Engineering Mechanics Tutorial Question Bank

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INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500 043

MECHANICAL ENGINEERING

TUTORIAL QUESTION BANK 2014 -2015

Course Name : ENGINEERING MECHANICS Course Code : A10302 Class : I - B. Tech Branch : Common for all Branches Year : 2014 2015 Course Faculty : Dr. D Govardhan, B D Y Sunil, Prof. N Krishna Mohan

OBJECTIVES

To meet the challenge of ensuring excellence in engineering education, the issue of quality needs to be addressed, debated and taken forward in a systematic manner. Accreditation is the principal means of quality assurance in higher education. The major emphasis of accreditation process is to measure the outcomes of the program that is being accredited.

In line with this, Faculty of Institute of Aeronautical Engineering, Hyderabad has taken a lead in incorporating philosophy of outcome based education in the process of problem solving and career development. So, all students of the institute should understand the depth and approach of course to be taught through this question bank, which will enhance learners learning process.

Short Answer Questions and Long Answer Questions

S. No Question Blooms Taxonomy

Level

Programme Outcomes

UNIT-I SHORT ANSWER QUESTIONS

1 State and explain Newtons law of gravitation Understand a,e,k,l 2 Explain the terms - concurrent and non concurrent force system :

planar and non planar system of forces Understand a,e,k,l

3 Define the term resultant and equilibrant Remember j,d 4 Define the term moment of a force Remember d,j 5 Explain the procedure to find the resultant of several forces acting at a

point Understand d,j

6 What is a couple? State its characteristics Remember a,e,d,j 7 Explain the terms 1)unit vector 2) position vector Understand a,e,l,k 8 Explain dot product of vectors Understand d,j 9 Explain the characteristics of the cross products Understand d,j

10 Define the moment of a force about a point write an expression in the vector form

Remember a,e

LONG ANSWER QUESTIONS 1 a) Define Lamis theorem Remember l,k

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b) A machine weighing 5KN is supported by two chains attached to some points on the machine. One chain goes to hook in the ceiling and has an inclination of 45 degrees with horizontal. The other chain goes to eye bolt in the wall and is inclined at 30 degrees to the horizontal. Find tensions induced in the chains

Remember a,e,l,k

2 a) Derive an equation for resultant using parallelogram law of forces d,j,l b) Find the magnitude of the two forces such that if they act at right

angles their resultant is sq. root 10N. But if they act at 60 degrees their resultant is sq. root 13N

Remember a,e,l

3 a) Explain the different types supports and support reactions Understand d,j b) A beam AB is supported and loaded as shown in fig.1. Find the

reactions at the supports.

Remember l,k

4 a) State and explain the theorem of Varignon Understand a,e,k b) Two spheres, of each of weight 1000 N and radius of 25 cm rest in

horizontal channel of width 90 cm as shown in fig 1. Find the reactions on the points of contact A, B and D

Remember a,e,l,k

5 a) Write the equations of equilibrium when the body is in space Remember d,j,l b) A ball of weight Q = 12 N rests in a right - angled trough, as shown in fig 1.

Determine the forces exerted on the sides ofthe trough at D (RD) and E (RE) if all surfaces are perfectly smooth.

e,d,l

6 a) State and explain the laws of forces: (i).Law of parallelogram of forces (ii). Law of triangle of forces,

Understand l,k

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(iii) Law of polygon of forces

b) A rigid bar is subjected to a system of parallel forces as shown in Fig 1. Reduce this system to (i) a single force, (ii) a single force-moment system at A and

(iii) a single force-moment system at B.

Remember a,e

7 a) Draw different types of supports and corresponding reactions a,e,l,k b) A system of connected flexible cables as shown in figure issupporting

two vertical forces 240 N and 300 N at points B and D. Determine the forces in various segments of the cable.

Evaluate a,e,l,k

8. a) Explain the classification of different system of forces Understand a,e,l,k b) Determine the magnitude and the direction of the resultant of two

forces 7 N and 8 N acting at a point with an included angle of 60o with between them. The force of 7 N being horizontal

Evaluate a,e,l,k

9. a) Define free body diagram, Transmissibility of a force and resultant of a force

Remember a,e,l,k

b) Two forces are applied to an eye bolt fastened to a beam. Determine the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Evaluate a,e,l,k

10. a) Two identical rollers, each of weight 100 N, are supported by an inclined plane and a vertical wall as shown in figure below. Assuming smooth surfaces, find the reactions induced at the points of support A, B and C.

