Problem Set
1
1.1. Determine the magnitude of the
resultant force and its direction, measured
counter-clockwise from the positive x-axis.
Ans: R = 998 N, θ = 135°
1.2. Two forces are applied at the end of a
screw eye in order to remove the post.
Determine the angle θ (0° ≤ θ ≤ 90°) and
the magnitude of the force F so that the
resultant force acting on the post is directed
vertically upward and has a magnitude of
750 N.
Ans: θ = 18.6°, F = 319 N
1.3. Determine the magnitude and
direction of F1 so that particle P is in
equilibrium.
Ans: θ = 12.9°, F1 = 552 N
Problem Set 2
2.1 Determine the angle θ between the
tails of the two vectors.
Ans: θ = 121°
2.2 Determine the magnitude and
directional sense of the resultant
moment of the forces about point P.
Ans: MP = 3.15 kN-m ccw
2.3 Determine the magnitude and
directional sense of the moment of the
force at A about point P.
Ans: MP = 3.15 kN-m ccw
2.4 Determine the moment of the force
at A about point O. Express the result
as a Cartesian vector.
Ans: MO = (260i + 180j + 510k)N-m
Problem Set 3
3.1 Determine the horizontal and
vertical components of reaction for the
beam loaded as shown. Neglect the
weight of the beam.
Ans:
Ay = 319 N, Bx = 424 N, By = 405 N
3.2 The lever ABC is pin-supported at
A and connected to a short link BD as
shown. If the weight of the members is
negligible, determine the components
of the force of the pin on the lever at A.
Ans: Ax = 533 N, Ay = 933 N
3.3 If the wheelbarrow and its contents
have a mass of 60 kg and a center of
mass at G, determine the magnitude of
the resultant force which the man must
exert on each of the two handles in
order to hold the wheelbarrow in
equilibrium.
Ans: FB = 105 N
3.4 Determine the distance d for
placement of the load P for equilibrium
of the smooth bar in the position θ as
shown. Neglect the weight of the bar.
Ans: d = a/cos3θ
Problem Set 4
4.1 Determine the force in each
member of the truss and state if the
members are in tension or compression.
Assume each joint as a pin.
Let P = 4 kN
Ans:
FAE = 8.94 kN (C), FAB = 8.00 kN (T),
FBC = 8.00 kN (T), FBE = 8.00 kN (C),
FCE = 8.94 kN (T), FDE = 17.9 kN (C)
4.2 Determine the force in members
BC, CH and GH of the bridge truss, and
indicate whether the members are in
tension or compression.
Ans:
FGH = 29.0 kN (C), FBC = 20.5 kN (T),
FCH = 12.0 kN (T)
4.3 Determine the force in members
CD, CF and FG of the Warren truss,
and indicate whether the members are
in tension or compression.
Ans:
FFG = 8.08 kN (T), FCD = 8.47 kN (C),
FCF = 0.770 kN (T)
Problem Set 5
5.1 The engine hoist is used to support
the 200-kg engine. Determine the force
acting in the hydraulic cylinder AB, the
horizontal and vertical components of
force at the pin C and the reactions at
the fixed support D.
Ans:
FAB = 9.23 kN
Cx = 2.17 kN
Cy = 7.01 kN
Dx = 0
Dy = 1.96 kN
MD = 2.66 kN-m
5.2 The compound arrangement of the
pan scale is shown. If the mass on the
pan is 4 kg, determine the horizontal
and vertical components of force at pins
A, B and C and the distance x of the
25-g mass to keep the scale in balance.
Ans:
Ay = 34.0 N, Ax = 0
Cy = 6.54 N, Cx = 0
By = 1.06 N, Bx = 0
x = 292 mm,
Problem Set 6
6.1 The coefficient of friction between
the shoes at A and B of the tongs and
the pallet is μ’s= 0.5, and between the
pallet and the floor is μs= 0.4. If a
horizontal towing force P = 300 N is
applied to the tongs, determine the
largest mass that can be towed.
Ans: m = 54.9 kg
6.2 A cylinder having a mass of 250 kg
is to be supported by the cord which
wraps over the pipe shown. Determine
the largest vertical force F that can be
applied to the cord without moving the
cylinder if the rope passes over the pipe
(a) once or (b) twice. Let μs= 0.2.
Ans:
(a) F = 4.60 kN
(b) F = 16.2 kN
6.3 Blocks A and B have mass of 7 kg
and 10 kg, respectively. Using the
coefficients of static friction shown,
determine the largest vertical force P
which can be applied to the cord
without causing motion.
Ans: P = 223 N
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