v.s.b. engineering college, karur … lami’s theorem. 6. a force 6i – 3j – 2k acts at a point...
TRANSCRIPT
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V.S.B. ENGINEERING COLLEGE, KARUR
DEPARTMENT OF MECHANICAL ENGINEERING
ACADEMIC YEAR: 2009-2010 (EVEN SEMESTER)
ENGINEERING MECHANICS (MECH – II SEM)
QUESTION BANK
UNIT – I
PART-A
1. Define Mechanics
2. What is meant by static’s & dynamics?
3. Distinguish between a particle and a rigid body.
4. List out the laws of mechanics.
5. State Lami’s theorem.
6. A force 6i – 3j – 2k acts at a point P(1,3,4). Determine the moment of this force about the
point of origin.
7. Classify the system of forces
8. Give the conditions of equilibrium of a particle in space
9. What is meant by coplanar concurrent force system?
10. a. Calculate the force F required for the equilibrium of the particle.
a. 60 N b. -60 N
c. 30 N d. 120 N
b. How you can get direction of Resultant R when number of forces acting on a particle
in plane.
11. What are all the branches of mechanics?
12. Define the branches of Dynamics.
13. List out the three types of Units. Give example for each one.
14. State Parallelogram law
15. Let F1 and F2 be the two forces acting on a particle A. Give the condition perpendicularity
and Parallelism of these two.
16. What is meant by force? List out its characteristics.
17. If two forces F1 = 20 KN and F2 = 15 KN act on a particle as shown in figure. Find their
resultant.
18. Give the conditions of equilibrium of a particle in plane
19. What is meant by single equivalent force
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20.a. Select the answer that expresses F as a Cartesian Vector
i. (-70.7i + 70.7j) N
ii. (-70.7i - 70.7j) N
iii. (70.7i + 70.7j) N
iv. (100i + 100j) N
b.How you can get the direction of the Resultant force of a system of forces in space.
21. Explain about sign convention of forces
22. Two concurrent forces of 12 N and 18 N are acting at an angle of 60°. Find
the resultant force.
23. Give the single equivalent force:
24. What is meant by resolution of forces? Explain.
25. Show that the forces 2i – 3j – k and -6i + 9j + 3k are parallel
26. What is meant by equilibrium and equilibrant
27. Define principle of transmissibility
PART - B
1. The forces shown in the figure below are in equilibrium. Determine the forces F1 and F2
2. Determine the tension in cables AB & AC to hold 40 Kg load shown in fig.
11 N
6 N
3 N
2 N
12 N
10 N
8 N
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3. A force P is applied at ‘O’ to the string AOB as shown in fig. If the tension in each part of
string is 50 N, find the direction an magnitude of force P for equilibrium conditions.
4. Members OA, OB and OC form a three member space truss. A weight of 10 KN is suspended
at the joint ‘O’ as shown in fig. Determine the magnitude and nature of forces in each of the
three members of the truss.
5.The lines of action of three forces are concurrent at the origin ‘O’, passes through points A, B,
and C having coordinates (3, 0,-3), (2, -2, 4) and (-1, 2, 4) respectively. If the magnitude of the
forces are 10 N, 30 N and 40 N. Find the magnitude and direction of their resultant.
B (2,-2, 4)
O
30 N
10 N
40 N
A (3, 0,-3)
C (-1, 2, 4)
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6.If five forces acting on a particle as shown in fig. Determine the resultant force
7.Five forces are acting on a particle. The magnitudes of the forces are 300 N, 600 N, 700 N, 900
N & P and they are acting as shown. If the sum of all the vertical component forces is -1000 N.
Find the value of P. Also calculate the magnitude and direction of the resultant.
8.Particle ‘O’ is acted on by the following forces
(i) 20 N inclined 30° North of East
(ii) 25 N towards North
(iii) 30 N towards North West
35 N inclined 40° to South of West, Find the resultant.
9.Eight points are taken on the circumference of a circle at equal distance and from one of the
points straight lines are drawn to the rest; if these straight lines represent forces acting at a point,
15°
40°
35°
15 KN
75 KN
105 KN
60 KN
45 KN
x
y
x
y
600 N
300 N
P
900 N
700 N
60°
30°
45°
0
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8 m
show that the direction of the resultant coincides with the diameter through that point and that its
magnitude is four time that diameter.
10.Four forces act on a bolt A as shown. Determine the resultant of the forces on the bolt.
