ANNA UNIVERSITY QUESTION BANKS FOR SECOND SEMESTER CSE,ECE,IT,MECH,EEE,AND OTHERS DEPT
6. Find the
support reactions of the truss shown below.
8. Find the
support reactions of the beam shown below.
10. Two rollers,
each of weight 50 N and radius 10 cm in a horizontal channel of width 36 cm as
shown in figure below. Find the reaction on the point of contact A, B and C.
11. The three
cables are secured to a ring at B and the turn buckle at C as shown in figure
is tightened until it supports a tension of 1.6 kN. Calculate the moment M,
produced by the tension in cable AB about the base of the mast at D
Engineering
Mechanics – Question Bank
Part A (2 Mark Questions)
1.
Determine the resultant of three forces
F1 = 3i+2j+5k and F2= -2i-j+4k and F3 =
7i-3j+6k which are concurrent at the point (1,-6, 5). The forces are in N and
the distances are in meters.
2.
A force F= 5i+2j+4k is acting at a point
A whose position vector is given by (4i+2j+3k). Find the moment of the force
about the origin.
3.
Find the vector 2A+3B+5C in terms of i,
j, k and its magnitude. A= i-2j-3k; B = 4i-3j+2k and C = 0.5i+j-k.
4.
Find the unit vector along the line
which originates at the point (3,4,-3) and passes through the point (2,1,6).
5.
Find the dot product and cross product
of the following vectors. A=3.3i-4.6j+5.5k and B=5.4i-7.6j-3.7k.
6.
A force F= 6i+4.35j+2k is applied at
point A (6, 4.35, 2). Find the moment of the force about the point B (6.5,
3.75, -0.5).
7.
Two forces 60 N and 65 N acts on a screw
at an angle of 250 and 850 from the base. Determine the
magnitude and direction of their resultant.
8.
Find the resultant of an 800 N force
acting towards eastern direction and a 500 N force acting towards north eastern
direction.
9.
Distinguish the following types of
forces with suitable sketch. (i) Collinear and (ii) Coplanar.
10. A Car is pulled by means of two
cars as shown in fig. If the resultant of the two forces acting on the car A is
40KN being directed along the positive direction of X axis, determine the angle
Ѳ of the cable
attached to the car at B, such that the force in the cable AB is minimum. what
is the magnitude of force in each cable when this occurs ?
11.
Define Principle of transmissibility of
forces.
12.
Find the magnitude of two forces, such
that if they act at right angles, their resultant is √10 kN. But if they act at
60o, their resultant is √13 kN.
13.
Distinguish between statics and
dynamics.
14.
What is the difference between a
particle and a rigid body.
15.
Define Lami’s theorem with suitable
example.
16.
State Parallelogram law of forces.
17.
State triangular law of forces.
18.
Define Varignon’s theorem.
PART B (8 Mark and 16 Mark Questions)
1.
A weight of 900 N is supported by two
chains of lengths 4m and 3m as shown below. Determine tension in each chain.
Figure 2
- If five
forces act on a particle as shown in the figure 3, determine the resultant
force by analytical method.
Figure
3
- Find the
support reactions of the beam shown in figure 4.
Figure 4.
4.A system of forces A,
B, C and D of magnitudes 10 kN, 15 kN, 18 kN and 12 kN acting on a body are
shown in rectangular coordinates as shown in figure. Find the moments of the
origin.
5. A string
ABCD attached to two fixed points A and D has two equal weights of 1000 N
attached to it at B and C. The weights rest with the portions AB and CD
inclined at angles 30o and 60o respectively, to the
vertical as shown below. Find the tensions in the portions AB, BC and CD of the
string, if the inclination of the portion BC with the vertical is 120o.
6. Find the
support reactions of the truss shown below.
7. Find the support reactions of the beam shown
below.
8. Find the
support reactions of the beam shown below.
9. Figure shows cylinders, A of weight 100 N and B
of weight 50 N acting on smooth inclined planes. They are connected by a bar of
negligible weight hinged to each cylinder at their geometric centres by smooth
pins. Find the force P, as shown, that holds the system in given positon.
10. Two rollers,
each of weight 50 N and radius 10 cm in a horizontal channel of width 36 cm as
shown in figure below. Find the reaction on the point of contact A, B and C.11. The three
cables are secured to a ring at B and the turn buckle at C as shown in figure
is tightened until it supports a tension of 1.6 kN. Calculate the moment M,
produced by the tension in cable AB about the base of the mast at D
12.
The resultant of the force system shown in figure is 520 kN along the negative
direction of Y axis. Determine P and θ.
