# QUESTION BANK SUBJECT-ENGINEERING MECHANICS (EME-102) UNIT-1 TOPIC-TWO DIMENSIONAL FORCE SYSTEM

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QUESTION BANK

SUBJECT
-
ENGINEERING MECHANICS

(EME
-
102)

UNIT
-
1

TOPIC
-
TWO DIMENSIONAL FORCE SYSTEM

Q1.A roller of weight 10 KN rests on a smooth horizontal floor and is connected to the
floor by the bar AC as shown in fig
-
1.Determine the force in the bar AC and reaction
from
floor, if

the roller is subjected to a horizontal force of 5 kN and is incline
d force of
7 KN as shown in fig
-
1.

Q2.A cord
ACB, 5

m long is attached at points A and B to two vertical walls 3 m apart
as shown in fig
-
2.A
pull

C of negligible

carries a suspended load of 200 N and is
free to roll without friction along the
cord.
Determine

the position of
equilibrium, as

defined by the distance X
, that

the
pulley

will assume and also the tensile force in the
cord.

Q3.A roller of radius R=300 mm and weight 2000N is to be pulled over a curb of height
150 mm by a horizontal force P applied to the end of a string would tightly around the
circumference of the
roller. Find

the magnitude of P required to start the roller m
ove
over the
curb. What

is the least pull P trough the centre of the wheel to just turn the
roller over the curb
?

Q4.
A system of connected flexible cables shown in Fig
-
4 is supporting two vertical
forces 200N and 250 N at points B and D.Determine the force
s in various segments of
cable.

Q5.A rope AB,4.5 m long is connected at points A and B at the same
level

4 m
apart. A

load of 1500N is suspended from a point C on the rope 1.5 m from A as shown in fig
-
5.What load connected at point D on the rope,1 m from B

will be necessary to keep the
position CD level?.

Q.6 A wire rope is fixed at two points A and D as shown in fig
-
6.Two weights 20 KN and
30 KN are attached to it at B and C
, respectively.The

weights rest with portions AB and
BC inclined at angles 30
o

and 50
o

respectively, to the vertical as shown in
fig. Find

the
tension in the wire in segments AB
, BC

and CD and also the inclination of segments CD
to vertical.

Q7.A wire is fixed at two points A and D as shown in fig
-
7.Two weights 20 KN and
25KN are su
pported at B and C
, respectively.When

equilibrium is reached it is found
that inclination of AB is 30
o

and that of CD is 60
o

to the
vertical. Determine

the tension
in segments AB
, BC

and CD of the rope and also inclination of BC to the vertical.

Q8.A 600 N

cylinder is supported by the frame BCD as shown in fig
-
8.The frame is
hinged at D.Determine the reactions at A
, B, C

and D.

Q9.Two smooth
spheres

each of radius 100 mm and weight 100N,rest in a horizontal
channel
walls, the

distance between which is 360 m
m.Find the reactions at the points of
contacts A,B,C and D shown in fig
-
9.

Q10.Two
cylinders, A

of weight 4000 N and B of weight 2000N rest on smooth inclines
as shown in fig
-
10.They are connected by a bar of negligible weight hinged to each
cylinder at it
s geometric centre by
pins. Find

the force P to be applied as shown in the
fig. such that it will hold the system in the given position.

Q11.The resultant of two
forces, one

of which is double the other is 260 N.If the
direction of the larger force is reversed and the other remains
unaltered, the

resultant
reduces to 180N.Determine the magnitude of the forces and the angle between the
forces
.

Q12. A body is subjected to the t
hree forces as shown in fig
-
12.If possible determine the
direction of the force F so that the resultant is in X
-
direction. When

(a) F=5000N,(b)
F=3000N.

Q13.The frictionless
pulley

A shown in fig
-
13 is supported by two bars AB and AC
which are hinged at B
and C to a vertical
wall. The

flexible cable DG hinged at D
, goes

over the pulley and supports a load of 20KN at G.The angles between the various
members are shown in the
figure. Determine

the forces in the bars AB and AC.Neglect
the size of the pulley.

