3.16 Draw the physical model and free-body diagram of the
frame of the swing (Figure P3.14).
Figure P3.14 Swing set.
4.16 (M2.8b) Determine forces in each bar Q = 1000 N, α = 300 and β = 600.
F
D
β
1
Q
2
α
E
Fig. P4.16
B53.* The sphere A has a volume of 0.7 m3 and weights 5 kN. It is hold underwater by three
equidistant anchors B, C and D planted at the same depth. Determine tension in each cable if each
makes angle of 450 with the vertical direction. The specific weight of water γ = 10 kN/m3.
A
C
B
D
M3.28 The homogenous L-shaped element ABC is suspended by the cable AD. Link BC is twice as
long as the link AB. Determine the angle α.
M4.56 Two smooth balls, radii R1 and R2, weights P1 and P2 are suspended by ropes AB = l1 and
AD = l2.Angle BAD = α. Determine angle θ , tension in the cables and contact force between the
balls.
A
D
E
θ
α
B
C2
C1
Ja12.2. Determine center of gravity of the structures shown, assuming that they are constructed
from the homogenous bars.
2.5
5
y
45°
x
O
6.9 Replace the distributed load (Figure P6.9) by a resultant force.
Figure P6.9
M9.1(286)
A
C
D
B
8.36 Determine forces in the members KL, FL and FG.
F1 = 20 N, F2 = 30 N, F3 = 40 N, F4 = 10 N, F5 = 60 N, a = 20 cm.
F1
J
I
K 30
L
H
o
A
B
C D E F G
a a a a a a
F 2 F 3 F4
8.85 Determine the force in each member of the truss. What are the reaction forces at A and B?
P1 = 2 kN, P2 = P3 = 4 kN, P4 = 6 kN, P5 = P6 = 2 kN, α = 30o.
P2
B
A
a
a
a
a
a
P3
P1
P4
8.? – 8.? Determine forces in each truss member , when P = 3 kN, Q = 2 kN, a = 20 cm, b =40cm
and c = 50 cm. Force P is always acting along the line AB and force Q along the line DE.
P
3
1
Q
A
2
6
E
c
D
5
4
a
B
b
9.13 Draw the diagrams of internal forces and moments in
the shelf for the load shown in Figure P9.6. Assume that the
shelf is simply supported on the left and is supported by a roller
on the right.
b) Weight of the left empty bottle is 1 lb, full bottle 4 lb and the
box – 10 lb, a=b=d=e=4 inches, and c=10 inches.
Figure P9.5 Shelf with the box and two bottles
185. Three homogeneous bars are connected as shown below. Force Q = 20 N is applied at the
center of the member CD. Determine the components of forces acting on members AB and CD.
Bar AB weights 50 N, bars BC and CD each weights 30 N. AB = 4 m and KB = 1m.
y
A
K
B
D
45°
x
45°
Q
C
11.1 Skier is going down the slope with a constant velocity
(Figure P11.1). Slope makes an angle of 40 degrees to the
horizontal. Find the force of friction between the skier and the
ground, assuming the coefficient of static friction is 0.0? and
coefficient of kinetic friction is 0.??
b) Weight of the skier is 170 lb.
Figure P11.1 Skier on the slope
Skier does not go anywhere, he just sits in the position
shown. What is the minimum slope required for him to start
moving down the slope without using poles?
Ja4.28
P1
60°
A
P2
P3
q
D
B
2.0
1.5
M1
E
C
3.5
2.0
2.5
3.0
2.0
Ja2.19
M0
q
3a
2a 2.5a
2q
α
3a
G
5.12 (M2.49) Smooth ring A can glide along the circular path AB. Determine angle φ as function of
P and Q for the system to be in equilibrium. Plot angle φ as function of the ratio Q/P in the range of
zero to 2.
B
A
ϕ
Q
P
O
C
Fig. P5.12
5.16 (M3.6) Determine the forces at A and B as function of the position of the cart C along the
crane. Weight of the crane P = 60 kN, weight of the cart with the load P1 = 40 kN. AC/AB=0.25.
Fig. P5.16
M4.4 Rigid link ABC weights 80 N, its weight is applied at point E which is 21.2 cm from the
vertical line BD. Determine angle φ if system is in equilibrium. P1 = 310 N, P2 = 100 N, AB = 40
cm, BC = 1 m.
C
D
ϕ
E
A
F
135°
E
B
80N
P2
P1
M4.15 A 2 kN cylinder Q is suspended from the homogenous rod AB ( weight 1 kN) and kept in
the equilibrium by weight G. Determine weight G and reaction at A, when BD = AB/4.
y
A
C
30°
45°
D
G
B
Q
x