11.A man pulls with a force of 300 N on a rope attached to a building as shown. What are the
horizontal and vertical components of the force exerted by the rope at a point A
UNIT – II
PART-A
1. What is a free body diagram?
2. What is meant by free body?
3. Give the procedure to get the unknown reaction forces when number of forces acting on a
body and keeping it in equilibrium.
4. What is meant by action and reaction?
5. Explain about moment of a force.
6. Explain about the types of moments & their sign conventions.
7. Define Varignon’s theorem.
8. Discuss about Types of Equilibrium.
30°
15°
20°
F1 = 150 N
F4 = 100 N
F2 = 80 N
F3 = 110 N
α
300 N
6 m
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A
B
60°
45°
150 N
C
B
C
D
E
A
.
.
F
9. What is a couple and how it is classified?
10.Distinguish between a moment and a couple.
11.Explain about Force-Couple system.
12.Give the conditions of Equilibrium of rigid bodies in two dimensions.
13.State the procedure for drawing free body diagram of a rigid body.
14.What is meant by Beam and Frame?
15.Discuss about the support reactions and it dependencies.
16.List the types of supports with diagram.
17.What are the different types loads usually applied on a beam?
18.Define Beam and list out its types.
19. An electric light fixture weighing 150 N hangs from a point C, by two strings AC and BC
as shown fig. Determine the forces in the strings AC and BC
.
20. Draw the free body diagram for the sphere’s A and B
21.Draw the freed body at B and C.
D
A
C
B
WB
WC
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60°
30°
120°
1000 N
1000 N
B
A
D
C
PART – B
1. 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 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°
2. Three smooth pipes each weighing 20 KN and of diameter 60 cm are to be placed in a
rectangular channel with horizontal base as shown. Calculate the reactions at the points of
contact between the pipes and between the channel and the pipes. Take width of channel as 160
cm.
3. ABCD is a weightless rod under the action of forces P, Q, S and T as shown in fig. If P = 10
N, Q = 4 N, S = 8 N and T = 12 N, calculate the resultant and mark the same in direction with
respect to the end A of the rod.
C
20 KN
B
20 KN
A
20 KN
G
F
E
D
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P
Q
S
T
A
B
C
D
60°
30°
30°
45°
1 m
1 m
1 m
4. Four forces of magnitude and direction acting on a square ABCD of side 2 m are shown.
Calculate the resultant in magnitude and direction and also locate its point of application with
respect to the sides AB and AD.
5. Calculate the resultant moment about the corner B shown in fig.
6. Forces acting on the Hexagon ABCDEF of side 40 cm are shown in fig. Determine the Net
moment about A.
A
D
B
C
60°
40 KN
15 KN
5 KN
10 KN
10√2 KN
2.5 m
60°
45°
30°
30°
6 KN
4 KN
10 KN
12 KN
A
B
C
D
2 m
A
E
F
D
C
B
3 KN
5 KN
6 KN
2.5 KN
8 KN
4 KN
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50 N
M = 18 Nm
200 N
300 mm
200 mm
60°
A
C
B
125N
7. A 3000 N vertical force is applied to the end of a lever which is attached to a shaft at O as
shown in fig. Determine
i. the moment of 3000 N force about O
ii. the magnitude of the horizontal force applied at A, which created the same amount
about O.
iii. the smallest force applied at A, which creates same moment about O.
iv. How far from the shaft a 750 N vertical force must act to create the same moment
about O.
8. The three forces and a couple of magnitude, M = 18 Nm are applied to an angled bracket as
shown in fig.
a. Find the resultant of this system of forces
b. Locate the points where the line of action of the resultant intersects line AB and line
BC
9.State and Prove Varignon’s theorem.
10. A System of parallel forces are acting on rigid bar as shown in fig. Reduce the system to
i. a single force
ii. a single force and a
couple at A
iii. a single force and a
couple at B
(5)
600 mm
3000 N
A
O
B
60°
30 N
150 N 10 N
70 N
A B C D 1 m 1 m 1.5 m
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W
30°
A
C
D
B
50 cm
25 cm
String 1 String 2
11.Blocks A and B of weight 200 N and 100 N respectively, rest on a 30° inclined plane and are
attached to the post which is held perpendicular to the plane by force P, parallel to the plane, as
shown in fig. Assume that all surfaces are smooth and that the cords are parallel to the plane.
Determine the value of P. Also find the Normal reaction of Blocks A and B.