Q1
4.A cord supported at A and B carries a load of 10 KN at D and a load W at C as
shown in fig
-
14.Find

the value of W so that CD remains horizontal.

Q15.Three bars hinged at A and D and pinned at B and C as shown in fig
-
15 form a
four bar mechanisem.Determin
e the value of P that will prevent movement of
bars
.

Q16.Two identical
rollers, each

of weights 100 N are supported by an inclined plane and
a vertical wall as shown in fig
-
16.Assuming smooth
surfaces, find

the reactio0ns induced

at the points of supports

A,B,C and D.

Q17.Two cylinders of

diameters 100 mm and 50 mm, weighing 200 N and 50 N
,
respectively

are placed in a trough as shown in fig
-
17.Neglecting
friction; find

the
reaction at contact surfaces 1
, 2, 3, and

4.

Q18.Three cylinders are piled in a rectangular ditch as shown in fig
-
18.Neglecting
friction, determine

the reaction between cylinder A and the vertical
wall. Weights

and
radii of the cylinders are as given W
A
=75N, W
B
=200N, W
C
=100N,R
A
=100mm
,
R
B
=150mm, R
C
=12
5mm.

Q19.Three spheres A,B and C having their dia
meters 500 mm,500 mm and 800
mm,respectively,are placed in a trench with smooth side walls and floor as shown in fig
-
19.The centre
-
to
-
centre distance of spheres A and B is 600 mm.The weights of the
cylinders

A,B and C are 4 KN,4KN and 8KN respectively. Determine the reactions at
P,Q,R and S.

Q20.Three uniform, homogeneous and smooth spheres A,B and C weighing 300N,600N
and 300N,respectively and having diameters 800 mm,1200mm and 800 mm respectively,
are
placed in a trench as shown in fig
-
20.Determine the reactions at the contact points
P,Q,R and S.

Q21.Find the moment of 100 N force acting at B about point A as shown in fig
-
21.

Q22.What will be the Y intercept of the 5000 N force if its moment about A is
8000N
-
m
in fig
-
22.

Q23.A system of loads acting on a beam is shown in fig
-
23.Determine the resultant of

Q24.Find the resultant of the force system shown in fig
-
24 acting on a lamina of
equilateral triangular shape.

Q25.Find the resultant of a se
t of coplanar forces acting on a lamina as shown in fig
-
25.Each square has side of 10 mm.

Q26.The system of forces acting on a bell crank is shown in fig
-
26.Determine the
magnitude, direction

and the point of application of the resultant.

Q27.Various forc
es to be considered for stability analysis of a dam are shown in fig
-
27.The dam is safe if the resultant force passes through middle third of the base. Verify
whether the dam is safe.

Q28.A building frame is subjected to wind loads as shown in fig
-
28.Deter
mine the

Q29.Determine the
magnitude, direction

and line of action of the
equilibrant

of the
given set of coplanar structure as shown in fig
-
29.

Q30.A beam AB of span 12 m shown in fig
-
30 is hinged at A and is on rollers at B.

Determine the reactions at A and B for the loading shown in the fig.

Q31.
Find the reactions at supports A and B in the beam AB as shown in fig
-
31.

Q32.Find the reactions at supports A and B of the loaded beam shown in fig
-
32.

Q33.The cantilever shown in fi
g
-
33 is fixed at A and is free at B.Determine the
reactions when it is loaded as shown in fig.

Q34.Determine the reactions at supports A and B of the overhanging beam shown in
fig
-
34.

Q35.Determine the reactions at A and B of the over
-
hanging beam shown i
n fig
-
35.

Q36.Find the reactions at supports A and B of the loaded beam shown in fig
-
36.