Remember a,e,l,k

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b) Determine the magnitude and direction of the resultant force as shown in fig

Evaluate a,e,l,k

11. a) Write the Equilibrium equations for concurrent force system in space Remember a,e,l,k b) A force 100 N is directed from A (2, 0, 4) to B (3, 3, 5). What is the

moment of force about the origin? Remember a,e,l,k

UNIT-II SHORT ANSWER QUESTIONS

1. Explain the types of friction with examples? Understand a,e,l,k 2. Define the following

i) Friction ii) Angle of friction iii) Limiting friction

Remember a,e,l,k

3. Define the following (i)Angle of Repose (ii)Coefficient of frictions

Remember a,e,l,k

4. Differentiate between static and dynamic friction? Analyze a,e,l,k 5. State laws of solid friction Remember a,e,l,k 6. Distinguish between quarter turn and compound belt drive Analyze a,e,l,k 7. What is meant by cross belt drive? Explain Remember a,e,l,k 8. Define coefficient of friction and limiting friction Remember a,e,l,k 9. Distinguish between initial tension and centrifugal tension Analyze a,e,l,k 10. Write down the conditions for transmission of maximum power. Remember a,e,l,k

LONG ANSWER QUESTIONS 1. a) Obtain an equation for the length of the belt in an open belt drive Analyze a,e,l,k b) A ladder 6m long and with 300N weight is resting against a wall at

an angle of 600 to the ground. A man weighing 750N climbs the

ladder. At what position along the ladder from bottom does he induce slipping? The coefficient of friction for both wall and the ground with ladder is 0.2.

Remember a,e,l,k

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2. a) Derive a relation for the efficiency of a screw jack, taking friction into account

Analyze a,e,l,k

b) An open belt running over two pulleys 1200 mm and 500 mm diameters connects two parallel shafts 4000 mm a part. The maximum tension in the belt is 1830 N. Coefficient of friction between the belt and the pulley is 0.3.The driven pulley of 1200 mm diameter runs at 200 rpm. Determine : a) Power transmitted b) torque on each of two shafts

Evaluate a,e,l,k

3. a) Derive an expression for length of crossed belt drive Remember a,e,l,k b) A ladder 5m long weighing 200N leans against a smooth vertical

wall at an angle of 600 with horizontal. A man weighing 700N stands at mid-height of ladder when it is about to slip. Calculate the coefficient of friction between the ladder and ground

Analyze a,e,l,k

4. a) Draw a neat sketch of simple screw jack and derive an expression for minimum effort required to raise a load

Remember a,e,l,k

b) Find the effort required at the end of the lever 300mm long of a screw jack, the mean diameter of the screw is 26mm, load acting is 10KN, helical angle is 150, and coefficient of friction between screw and nut is 0.22.

Remember a,e,l,k

5. a) What is angle of repose? Prove that angle of repose is equal to the angle of friction.

Remember a,e,l,k

b) A shaft running at 100 rpm drives another shaft at 200 rpm and transmits 12kW. The belt is 100 mm wide and 12mm thick and coefficient of friction is 0.25. the distance between the shaft is 2.5 m and the diameter of smaller pulley is 500 mm. Calculate the stress in (i) an open belt and (ii) crossed belt, connecting two pulleys

Analyze a,e,l,k

6. a) Explain the difference between coefficient of friction and angle of friction.

Understand a,e,l,k

b) A body weighing 50N is just pulled upon inclined plane of 300 by a force of 40N applied at 300 above the plane. Find the coefficient of friction.

Remember a,e,l,k

7. a) What is a wedge? Explain how wedge is used to raise the heavy load.

Remember a,e,l,k

b) A block over lying a 100 wedge on a horizontal floor and leaning against a vertical wall and weighing 1500N is to be raised by applying horizontal force to the wedge. Assume the coefficient of friction between all the surfaces in contact to be 0.3. Determine the minimum horizontal force to be applied to raise the block.

Evaluate a,e,l,k

8. a) Derive an expression for the velocity ratio of a belt drive considering the thickness of the belt.

Remember a,e,l,k

b) A leather belt is required to transmit 9KW from a pulley 1200mm in diameter running at 200rpm. The angle embraced is 1650 and coefficient of friction between leather belt and pulley is 0.3. If the safe working stress for the leather belt is 1.4N/mm2, the mass of the leather is 100Kg/m3 and the thickness of the belt is 10mm, determine the width of the belt taking the centrifugal tension in to the account.

Evaluate a,e,l,k

9. a) Derive an expression for the ratio of tensions for a flat belt passing over a pulley when it is just on the point of slipping.