12.A uniform meter rod AB, assumed rigid of mass 0.5 kg is suspended from its ends in an
inclined position and a mass of 1 kg is suspended from a point D, as shown in fig. Determine the
tension in each string. Where the suspended mass should be placed in order to get equal tension
in the strings.
0.25 m
0.25 m
0.5 m
A
B
P
30°
O
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4 KN
6 KN
16 KN
R1
R2
.
A
B
C
D
R3
1 m 4 m 1 m
4 m
3 m
3 m
13.Find the reactions at the supports A and B of the beam shown in fig.
15.Calculate the reactions R1, R2, and R3 for the two beams AB and CD supported as shown in
fig. There being a Hinge connecting B and C.
UNIT – III
PART - A
1. Define Centre of gravity
2. Define Centroid
3. Write short note on centroid of plane figures.
4. Give the centroids of the following: Rectangle, Right angle Triangle, Semicircle,
Trapezium
5. How you can find centroid of a composite plane figure.
6. Distinguish between centroid and centre of gravity
7. What are the methods to determine centre of gravity?
8. Differentiate between reference axes and centroidal axes.
9. Define moment of inertia of a body
D
B
E
A
C
60°
60°
40 KN
80 KN
50 KN
20 KN/m UDL
60°
2 m 2 m 2 m 2 m
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110 mm
30 mm
30 mm
20 mm
50 mm
20
mm
40 mm
30 mm
10mm
X
Y
O
10. What is meant by moment of moment (I)?
11. State Parallel axis theorem
12. State Perpendicular Axis theorem
13. Give the M.I of the following about XX and YY axis:
a. Rectangle b. Hollow rectangle
c. Triangle d. Circle
14. Give the M.I of the following about XX and YY axis:
a. Square b. Hollow circle
c. Semicircle d. Quadrant
15. What is meant by polar moment of inertia?
16. Define radius of gyration.
17. Give radius of gyration for a rectangular section about XX and YY axis.
18. Define mass moment of inertia of a solid.
19. What is the relation between area moment of inertia and mass moment of inertia?
20. Differentiate area moment of inertia and mass moment of inertia.
21. Define radius of gyration of a solid body.
22. Give Mass M.I of the following:
a. Cylinder b. Sphere
23. Give the Mass M.I of Prism about XX, YY, ZZ and Base.
PART - B
1. Find centroid G for a rectangle by integration.
2. Find the centroid of the lamina shown in fig.
3.
4.
5. Locate the centroid of the
sectioned area shown in fig.
100
Ø 60 Hole
10
80
140
80
80
All dimensions are in mm
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Y
X
O
y
y
x
x
G
60 mm
12 mm
12 mm
40 mm
6 cm
18 cm
20 cm
10 cm
Y
X
O
x
x
y
y
G
100 mm
20 mm
60 mm
6. Determine the area moment of inertia about XX, YY axis and base AB for a rectangular
section.
7. Determine the area moment of inertia about its base AB and XX axis for a triangular
section.
8. Find the moment of inertia of a T section of flange 100 mm x 30 mm and web 20 mm x
80 mm about its centroidal axes.
9. Find the moment of inertia of an I section shown in fig. about its centroidal axes.
10.Find the Polar moment of inertia and radius of gyration of an angle section shown in
fig. about its centroidal axes.
10. Find the moment of inertia of the section
shown in fig. about its horizontal
centrodial axis.
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11. A trapezoidal lamina of 40 mm top edge and 60 mm bottom edge and a height of 60 mm
has a central circular hole of 20 mm diameter. Find out the M.I of the plane about the
longer edge of the trapezium.
12. A hollow square cross section consists of 80 mm x 80 mm square from which is
subtracted a concentrically place square of 40 mm x 40 mm. find the polar moment of
inertia and polar radius of gyration with respect to ‘z’ axis, passing through on of the
outside corners.
13. Determine the mass moment of inertia of a solid cylinder about XX, YY and ZZ axis.
14. Drive the mass M.I of prism about XX, YY, ZZ and Base by integration.
15. Find out Imass about XX, YY and ZZ axis for a Sphere.
UNIT – IV
PART - A
1. Write the expression for the distance traveled by a body with nth
second.
2. A body starts with an initial velocity of 5 m/s and moves with a uniform acceleration of
1.5 m/s2. Find the velocity of the body after 8 seconds.
3. Define curvilinear motion
4. Define relative velocity.
5. What is projectile?
6. Define time of flight.
7. State Newton’s second law of motion.
8. State D’Alembert’s principle.
9. State the law of conservation of momentum.
10. Define impact.
11. A car starts form rest with a constant acceleration of 4 m/s2. Determine the distance
traveled in the 7th
second.
