R
4.33 B19.
The cylinder M (weight P) is held in equilibrium on the frictionless surface by the
weight Q. Determine the angle α and the force between the surface and the cylinder M. What must
be the relationship between P and Q to maintain the equilibrium?
O
A
α
M
Q
5.2 The front-end loader shown in Figure P5.2 has total weight of 5 tons. Assume that the weight is
applied at the midline between the front and rear wheels. By activating the cylinder, the loader is
capable to lift the front wheel from the ground by pushing the bucket against the ground. What is
the force necessary to apply between the bucket and ground to lift the front wheel from the ground?
Figure P5.2 Error! No text of
specified style in document.
4.31 (M2.24) A 20 kN roller is pulled by the horizontal force P over the obstacle C. Determine the
force P required to move the roller over the obstacle.
8cm
60cm
P
Fig. P4.31
B106. Model of airplane is tested in the wind tunnel. The resultant of the wind is represented F.
Model is free to rotate about axis O, it is held in the position shown by two identical springs, each
having stiffness c (c is the force necessary to extend the spring by unit length). Before the test,
model was oriented in the horizontal direction and springs were unstretched. Determine force F.
F
β
α
K
O
a
b
Ja12.18. Determine the centroid of the area shown , assuming that they are constructed from the
homogenous plate. All dimensions are in cm.
y
R1
0
15
x
O
5
R2
B, 125. For the load and supports shown, determine the reactions. Neglect the weight of the beam.
y
q
A
B
x
a
l
8.11 Using method of joints, calculate the force in each member of the truss shown.
F = 40 N and a = 30 cm. (Ja 1.19 – 1.20)
a
a
a
a
A
F
G
F
60
E
D
o
Figure P8.11
B
C
3/2 h
h
8.54 Determine forces in the members HG and CD.
F1 = 20 N, F2 = 30 N, F3 = 40 N, F4 = 10 N, F5 = 60 N, a = 20 cm.
F1
o
90
F
E
H G
D C F2
I
A
J
a
K L M N
F3
F4
a a a a a
B
(241 -249) Determine forces in all members of the truss when a = 50 cm and P1=P2=25 kN, P3=30
kN P4=40 kN, and P5=20 kN.
a
a
a
a
a
1.2a
P3
B
A
P1
30°
P2
d
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
A
1
c
2
4
6
5
a
B
b
(M2.31a) and (M2.31b) The weightless beam AB is supported as shown and loaded by force F =
30 kN. Determine the reaction at A and force in the link CD.
F
A
B 60°
2m
C
1m
D
B109. The structure below is supported as shown. Determine the reactions at A and C, if P1 = 1 k
N, P2 = 500 N, P3 = 500 N. Force P3 is acting in the middle of the member BC. Use BC = 2b and
α = 450.
y
P1
α
α
B
P2
x
C
b
P3
A
214. Cylinder of radius R and is moved along the horizontal plane by the force Q. Coefficient of
rolling friction equals to k. What should be coefficient of friction µ to assure that cylinder will
roll without slip. (Hint: to assure the cylinder will roll without slip Q should be less than Fµ.).
(Fig. ___).
Q
Ja4.15
A
60°
M1
P1
P2
D
C
M2
B
3.5
2.0
2.0
1
3
2.5
Ja5.7
2
C
D
q
60°
B
A
3
3
2.0
2.5
45°
P3
E
1.5
4.8 Find the resultant of the force 200 N and the force 400 N (Figure P4.7)
400 N
200 N
0
20
300
250
Figure P4.7
100 N
M6.10(220) The force P = 1 kN is acting in the plane ABCD and its line of action makes angle of
450 with the horizontal AC. Angle EAK = angle FBM = angle NDB = 900, AE = AK, BF = BM
and ND = BD. Determine the forces in each of the six members.
B
6
45°
3
5
F
P
4
N
45°
A
2
E
45°
D
1
M
45°
K
C
5.21 (M3.21) Safety valve A (diameter d = 6 cm) of the pressure vessel is attached by the link AB
to the bar CD (weight of the bar CD = 10 N). Determine the weight Q that will allow the valve to
open when inside pressure will reach 11 N/cm2. CD = 50 cm, BC = 7 cm.
C
B
D
A
Q
d
Fig. P5.21
163. Determine the reaction forces and moments at A, B and C.
y
F
C
A
B
D
x
a
b
l
Ja12.8. Determine the centroid of the area shown , assuming that they are constructed from the
homogenous plate. All dimensions are in cm.
y
O
30
R2
0
5
5
R1
x