Q37.A beam AB 20 m long supported on two intermediate supports 12 m
apart, carries

a uniformly distributed load of 6 KN/m and two concentrated loads of 30 KN at left e
nd
A and 50
KN at

the right end B as shown in fig
-
37.How far away should the first
support C can be located from the end A so that the reactions at both the supports are
equal?

Q38.determine the reactions at A,B and D of the system shown in fig
-
38.Neglect
the self
weight of the members.

Q39.The beams of AB and CF are arranged as shown in fig
-
39.Determine the reactions
at A
, C, and

D due to the forces acting on the beam as shown in the fig.

Q40.A 12 m boom AB weighs 1
KN, the

distance of the centre of gravit
y G being 6 m
from
A. For

the position shown in fig
-
40, determine

the tension T in the cable and the
reaction at B.

Q41.A cable car used for carrying materials in a hydroelectric project ia at rest on a
track formed at an angle of 30
0

with the
vertical.
The

gross weight of the car and its
load is 60 KN and its centroid is at a point 800 mm from the track half way between the
axles. The

car is held by a cable as shown in fig
-
41.The axles of the car are at a distance
1.2 m.Find the tension in the cables and

reaction at each of the
axles, neglecting

friction
of the track.

Q42.A hollow right circular cylinder of radius 800 mm is open at both ends and rests on
a smooth horizontal plane as shown in fig
-
42
.Inside the cylinder there are two spheres
having weights
1 KN and 3 KN and radii 400 mm and 600 mm,respectively.The lower
sphere also rests on the horizontal
plane. Neglecting

friction find the minimum weight
W of the cylinder for which it will not tip over.

Q43.A 500 N cylinder,1 m in diameter is loaded between

the cross pieces which make an
angle of 60
0

with each other and are pinned at C.Determine the tension in the horizontal
rope DE assuming a smooth floor.(refer fig
-
43)
.

Q44.The frame shown in fig
-
44 is supported by a hinge at A and a roller at E.Compute
the horizontal and vertical components of the hinge forces at B and C as they act upon
member AC.

Q45.Determine the resultant of the parallel coplanar force system shown in fig
-
45.

Q46. An equilateral triangular plate of sides 200 mm is acted upon by four
forces as
shown in fig
-
46.Determine the magnitude and direction of the resultant of this system of
forces and its position.

Q47.
Determine

the
magnitude, direction

and the line of application of the
equilibrant

of the set of forces shown in fig
-
47
, which

w
ill keep the plane body ABCDEFGH in
equilibrium.

Q48.Determine the resultant of the four forces acting on a body as shown in fig
-
48.

Q49.A bracket is subjected to the system of forces and couples as shown in fig
-
48.Find
the resultant of the system and the
point of intersection of its line of action with (a) line
AB,(b) line BC and (c) line CD.

Q50.Determine the resultant of the three forces acting on the dam section shown in fig
-
50 and locate its intersection with the base AB.For a safe design this intersec
tion should
occur within the middle
third. Is

it safe design?

Q51.
Beam AB 8.5 m
long is

hinged at A and supported on roller at B.The roller support
is inclined at 45
0

to the
horizontal. Find

the reactions at A and B,if the loads on it are as
shown in fig
-
5
1.

Q52.

Determine the reaction at A and B on the over
-
hanging beam shown in fig
-
52.

Q53.An over
-
hanging beam is on rollers at A and is hinged at B and is loaded as shown
in fig
-
53.Determine the reactions at A and B.

Q54.

Find the reaction at A and B on the

structure shown in fig
-
54.

Q55.
Determine the reactions at supports A,C and D in the structure
shown

in fig
-
55.

Q56.Determine the reactions at the supports A,B,C and D for the arrangement of beams
shown in fig
-

56.Neglect the self weight of beams.

Q58 A 10
00N cylinder is supported by a horizontal rod AB and a smooth uniform rod
CD which weighs 500 N as shown in fig
-
58.Assuming the pins at A,B,C and D, to be
frictionless and weight of AB
negligible, find

the reactions at C and D.

