected to the two forces shown. Determine the components of
reaction of A assuming it to be a ball-and-socket joint.

F
Thrust Bearing
2. The shaft assembly (consisting of welded pieces AB, ED and CD) is supported
by a thrust bearing at A and a radial bearing at B. The assembly is subjected to a


force F at C and a couple M . If it is known that the y component of the reaction



at bearing B is 104 j (N), determine the vector expressions of the force F , couple M
and the bearing reactions at A and B. Link ED lies in the yz plane. ED=250 mm.
By
Bz
Ax
Ay
Az
3. Under the action of the 40 N&middot;m torque
applied
to
the
vertical
shaft,
the
restraining cable AC limits the rotation of
the arm OA and attached shaft to an angle
of 60&deg; measured from the y axis. The
collar D fastened to the shaft prevents
downward motion of the shaft in its
bearing. Calculate the bending moment
M, the compression P and the shear force
V in the shaft at section B.
(Bending
moment, expressed as a vector, is normal
to the shaft axis and shear force is also
normal to the shaft axis.)
B
Mx
Bx
By
Bz
T
My
4. Structure ABCD is supported by a collar at D that can rotate and slide along bar EF which is
fixed and is frictionless. Structure ABCD makes contact with smooth surfaces at A and C

where normal direction n to the surface at A lies in a plane that is parallel to the xy plane.
Force P is parallel to the y axis. If P=10 kN, determine the reactions at A, C and D. Note that
collar D acts like a wide radial bearing.
Dy
My
Dz
Mz
NC
NAy
NAx
NA
5. Because of friction a very large force T is required to raise the 10 kg body when the cable
is wound around a fixed rough cylinder as shown. For the static equilibrium values shown,
determine all of the reactions at point O. The 0.3 m dimension refers to the point A where
the cable loses contact with the cylinder. Neglect the weight of the fixed cylinder.
50 cm
50 cm
40 cm
15 cm
25 cm
15 cm
6. Two rods are welded to form a T-shaped structure. The end D of the structure rests
against a frictionless vertical wall, while ends A and B are supported by radial bearings.
When a 600 N magnitude vertical force P is applied to the midpoint E of the part DC of the
structure, determine the reactions at D.
7. The uniform 900- by 1200-mm trap door has a mass of 200 kg and is propped open by the
light strut AB at the angle q=tan-1(3/4). Calculate the compression FB in the strut and the force
supported by the hinge D normal to the hinge axis. Assume that the hinges act at the extreme
ends of the lower edge.
z
Dz
y
FB
Cz
Dy
Dx
Cy
Cx
W
G
x
W=200(9.81) N
8. The electric sander has a mass of 3 kg with
mass center at G and is held in a slightly tilted
position (z-axis vertical) so that the sanding
disk makes contact at its top with the surface
being sanded. The sander is gripped by its
handles at B and C. If the normal force R
against the disk is maintained at 20 N and is
due entirely to the force component Bx (i.e., Cx
= 0), and if the friction force F acting on the
disk is 60 percent of R, determine the
components of the couple M which must be
applied to the handle at C to hold the sander in
position. Assume that half of the weight is
supported at C.
R  20 N
Cx  0
 Fx  0 

60
 12 N
100
W 3  9.81
Cz 

 14.715 N
2
2
20  Bx  0

F  20 
Bx  20 N
 Fy  0 

12  C y  0
C y  12 N
 Fz  0 
W  Bz  C z  0
Bz  C z  14.715 N

29.43 N

MC  0




 0.12i  0.4k  20i  12 j 





  0.04i  0.2 j  0.3k   20i  14.715k



  0.04i  0.3k  29.43k



 M xi  M y j  M z k  0





M x  1.857 Nm


M y  1.411 Nm

My
M z  2.56 Nm
Cy
Cz
Mx
Mz
```