Remember a,e,l,k

b) An open belt drive connects two pulleys 100mm and 500mm Analyze a,e,l,k

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Programme Outcomes

diameter on parallel shafts 4m apart. The maximum tension in the belt is 1830N. The coefficient of friction is 0.3. The driven pulley of 1200mm diameter runs at 200rpm. Calculate (a) power transmitted (b) torque on each of two shafts.

10. a) Draw a neat sketch of differential screw jack and explain its working.

Remember a,e,l,k

b) The following are the specifications for a differential screw jack: Pitch of the smaller screw is 5mm Pitch of the larger screw is 10mm Lever arm length from center of screw is 500mm The screw jack raises a load of 15KN with an effort of 185N. Determine the efficiency of the differential screw jack at this load.

Evaluate a,e,l,k

UNIT-III SHORT ANSWER QUESTIONS

1. Define and Explain centre of gravity and Distinguish between centre of gravity and centroid Remember b,d,j,l

2. Derive an expression for the centre of gravity of a plane area using method of moments.

Remember a,e,l,k

3. Describe the various methods of finding the centre of gravity of a body Remember a,e,l,k 4. What do you understand by axes of reference? Explain

Prove that the first moment of area wrt the centroidal axis is zero Remember a,e,l,k

5. Explain the difference between the centre of gravity and centre of mass. Understand a,e,l,k 6. Explain the difference between the centre of gravity and centre of mass. Understand a,e,l,k 7. How would you find out the centre of gravity of a section, with a cut out

hole? Remember a,e,l,k

8. State and prove first theorem of Pappus. Evaluate a,e,l,k 9. State and prove second theorem of Pappus. Evaluate a,e,l,k 10. Where does the centre of gravity of the following section lies

(i). Semi circle, (ii).Trapezium, (iii). Hemisphere, (iv). Right circular solid cone

Remember a,e,l,k

LONG ANSWER QUESTIONS 1. a) Find the centroid of a semi circular lamina of radius R fromits base Remember a,e,l,k b) Determine the Centroid of the parabolic spandrel as shown in

figure.

Evaluate a,e,l,k

2. a) Locate the centroid of shaded area obtained by removing a semicircle of diameter a from a quadrant of a circle of radius a as shown in figure.

Evaluate a,e,l,k

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b) Find the moment of inertia of the shaded area shown in fig. about its centroidal axis parallel to X-axis.

Remember a,e,l,k

3. a) Find the centre of gravity of the T lamina as shown in figure. All dimensions are in mm

Remember a,e,l,k

b) Determine the coordinates of centroid of the shaded area as shown in figure, if the area removed is semicircular. All dimensions are in mm

Evaluate a,e,l,k

4. a) a)Find the centroid of the plane lamina shown in _Figure

Remember a,e,l,k

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b) Find the centroid of the plane lamina shown in _gure

Remember a,e,l,k

5. a) Find the centroid of the shaded plane area shown in figure.

Remember a,e,l,k

b) Uniform lamina shown in fig consists of rectangle, a semi circle and a triangle. Find the centre of gravity.

Remember a,e,l,k

6. a) State and prove parallel axis theorem of area moment of inertia.

Evaluate a,e,l,k

b) Find the moment of inertia for the shaded area parallel to x axis. As shown in the Figure

Remember a,e,l,k

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Programme Outcomes

7. a) State and prove perpendicular axis theorem. Evaluate a,e,l,k b) Find the moment of inertia of the area in the given figure about

the axis AB

Remember a,e,l,k

8. a) Determine the moment of Inertia of a triangle with respect to its centroidal x axis parallel to the base.

Evaluate a,e,l,k

b) Find the moment of the inertia of the section shown in the figure 5 about horizontal and vertical centroidal axes. All dimension in cm R = 8.

Remember a,e,l,k

9. a) Find the moment of inertia about the horizontal centroidal axis of shaded portion for the Figure

Remember a,e,l,k

b) Determine the moment of inertia of the inverted T-section shown in figure about an axis passing through the centroid of the section and perpendicular to the stem

Evaluate a,e,l,k

10. a) Derive an expression for the moment of inertia of a circular ring of Remember a,e,l,k

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Programme Outcomes

uniform cross section of radius R about its diametrical axis b) Derive an expression for the moment of inertia of a circular plate of

radius R and thickness t about its centroidal axis Remember a,e,l,k

11. a) Determine the moment of inertia of a solid sphere of radius R about its diametrical axis.

Evaluate a,e,l,k

b) Find the Mass moment of inertia of a rectangular plate of size a x b and thicknesst about its centroidal axis.