12. Write the equations of motion.
13. Give the equation of the trajectory.
14. Define co-efficient of friction.
15. What is meant by angle of response?
16. Give the expression for belt friction.
17. Define co-efficient of rolling resistance.
18. A car accelerates uniformly from a speed of 30 kmph to a speed of 75 kmph in 5 seconds.
Determine the acceleration of the car and also the distance traveled during 5 seconds.
19. Classify the plane motion.
20. Define trajectory.
21. Range of projection – Explain.
22. State the law of conservation of energy.
23. What is meant by line of impact?
24. Distinguish between perfectly elastic impact and perfectly plastic impact.
25. A train starts from rest and attains a velocity of 45 km per hour in 2 minutes. Calculate
acceleration and distance traveled in this time.
26. Write the equations of vertical upward motion.
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27. Car A travels at a speed of 30 m/s, car B travels at a speed of 20 m/s in the same
direction. Determine,
i. the velocity of Car A relative to Car B
ii. the velocity of Car B relative to Car A.
28. Give the expression for total time of flight (T) and Maximum height hmax.
29. Define types of friction.
30. What is meant by impending motion?
31. What is meant by rolling resistance?
32. State Newtons second law of motion and give the expression for it.
33. A body of mass 4 kg is moving with a velocity f 2 m/s and when certain force is applied,
it attains a velocity of 8 m/s in 6 seconds. Determine that force.
34. Define Energy.
35. Define types of Mechanical Energy.
36. What is meant by Kinetic and Potential Energy?
37. Give the Work-Energy equation and express it terms.
38. What is meant by Work-Energy principle?
39. Define law of Conservation of Energy.
40. What is meant by Impulse?
41. Give the Impulse-Momentum equation?
42. State Law of conservation of momentum.
43. What are the types of impact?
44. What is meant by line of impact?
45. Define co-efficient of restitution.
46. Give the expression for ‘e’ in impact.
PART – B
1. A stone is thrown vertically upwards. It reaches the maximum height 12 m. Determine,
(i) the velocity with which the stone was thrown
(ii) the time takes to each maximum height
(iii) total time taken by the stone, to return to the ground surface, after
projected upwards.
2. Block 2 rests on block 1 and is tensed by a horizontal rope AB to the wall. What force p is
necessary to cause motion of block 1 to impend? The co-efficient of friction between the blocks
is ¼ and between the floor and block 1 is 1/3. Mass of blocks 1 and 2 are 14 kg and 9 kg
respectively. Take the angle made by the force P with the horizontal is 45°.
3. An aeroplane, flying at 750 km/hr, towards west passes over a train, which is traveling at 80
km/hr, towards north. Calculate the velocity of the aeroplane relative to the velocity of the train.
4. A body of mass 15 kg is initially at rest on a 10°inclined plane. Then it slides down. Calculate
the distance moved by the body, on the inclined plane, when the velocity reaches to 6 m/s. The
co-efficient of friction between the body and the plane is 0.1.
5. Two blocks A and B of weight 80N and 60 N are connected by a string, passing through a
smooth pulley as shown in fig. Calculate the acceleration of the body and the tension in the
string.
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6. Two blocks of weight 150 N and 50 N are connected by string and passing over a frictionless
pulley as shown in fig. Determine the acceleration of blocks A and B and the tension in the
string.
7. An aeroplane of mass 8T is flying at a rate of 250 kmph, at aheight of 2 km above the ground
level. Calculate the total Energy possessed by the aeroplane.
8. A car of mass 300 kg is traveling at 36 km/h on level road. It is brought to rest, after traveling
a distance of 5m. What is the average force of resistance acting on the car. Find it by applying (i)
Law of conservation of Energy
(ii) Work-Energy method
(iii) D-Alembert’s principle
9. A car of mass 150 kg is traveling on a horizontal track at 36 km/hr. Determine the time needed
to stop the car. The co-efficient of friction between the tyres and the road is 0.45.
Apply (i) Impulse-momentum principle
(ii) Work-Energy method
(iii) D-Alembert’s principle
10. A 500 N block is in contact with a level plane, the co-efficient of friction between two
contact surfaces being 0.25. If the block is acted upon by a horizontal force of 1300 N, what time
it will elapse before the block reaches a velocity of 24 m/s. Apply impulse-momentum equation.
