l t p c i year - ii semester 4 0 3 enigineering mechanics

Department of Mechanical Engineering, VLITS

L T P C I Year - II Semester

4 0 0 3

ENIGINEERING MECHANICS

(CSE & IT)

Objectives: The students completing this course are expected to understand the concepts of forces

and its resolution in different planes, resultant of force system, Forces acting on a body, their free

body diagrams using graphical methods. They are required to understand the concepts of centre of

gravity and moments of inertia and their application, Analysis of frames and trusses, different types

of motion, friction and application of work - energy method.

UNIT – I Objectives: The students are to be exposed to the concepts of force and friction, direction and its application. Introduction to Engg. Mechanics – Basic Concepts.

Systems of Forces: Coplanar Concurrent Forces – Components in Space – Resultant – Moment of Force and its Application – Couples and Resultant of Force Systems.

Friction: Introduction, limiting friction and impending motion, coulomb’s laws of dry friction, coefficient of friction, cone of friction

UNIT II Objectives: The students are to be exposed to application of free body diagrams. Solution to

problems using graphical methods and law of triangle of forces.

Equilibrium of Systems of Forces: Free Body Diagrams, Equations of Equilibrium of Coplanar

Systems, Spatial Systems for concurrent forces. Lamis Theorm, Graphical method for the

equilibrium of coplanar forces, Converse of the law of Triangle of forces, converse of the law of

polygon of forces condition of equilibrium, analysis of plane trusses.

UNIT – III Objectives : The students are to be exposed to concepts of centre of gravity. Centroid: Centroids of simple figures (from basic principles ) – Centroids of Composite Figures

Centre of Gravity: Centre of gravity of simple body (from basic principles), centre of gravity of composite bodies, Pappus theorems.

UNIT IV Objective: The students are to be exposed to concepts of moment of inertia and polar moment

of inertia including transfer methods and their applications. Area moments of Inertia: Definition – Polar Moment of Inertia, Transfer Theorem, Moments of

Inertia of Composite Figures, Products of Inertia, Transfer Formula for Product of Inertia. Mass

Moment of Inertia: Moment of Inertia of Masses, Transfer Formula for Mass Moments of Inertia,

mass moment of inertia of composite bodies.

Engineering Mechanics (JNTUK 2016-17) Unit-1

S.Rajesh Asst.Prof, Department of Mechanical Engineering, VLITS

UNIT – V Objectives: The students are to be exposed to motion in straight line and in curvilinear

paths, its velocity and acceleration computation and methods of representing plane motion.

Kinematics: Rectilinear and Curvelinear motions – Velocity and Acceleration – Motion of Rigid

Body – Types and their Analysis in Planar Motion. Kinetics: Analysis as a Particle and Analysis

as a Rigid Body in Translation – Central Force Motion – Equations of Plane Motion – Fixed

Axis Rotation – Rolling Bodies. UNIT – VI Objectives: The students are to be exposed to concepts of work, energy and particle motion

Work – Energy Method: Equations for Translation, Work-Energy Applications to Particle

Motion, Connected System-Fixed Axis Rotation and Plane Motion. Impulse momentum method. Text Books :

1. Engg. Mechanics - S.Timoshenko & D.H.Young., 4th

Edn - , Mc Graw Hill publications. References:

1. Engineering Mechanics statics and dynamics – R.C.Hibbeler, 11th

Edn – Pearson

Publ.

2. Engineering Mechanics, statics – J.L.Meriam, 6th

Edn – Wiley India Pvt Ltd. 3. Engineering Mechanics, statics and dynamics – I.H.Shames, – Pearson Publ. 4. Mechanics For Engineers, statics - F.P.Beer & E.R.Johnston – 5

th Edn Mc Graw Hill

Publ. 5. Mechanics For Engineers, dynamics - F.P.Beer & E.R.Johnston –5

th Edn Mc Graw

Hill Publ. 6. Theory & Problems of engineering mechanics, statics & dynamics – E.W.Nelson,

C.L.Best & W.G. McLean, 5th

Edn – Schaum’s outline series - Mc Graw Hill Publ. 7. Singer's Engineering Mechanics: Statics And Dynamics, K. Vijay Kumar Reddy, J.