Remember a,e,l,k

12 Find the Mass moment of inertia of a solid cone of height H and base radius R about 1) axis of rotation 2) an axis through the vertex mormal to the axis of rotation.

Remember a,e,l,k

UNIT IV SHORT ANSWER QUESTIONS

1. Define the terms velocity and acceleration Remember a,e,l,k 2. Define angular displacement angular velocity angular acceleration Remember a,e,l,k 3. A stone is thrown vertically upwards and returns in 5sec.How high does

it go Remember a,e,l,k

4. A body falling freely under the action of gravity passes two points 9m apart vertically 0.2sec.from what height above the higher point did it start to fall?

Remember a,e,l,k

5. Explain the term recoil of gun. How will you find the velocity of the bullet?

Understand a,e,l,k

6. Explain types of motion and distinguish between uniform motion and accelerated motion

Understand a,e,l,k

7. A car weighing 18kn rounds a curve of 60mts radius banked at an angle of 300.find the frictional force acting on the tires when the is travelling at 96.54kmph.the coefficient of friction between tires and road is 0.6.

Remember a,e,l,k

8. Derive a relation for the distance travelled by a body in the nth second. Evaluate a,e,l,k 9. Define the terms i) velocity of projection ii) angle of projection iii) time

of flight iv) range of a projectile Remember a,e,l,k

10. Obtain an equation for the trajectory of a projectile and show that it is a parabola.

Evaluate a,e,l,k

LONG ANSWER QUESTIONS 1. The motion of a particle in rectilinear motion is defined by the relation

= 2 9

+ 12 10 where s is in meters and t in seconds. Find

(a) Acceleration of particle when the velocity is zero (b) the position and the total distance travelled when acceleration is zero.

Remember a,b,d,e,j,k,l

2. An auto is accelerated from rest to a speed of 100kmph and then immediately decelerated to a stop. If the total elapsed time is 20sec, determine the distance covered. The acceleration and deceleration are both constant but not necessarily of the same magnitude

Evaluate d,j

3. A train travelling 96kmph has to slow down an amount of work being done on the line. Instead of continuing a constant speed it, therefore moves with a constant retardation of 1.6kmph/s until the speed is reduced of 24kmph. It is then travels at a constant speed for 400m and then accelerates at 0.8kmph/s until its speed is once more 90kmph. Find the delay period


4. The distance covered by a freely falling body in the last one second of its motion and that covered in the last but one second are in the ratio 5:4. Calculate the height from which the body was dropped and the velocity with which it strikes the ground

Analyze a,b,d,e,j,k,l

5. A stone is thrown vertically upwards with a velocity of 19.6m/s from the Analyze a,b,d,e,j,k,l

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top of a tower 24.5m height. Calculate the a) time required for the stone to reach the ground. b) velocity of the stone in its downward travel at the point in the same level as the point of projection. c) The maximum height to which the stone will rise in its flight

6. An aircraft is moving at a speed of 150kmph at an altitude of 750m towards a target on the ground, release a bomb which hits the target. Estimate the horizontal distance of the aircraft from the target when it releases the bomb. Calculate also the direction and velocity with which the bomb hits the ground

Analyze a,b,d,e,j,k,l

7. a) Two bodies of weight 20N and 10N are connected to ends of a light in extensible spring passing over a smooth pulley. The weight of 20N is placed on a horizontal surface while the weight of 10N is hanging free in air. The horizontal surface is a rough one, having coefficient of friction between the weight 20N and the plane surface equal to 0.3. Determine a) the acceleration of the system b) The tension in the string

Evaluate a,b,d,e,j,k,l

b) Explain the terms momentum of a body and angular momentum of a body.

Understand a,b,d,e,j,k,l

8. a) Two bodies of weights 40N and 25N are connected to the two ends of a light in extensible spring passing over a smooth pulley. The weight of 40N is placed on a rough horizontal surface while the weight of 25N is hanging free in air. The angle of plane is 150. Determine a) the acceleration of the system b) The tension (=0.2) in the string. C) The distance moved by the weight 25N in 3 seconds starting from rest


b) State DAlemberts Principle. Explain it for a rigid body in plane motion giving equations.

