1. The force F has a magnitude of F = 20 lb and
acting at point C, the coordinate direction angles of
the force are α = 60°, β = 120°, γ = 45°. Determine
the reaction at the fixed support O.
Ans. -10 lb, 10 lb, -14.142 lb.
-297.99 lb-ft, -15.15 lb-ft, 200 lb-ft.
2. Calculate the reactions at the fixed
support of the cantilevered beam loaded as
shown.
Ans. 225 N, 189.71 N, 62.0671 N-m
3. 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
C
4. 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
5. 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
6. 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. 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
7. 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. 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.

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