ASSIGNMENT 3
Q.1. Draw the FBD for the member AB and for cylinder D in Fig.1. Neglect the friction at
the contact surface of the cylinder. The weights of the cylinder and the member are
denoted as WD and WAB, respectively.
cord
C
B
D
A
Fig. 1
Q.2. sketch FBD diagram for each member (AB, CD and EF) of the system loaded by forces
P shown in Fig.2. Neglect masses of the members. Find the determinacy of the
problem.
A
C
E
F
P
D
B
P
Fig. 2
Q.3. Compute the supporting forces for simply supported beam as shown in in Fig.4.
1m
y
2m
2m
210N
140N
x
1m
Fig. 3
210
210N
Q.4. Compute the supporting forces for the left side over hanged beam as in Fig.4.
30 kN/m
50 kN
100 kNm
A
C
B
D
1m
3m
Fig. 4
E
1m
1m
Q.5. Solve for the supporting force at A and C in Fig.5. AB has a mass of 40 kg and BC has
a mass of 70 kg.
Ans: Ax = 923.78N, Ay = 336.75N, Cx = 923.78N, Cy = 2414.62N
A
30
C
60
B
o
30
1m
Fig. 5
o
o
0.6m
1000N
Q.6. Draw a F.B.D. of the beam AB and the pulley D in fig.2. The weight of the pulley is WD
and weight of the beam WAB.
A
B
D
C
Fig. 6
500N
Q.7. Draw F.B.D. for each member of the system shown in Fig.7. Neglect masses of the
members. Replace the distributed load by the resultant. Find the determinacy of the
problem. Make the problem determinate.
D
W(x)
E
B
C
A
W
a
F
b
Fig.7
Q.8. Make F.B.D. of the portion of the beam that is exposed from the wall in Fig.8. Replace
all distribution by simpler equivalent force system. Neglect the mass of the beam.
W = 3N/m
A
B
3m
Fig.8
Q.9. Two beam AB and AC are pinned together at A in Fig.9. Draw F.B.D. of each beam.
Neglect the mass of the beam.
Wo
W1
B
C
A
Fig.9
Q.10. Find the force transmitted by wire BC shown in Fig.10. The pulley e can be assumed to
be frictionless in the problem.
Ans.: 565.68N
C
45
o
B
A
D
E
400N
500N
Fig.10
Q.11. Cylinder A and B have a mass of 200 kg each having diameter of 0.3 m and cylinder C
has a mass of 400 kg having diameter of 0.6 m in Fig. 11. Compute all contact forces.
Ans.: 247.5 kg, 425 kg 7 318.2 kg
C
A
B
Fig. 11
1m
Q.12. A cylinder D having a diameter of 1.5 m and a mass of 100 kg is supported by beam
AB of length 7m and mass of 25 kg as shown in Fig.12. If the contact surfaces of the
cylinder are frictionless, find the reactions in x and y direction at A.
Ans.: Ax = 262.87N & Ay = 1311.64N
C
30
o
B
D
A
45
o
500N
Fig. 12
Q.13. In Fig.13, the pulley at D has a mass of 200 kg. neglecting the weight of the bars, find
the force transmitted from one bar to other at C.
Ans.: Cx = 2430.8N, Cy = 11313.2N
0.6m
C
B
D
2.5m
7 N/m
5000N
A
2m
0.3m
1.7m
Fig. 13
2.5m
Q.14. What is the resultant at a cross section at A in Fig. 14? Couple is parallel to plane M.
3m
A
500N
3m
M
225Nm
4m
Fig. 14
250N
Q.15. Find the supporting force system for the cantilever beam ABC shown in Fig.15. What
is the force system transmitted through a cross-section of the beam at B?
⃗ N & ⃗𝑪𝑨 = + 41250𝒋 + 13900𝒌
⃗ Nm
⃗ = + 𝟐𝟓𝟎𝟎𝒊 - 7500𝒌
Ans. Supporting force at A; ⃗𝑹
1500N/m
5m
3m
B
A
3m
150Nm
2.5m
2500N
C
Fig. 15
Q.16. Determine the force component at G.
Ans. Gx = 4000N & Gy = 4000N
D
E
B
3m
1.5m
1.5m
G
0.6m
A
5000N
1.5m
C
Fig. 16
Q.17. A vertical cable AB and other two inclined cable BD and CB restrain the 500N force
shown in Fig.17. Compute the tensile forces in the cables.
Ans. TAB = 292.10N, TBC = 161.01N, TBD = 85.46N
5m
D
3m
C
A
6m
2m
B
10m
Fig. 17
500 N
Q.18. Shown in Fig. 18 is a bar with two right angle bends and supporting a force 𝐹 = 50𝑖
⃗ N. If the bar has a mass of 15N per meter, what is the supporting
+ 𝟏5𝑗 + 500𝑘
⃗ N & ⃗𝑪𝑨 = + 942.83𝒊 + 6422𝒋 Nm
⃗𝑹
⃗ = + 𝟓𝟎𝒊 + 𝟏𝟓𝒋 - 2442.95𝒌
force at A?
z
y
A
𝐹
C
7m
B
x
Fig. 18
10m
Q.19. Compute the supporting force at pin A in Fig. 19. Do so by forming a force triangle.
The block has a mass of 100 kg having centre of gravity as shown.
⃗ 𝑨 = 𝟑𝟗𝟔. 𝟐 𝑖 + 294.8𝑗 N, FA = 492.58N
Ans. 𝑭
60o
A
C.G
3m
7m
Fig.19
Q.20. Compare the forces F required to just start the 900N lawn roller of diameter 0.6m over
a 75mm step when (a) the roller is pushed and (b) the roller is pulled.
F
F
30o
O
O
30o
B α A
B α A
75mm
75mm
Fig. 20(b)
Fig. 20(a)
Q.21. Two smooth cylinders each of weight P and Q, respectively, rest in a horizontal
channel having one inclined wall and one vertical wall as shown in Fig. 21, the
distance between them at bottom which is ‘𝑎’. Find the reactions exerted on the walls
and floor at point of contact A, B, C and D. the following numbered data are given as:
P = 2000N, Q = 800N, 𝑟1 = 100 mm, 𝑟2 = 50 mm, 𝑎 = 200 mm and α = 60o.
Ans. RA = 720.42N, RB = 2440N, RC = 1014.52N, RD = 623.9N
Q
𝑟1
𝑟2
P
E
C
β
H
α
A
I
D
B
G
𝑎
O
Fig. 21
Q.22. A smooth right circular cylinder of radius 𝑟 rests on a horizontal plane and is kept
from rolling by an inclined string AC of length 2𝑟 as in Fig. 22. A prismatic bar AB of
length 3𝑟 and weight Q is hinged at point A and leans against the roller as shown. Find
the tension S that will be induced in the string AC.
Ans. S = 0.433Q
B
3𝑟
E
𝑟
C
θ
A
2𝑟
θ
F
Fig. 22