1. Replace the force F having a magnitude of F = 20
lb and acting at point C by an equivalent force and
couple moment at point O. The force has coordinate
direction angles of α = 60°, β = 120°, γ = 45°.
Express the result as a Cartesian vector.
Ans. F = 10i – 10i + 14.14k lb, M = 297.99i +
15.15j – 200k lb-in.
2. A force F = 80 N acts vertically downward
on the z bracket. Determine the moment of this
force about the bolt (z –axis), which is directed
at 15o from the vertical.
Ans. M = - 23.18i – 23.18j – 6.21k N-m.
3. Replace the force F having a magnitude of
F = 50 lb and acting at point A by an
equivalent force and couple moment at point
C.
Ans. F = 100/7i + 150/7j – 300/7k lb, Ans.
M = - 1928.57i + 428.57j – 428.57k lb–ft.
C
4. Replace the loading system acting on the
beam by an equivalent resultant force and
couple moment at point O.
Ans. F = 294.3 N @ 139,86o C.W. w.r.t xaxis. M = -39.57 N-m
5. Determine the centroid (x, y) of the shaded area.
Ans. X = 4.57 m, Y = 0.8 m.
6. Locate the centroid (x, y) of the shaded area.
Ans. X = 6 m, Y = 2.8 m.
7. Determine the centroid (x, y) of the shaded area.
Ans. X = 2 in, Y = 2.849 in.
8. Locate the centroid ( , ) of the thin plate
Ans. X = -0.2624 m, Y = 0.2624 m.
9. Locate the centroid (x, y) for the strut’s crosssectional area.
Ans. X = 0 mm, Y = 53.414mm.
10. Determine the magnitude of the moment of the
force Fc about an axis formed by points D and A of
the door.
MDA = 94.462 N-m
D
11. Determine the reactions at A and E if P = 500 N.
What is the maximum value P may have for static
equilibrium? Neglect the weight of the structure
compared with the applied loads.
a)Ans. Ax=1285.5 N, Ay=2964.1 N, Ex=3285.5.
b) P = 1732.1 N
12. The two light pulleys are fastened together
and form an integral unit. They are prevented
from turning about their bearing at O by a cable
wound securely around the smaller pulley and
fastened to point A. Calculate the magnitude R
of the force supported by the bearing O for the
applied 2–kN load.
Ans. R = 4.378 kN
13. The man pushes the lawn mower
at a steady speed with a force P
which is parallel to the incline. The
mass of the mower with attached
grass bag is 50 kg with mass center
at G. If θ = 15o, determine the
normal forces NB and Nc under each
pair of wheels B and C. Neglect
friction. Compare with normal
forces for the conditions of θ = 0o
and P = 0.
Ans. NB = 214.19 N, NC = 259.6 N
14. The boom AB lies in the vertical y–z plane and is
supported by a ball–and–socket support at B and by the two
cables at A. Calculate the tension in each cable resulting from
the 20 kN force acting in the horizontal plane and applied at
the midpoint M of the boom. Find also the reactions at B.
Neglect the weight of the boom.
Ans. T1=32.97 kN, T2=22.819 kN, RBx=-3.42 kN, RBy=4.7 kN,
RBz = 46.98 kN
15. Determine the tensions TAE and TGF in the two
supporting cables resulting from the 1.2–kN tension in
cable CD. Assume the absence of any resisting
moments on the base of the pole at O about the x– and
y–axes, but not about z–axis. Find also the reactions at
O. Use vector approach.
Ans. TAE=4.303 kN, TGF=3.469 kN, Mz=2.886 kN-m,
Rx = -0.321 kN, Ry = -0.6414 kN, Rz = 7.697 kN.