11. Two bodies one of mass 30 kg, moves with a velocity of 9 m/s strikes on an another body of
mass 15 kg, moving in the opposite direction with the velocity of 9 m/s centrally. Find the
velocity of each body after impact, if the coefficient of restitution is 0.8.
12. Two bodies one of which is 200 N with a velocity of 10 m/s and the other of 100 N with a
velocity of 10 m/s move towards each other and impinges centrally. Find the velocity of each
body after impact if the co-efficient of restitution is 0.6. Find also the loss in kinetic energy due
to impact.
13. A train is traveling from A to D along the track shown in fig. Its initial velocity at A is zero.
The train takes 5 min to cover the distance AB, 2250 m length and 2.5 minutes to cover, the
distance BC, 3000 m in length, on reaching the station C, the brakes are applied and the train
stops 2250 m beyond, at D (i) Find the retardation on CD, (ii) the time it takes the train
to get from A to D, and (iii) its average speed for the whole distance.
UNIT – V
PART – A
1. Give mathematical definitions of velocity and acceleration.
2. A Car traverses half of a distance with a velocity of 40 Kmph and the remaining half of
distance with a velocity of 60 Kmph. Find the average velocity.
3. Define friction and classify its types.
4. Classify the types of friction.
5. Define Limiting friction.
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6. Define coefficient of static friction.
7. State coulomb’s laws of dry friction.
8. Define rolling resistance.
9. What is coefficient of rolling resistance?
10. Define coefficient of friction and express its relationship with angle of friction.
11. If x=3.5t3– 7 t2, determine acceleration, velocity and position of the particle, when t = 5
sec.
12. Consider a wheel rolling on a straight track. Illustrate the characteristics of general plane
motion.
13. Write work energy equation of rigid body. Mention the meaning for all parameters used
in the equation.
14. What us general plane motion? Give some examples.
15. Define Limiting friction.
16. Define Co-efficient of friction and angle of friction
17. Define coulomb’s laws of dry friction.
18. Define impending motion.
19. Define angle of repose
20. Define cone of friction.
21. Define the following terms i) Ladder friction. ii) Wedge friction iii) Screw friction iv)
Belt friction.
UNIT V - PART-B
1. Block (2) rests on block (1) and is attached by a horizontal rope AB to the wall as shown
in fig. What force P is necessary to cause motion of block (1) to impend? The co-efficient of
friction between the blocks is ¼ and between the floor and block (1) is 1/3. Mass of blocks
(1)and(2) are 14kg and 9 kg respectively.
2. Block A weighing 1000 N rests on a rough inclined plane whose inclination to the
horizontal is 45°. It is connected to another block B, weighing 3000 N rests on a rough
horizontal plane by a weightless rigid bar inclined at an angle of 30° to the horizontal as
shown in fig. Find the horizontal force required to be applied to the block B just to move the
block A in upward direction. Assume angle of friction as 15° at all surfaces where there is
sliding.
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3. A 7m long ladder rests against a vertical wall, with which it makes an angle of 45° and on
a floor. If a man whose weight is one half that of the ladder climbs it, at what distance along
the ladder will he be, when the ladder is about to slip? Take coefficient of friction between
the ladder and the wall is 1/3 and that between the ladder and the floor is ½.
4. In a screw jack, the pitch of the square threaded screw is 5.5 mm and means diameter is
70 mm. The force exerted in turning the screw is applied at the end of lever 210 mm long
measured from the axis of the screw. If the co-efficient of friction of the screw jack is 0.07.
Calculate the force required at the end of the lever to (i) raise a weight of 30 KN (ii) lower
the same weight.
5. An effort of 200 N is required just to move a certain body up an inclined plane of angle
15°, the force is acting parallel to the plane. If the angle of inclination of the plane is made
20°, the effort required being again parallel to the plane, is found to be 230 N. Find the
weight of the body and coefficient of friction.
6. Find the force P inclined at an angle of 32° to the inclined plane making an angle of 25
degree with the horizontal plane to slide a block weighing 125 KN (i) up the inclined plane
(ii) Down the inclined plane, when P = 0.5.
7. What should be the value of the angle θ so that motion of the 390 N block impends down
the plane? (fig.) The co-efficient of friction μ for all surfaces is 1/3.
130 N
390 N
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8. A 100 kg mass is lifted by a rope, rolling on a cylinder of 150 mm dia with θ=180°. Determine
the force required on the other side if the co-efficient of friction is 0.20. Also calculate the torque
and power transmitted, if the velocity is 30 m/s.
9. State coloumb’s law of dry friction.