13. A cylindrical
roller has a weight of 10 kN and it is being pulled by a force which is
inclined at 30o with the horizontal as shown in figure. While moving
it comes across an obstacle 10 cm high. Calculate the force required to cross
this obstacle, if the diameter of the roller is 1m.
14. A String ABCD, attached to
two fixed points A and D has two equal weights of 1000N attached to it at B and
C. the weights rest with the portions AB and CD inclined at angles of 30° and
60° respectively, to the vertical as shown in fig. Find the tensions in the
portions AB, BC AND CD of the string, IF the inclination of the portion BC with
the vertical is 120°.
15. ABCDE is a light string whose end A is fixed. The weights
W1 and W2 are attached to the string at
B and C and the string passes round a small smooth wheel at D carrying a weight
40KN at the free end E.In the position of equilibrium, BC is horizontal and AB and CD make angles 150° and 120° with
horizontal.
Find (1) the
tensions in AB,BC and DE of the given string. (2) magnitudes of W1 andW2.
16. The
four coplanar forces are acting at a point as shown in fig. Determine the
resultant in magnitude and direction.
17. Five forces
are acting on a particle. The magnitude of the forces are 300N, 600N,700N,900N
and P and their angles with horizontal
are 0°,60°,135°,210° and 270°. If the vertical component of all forces is
-1000N, find the value of P. Also calculate the magnitude and the direction of
the resultant, assuming that the first force acts towards the point, while all
the remaining forces act away from the point.
18.
Five forces act on a bolt ‘B’ as shown in fig.
Determine the resultant of the forces on the bolt.
19.
A road roller of weight 5000N, which is of cylindrical shape, is pulled by a
force F at an angle of 30° with the horizontal as shown in fig. It has to cross
an obstacle of height 3 cm. Calculate the force F required to just cross this
obstacle. The radius of the roller is equal to 30 cm.
20.
Three coplanar forces are acting at a point as shown in fig. One of the forces
is unknown and its magnitude is shown by P. The resultant is having a magnitude
500N and is acting along Y axis (positive direction). Determine the unknown
force P and its inclination with X axis.
21.
Two cables which have known tensions are attached to the top of the tower AB. A
third cable AC is used as a Guy wire as shown in fig. Determine the tension in
AC if the resultant of the forces exerted at A by the three cables acts
vertically downwards.
22.
The forces 10N, 20N, 30N and 40N are acting on one of the vertices of a regular
pentagon, towards the other vertices taken in order. Find the magnitude and the
direction of the resultant force R.
23.
Two cylinders of diameters 25 cm and 70cm weighing 50N and 200N respectively
are placed as shown in fig. Assuming all the contact surfaces to be smooth,
find the reactions (a) When the surface AB is horizontal and (b) for the case
when the surface AB is made 30° with the horizontal.
24.
Two identical rollers, each of weight 50N, are supported by an inclined plane
and a vertical wall as shown in fig. Determine the reactions at the points of
supports A, B, and C assuming all the surfaces to be smooth. Also find the
reaction force between the spheres.
24.
Two smooth spheres rest between two vertical columns as shown in fig. The large
and small spheres weigh respectively 1200N and 360N. The diameters of the large
and small spheres respectively are 60cm and 32cm. Determine the reactions at 1,
2, and 4.
25.
Three smooth pipes each weighing 20KN and of diameter 60cm are to be placed in
a rectangular channel with horizontal base as shown in fig. calculate the
reactions at the points of contact between the pipes and between the channel
and the pipes. Take width of the channel as 160cm.
27.
Determine the reactions at the supports P, Q, T AND V for the beam subjected to
loading as shown in fig.
28.
Determine the reactions at the supports A and E for the beam as shown in fig.
29.
P, Q and R are the concurrent forces. Magnitude of P and Q are 30 kN and 40 kN
respectively. P and Q are on the horizontal plane acting along positive side of
x axis and negative y axis respectively. R acts along the positive Z axis.
Calculate the resultant force if the magnitude of the force R is 3 7.5 kN and
the direction cosines.
30.
The components of force F are Fx = 225 N, Fy= - 300 N and Fz = 450 N. Determine
its magnitude F and the angle made by F with three co ordinate axes.
References
1. Natarajan. K.V., “ Engineering Mechanics”,
Dhanalakshmi Publications, Chennai.
2. Ramesh Babu. V, “ Engineering Mechanics”, VRB Publishers
Pvt., Ltd.,
3. Kottiswaran, “Engineering Mechanics”, Sri Balaji
Publications, Coimbatore.
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