Q59.The frame

shown in fig
-
5
9 is supported by a hinge at E and by a roller at
D.Determine the horizontal and vertical components of the reaction at hinge C as it acts
upon member BD.

FRCTION

Theoretical Question

Q1
-

Define the following terms:Friction, limit
ing force of friction,co
-
efficient of friction
and a

angle of friction.

Q2
-

Explain the difference between co
-
efficient of friction and angle of friction.

Q3
-

(a) State the laws of static and dynamic friction.

(b) State the laws of solid friction.

Q4
-

What do you mean by ‘angle of response’ ?Prove that angle of response is equal to
the

Angle of friction.

Q5
-
What is a wedge? Explain how a wedge is used to raise heavy loads.

Numerical Questions

Q1
-

A body of weight 90 N is placed on a rough horizontal plane.Determine the co
-
efficient of

Friction if a horizontal force of 63 N just causes the body to slide over the horizontal
plane.

[Ans.0.7]

Q2
-

A body of weight 150 N is placed on a rough horizontal plane.If the co
-
efficient of
friction

Between the body and the horizontal plane is 0.4,determine the horizontal force
required to

Just slide the body on the plane
.
[Ans.60 N]

Q3
-

The for
ce required to pull a body of weight 40N on a rough horizontal plane is 15
N. Determinethe co
-
efficient of friction if the force is applied at an angle of 20
0

with the
horizontal.

[Ans.0.404]

04
-

A body of weight 60N is placed on a rough horizontal plane .To just
move the body
on the horizontal plane,a push of 18N inclined at 20
0

to the horizontal plane is
required.Find the co
-
efficient of friction.

[Ans.0.255]

Q5
-

A pull of 60 N inclined at 25
0
to the horizontal plane,is required just to move a
body placed on a rough horizontal plane.But the push required to move the body is 75
N.If the push is inclined at 25
0
to the horizontal,find

the weight of the body and co
-
efficient of friction.

[Ans.253.83 N, .238 ]

Q6
-

Find the least force require
d to pull a body of weight W placed on a rough
horizontal plane,when the forces is applied at an angle

with the horizontal.
[Ans.W sin

Q7
-

A body of weight 450 N is pulled up an inclined plane.by a force of 300 N.The
inclination of the plane is 30
0
to the horizontal and the force is applied parallel to the
plane.Determine the

co
-
efficient of friction.

[Ans. .192]

Q8
-

A body of weight 400 N is pulled up an inclined plane having inclination 30
0
to the
h
orizontal at a steady speed.If the co
-
efficient of friction between the body and the plane
is 0.3 and force is applied parallel to the inclined plane,find the force required.Find also
the work done on the body if the distance travelled by the body is 10m a
long the plane.
[Ans.303.92 N,3039.2 N m]

Q9
-

An effort of 180 N is required just to move a certain body up an inclined plane
of angle 15
0
, the forces being parallel to the plane.If the angle of inclination of the plane
is

0
,the effort required,again applied parallel to the plane,is found to be 210
N.Find the weight of the body and co
-
efficient of friction.

[Ans.386
.68 N,0.214]

Q10
-

Block A weighing 20N is a rectangular prism resting on a rough inclined plane
.The block is tied up by a horizontal string which has a tension of 6 N.Find:(i)the
frictional force on the block,(ii) the normal reaction of the inclined p
lane,and(iii) the co
-
efficient of friction between the surface of contact.

[Ans.(i)9.898 N (ii) 18.382 N (iii) 0.538]

Q11
-

A cord connects two bodies of we
ight 500 N AND 1000 N.The two bodies are
placed on an inclined plane and cord is parallel to inclined plane.The co
-
efficient of
friction for the weight of 500 N is 0.20 and that of 1000 N IS 0.4.Determine the
inclination of the plane to the horizontal and

tension in the cord when the motion is
about to take place,down the inclied plane.The body weight 500 N

is below the body
weighing 1000 N. [
18.417
0
, 63.086 N]

Q12
-

A uniform ladder of length 13m and weighing 30 N is placed against a smooth
vertical wall with its lower end 10 m from the wall.In this position the ladder is just to
slip.Determine:(i) the co
-
efficient of friction between the ladder and (ii) Friction
al force
acting on the ladder at the point of contact between ladder and floor.