Understand a,b,d,e,j,k,l

9. a) Explain the laws of motion for a body in rotational motion Understand a,b,d,e,j,k,l b) A wheel rotating about a fixed axis at 20rpm is uniformly

accelerated for 70seconds, during which time it makes 50 revolutions. Find the a) angular velocity at the end of this interval and b) the time required for the speed to reach 100 revolutions per minute


10. A stone is dropped into a well while splash is heard after 4.5 seconds. Another stone is dropped with an initial velocity, v and the splash is heard after 4 seconds. If the velocity of the sound is 336m/s, determine the initial velocity of second stone


UNIT-V SHORT ANSWER QUESTIONS

1. Define the following terms: Work Energy Impulse and momentum

Remember a,e,l,k

2. What are the units of work done? What is the relation between work done and power?

Remember a,e,l,k

3. Explain the principle of conservation of energy. Understand d,j 4. State law of conservation of momentum. Understand a,e,l,k 5. Explain work-energy method and its applications Understand a,e,l,k 6. Explain the terms simple harmonic motion, amplitude, frequency,

oscillation and period of simple harmonic motion. Understand a,e,l,k

7. What are the important types of free vibrations? What type of stresses is Remember a,e,l,k

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produced in case of free vibrations of different types? 8. What are the different methods of finding the natural frequency of free

longitudinal vibrations? Explain in detail any two methods. Remember a,e,l,k

9. Define and explain the term torsional vibrations. Remember a,e,l,k 10. Find the expression for natural frequency of free torsional vibrations

when (i) the effect of inertia of the shaft is not considered (ii) the effect of inertia of the shaft is considered.

Remember a,e,l,k

LONG ANSWER QUESTIONS 1. a) Derive work energy equation for translation. Analyze a,e,l,k

b) The bullet weighing 0.3 N and moving at 660m/s penetrates the 45 N body emerges with a velocity of 180m/s as shown. How far and How long the body moves? Take coefficient of friction as 0.4

Remember a,e,l,k

2. a) Derive an expression for kinetic energy of a body rotating about a fixed axis

Analyze a,e,l,k

b) A bullet of mass 25gms moving horizontal with a velocity of 600m/s strikes a wooden block of mass 5Kg resting on a rough horizontal surface. The bullet after striking the block remains buried in the block and both travels a distance of 90cms before coming to rest. Determine: (a) average resistance between the block and horizontal surface (b) coefficient of friction between block and horizontal surface.

Evaluate a,e,l,k

3. a) Prove that the work done by body is equal to change in its kinetic energy

Evaluate a,e,l,k

b) A hammer of mass 1500Kg drops from a height of 60cms on a pile of mass 750Kg. find (i) the common velocity after impact assuming plastic impact (ii) average resistance of the ground the pile comes to rest after penetrating 5cms in to the ground.

Remember a,e,l,k

4. a) Define the law of conservation of momentum and prove it Remember a,e,l,k b) A block of mass 5Kgs resting on a 300 inclined plane is released.

The block after travelling a distance of 0.5m along the inclined plane hits a spring of stiffness 15N/cm. Find the maximum compression of the spring. Assume coefficient of friction between the block and inclined plane is 0.2.

Remember a,e,l,k

5. a) What is a simple pendulum? Derive an equation for the time period Remember a,e,l,k b) Two blocks A and B are connected with the inextensible string as

shown in figure. The system is released from rest. Determine the velocity of block A after it has moved 1.5m. Assume the coefficient of friction between block A and the plane is 0.25, masses of A and B are 200Kgs and 300Kgs respectively.

Evaluate a,e,l,k

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6. a) Explain mathematically the effect of variations in g (acceleration due to gravity) on the oscillations of a simple pendulum

Understand a,e,l,k

b) A flywheel 50KN and having radius of gyration 1m lost its speed from 400rpm to 280rpm in 2 minutes. Calculate (i) torque acting on it (ii) change in Kinetic Energy (iii) change in angular momentum.

Analyze a,e,l,k

7. a) Derive the work energy equation for translation. Remember a,e,l,k b) A man wishes to move a wooden box of 1m3 to a distance of 5m

with least amount of work. If the block weighs 1KN and coefficient of friction is 0.3, find whether he should tip it of slide it?

Remember a,e,l,k

8. a) How a Torsional pendulum differs from simple pendulum? Derive an expression for the time period of a Torsional pendulum.

Remember a,e,l,k

b) Determine the magnitude and the direction of the resultant of two forces 7 N and 8 N acting at a point with an included angle of 60o with between them. The force of 7 N being horizontal

Evaluate a,e,l,k

9. a) Define the term coefficient of restitution. State the principle of conservation of linear momentum of a particle.

Remember a,e,l,k

b) Determine the velocity of block B shown in figure after 5s staring from rest.

Evaluate a,e,l,k

10. a) Define the following (i) Kinetic Energy (ii) Potential Energy. Remember a,e,l,k b) Find the length of a seconds pendulum assuming the value of g as

9.81m/s2. Remember a,e,l,k

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Engineering Mechanics Tutorial Question Bank