[Ans.(i).602 (ii) 18.06 N]

Q13
-

A uniform ladder of length 10 m and weighing 20 N is placed against
a smooth
vertical wall with its lower end 6 m from the wall.The co
-
efficient of friction between the
ladder and floor is 0.45.Show that the ladder will remain in equilibrium in this
position.What is the frictional force acting on the ladder at the point of

contact between
[Ans.7.5 N]

Q14
-

A uniform ladder of weight 800 N and of length 7 m rests on a horizontal ground
and leans against a smooth vertical wall.The angle made by the ladder with the
horizon
tal is 60
0

.When a man of weight 600 N stands on the ladder at a distance 4m
from the top of the ladder,the ladder ai at the point of sliding.Determine the co
-
efficient
of friction between the ladder and the floor.

[Ans.0.237]

Q15
-
A uniform ladder of weight 250 N and of length 5 m rests on a horizontal ground
and leans against a rough vertical w
all.The co
-
efficient of friction between the ladder
and floor is 0.3 and between the ladder and vertical wall is 0.2. When a weight of 900 N
is placed on the ladder at a distance of 2m from the top of the ladder:the ladder is at the
point of sliding.

Find

(ii) Reaction at the floor of the ladder,and

(iii)Reaction at the top of the ladder
. [Ans.(i)61.52
0

(ii) 1084.9 N
(iii) 325.47 N]

Q16
-

A uniform

ladder of length 15m rests against a vertical wall making an angle of
60
0
with the horizontal.Co
-
efficient of friction between wall and ladder,and ground and

0.25.A man weighing 500 N ascends the ladder.How high will he be able to bef
ore the
ladder slips ? Find the weight necessary to be put at the bottom of the ladder so as to be
just sufficient to permit the man to go to top.Assume weight of ladder as 850 N.
[Ans.6.39 m, 607.6 N]

Q17
-

A
uniform ladder 3 m long weighs 18 N.It is placed against a wall making an
angle 60
0

with the floor as shown in Fig.The co
-
efficient of friction the wall and ladder
w
eight, has to support a man weighing 90 N at its top at A.Calculate:

(i)

The horizontal force F to be applied to the ladder at the floor level to prevent
slipping.

(ii)

If the force F is not applied what would be the minimum inclination of the ladder
with the horizontal so that there is no slipping of it with the man at the top

[Ans.(i) 16.6 N,(ii) 69
0
]

Q18
-

A ladder 5m long rests on a horizontal ground and leans a smooth vertical wall at
an angle of 70
0

with the horizontal.The weight of the ladder is 90 N and acts at its
middle.T
he ladder is at the point of sliding,when a man weighing 75 N stands on a rung
3.5 m from the top of the ladder. Calculate the co
-
efficient of the friction between the
Ans.0.15]

Q19
-

7 m rests against a vertical wall which it makes an angle of
45
0
.The co
-
efficient of friction between the ladder and the walls is 1/3 and that between
ladder and floor is 1/2.If a man whose weight is one
-
half of that of the ladder, ascends
its. How high will it be when the ladder slips.

[Ans.5.25 m]

Q20
-

A body of weight 100 N is at rest on a horizontal plane.A horizontal force of 70 N
just causes the body to slide. Determine:

(i)

Liming Forc
e of friction and

(ii)

Co
-
efficient of friction
.
[Ans.(i)70 N, (ii) 0.7]

Q21
-

The co
-
efficient of friction between a body of weight 100 N and the rough
horizontal plane on which the body rests is 0.3.Calculate the horizontal force required
just to cause to slide over the horizontal plan