Suresh Kumar, Bs Publications 8. Engineering Mechanics, Fedinand . L. Singer, Harper – Collins. 9. Engineering Mechanics statics and dynamics , A Nelson , Mc Graw Hill publications



ENGINEERING MECHANICS CONTENTS

UNIT-I

Engineering Mechanics Basics Laws of Mechanics Force & Characteristics System of Forces Resultant of system Components in Space Friction

UNIT-II Free Body Diagram Equilibrium system of forces Lami’s Theorem Equilibrium for spatial system of forces Analysis of Plane Trusses(Beams)

UNIT-III Centroid Center of Gravity Pappu’s and Guldinus Theorems

UNIT-IV Moment of Inertia Product of Inertia Mass Moment of Inertia

UNIT-V Kinematics Motion Types and Analysis Kinetics

UNIT-VI

Work Energy Method Work Energy Method for connected bodies Impulse-Momentum Method



UNIT – I : SYSTEMS OF FORCES AND FRICTION

Objectives: The students are to be exposed to the concepts of force and friction, direction and its application.

Parallelogram law of Forces

1. If two forces magnitude 15 N and 12 N are acting at a point. If the angle between two forces is 60o. Determine the resultant of the forces in magnitude and direction.

2. Two forces are acting at appoint O as shown in figure. Determine the resultant in magnitude and direction.

3. Find the Magnitude of the two forces such that if they act at right angles their resultant is

√10 N. But if they act at 60o their resultant is √13 N. 4. Two equal forces are acting at a point with an angle of 60o between them. If the resultant

force is equal to 20√3 N. Find magnitude of each other. 5. The resultant of two concurrent forces is 1500 N and angle between the forces is 90o. The

resultant makes an angle of 36o with one of the force. Find the magnitude of each force.

Resolution of Force 1. Find the resultant of coplanar concurrent forces acting at the point O.

2. Determine the resultant of the force system shown in figure



3. A system of four forces acting on a body is shown in the fig 2. Determine resultant force

and its direction. [6M]`14

Moment

1. Find the moment of force about point O

2. A horizontal line PQRS is 12m long. Where PQ= QR=RS=4m. Forces of 1000 N,

1500 N and 500 N act at P,Q,R and S respectively with downward direction. The lines of action of these forces make angles of 90, 60, 45 and 30 respectively with PS. Find the magnitude and direction of resultant.



Spatial components

1. If the force multiplier of a force P acting from A to E is Pm= 40N/m, referring Fig. 9Find

out the following (i) Component of P along AC (ii) Moment of P about D

Friction:

1. State the Coloumbs laws of dry friction? 2. A block weighing 1000N is kept on a rough plane inclined at 400 to the horizontal The

coefficient of friction between the block and the plane is 0.4. Determine the smallest force inclined at 150 to the plane required just to move the block up the plane?

3. For the system shown in the figure determine the magnitude P so that the system just starts to move down. Assume that the pulley is smooth and coefficient of friction as 0.26 for horizontal and inclined planes.



4. Block A has mass of 30kg and block B has a mass of 20kg. Knowing that the Coefficient of friction is 0.2, between the two blocks and zero between the block B and the slope, find the magnitude of frictional force between the two masses. What is the force in the string tying the blocks? Refer the fig given below. Take g= 9.81 m/s2?

5. A block weighing 5000N is to be raised by means of a 120 wedge as shown in fig. Assume μ =0.4 for all the surfaces of contact. What is the horizontal force P that should be applied to raise the block? Weight of the wedge is 150N.



UNIT – II: EQUILIBRIUM OF SYSTEMS OF FORCES

Objectives: The students are to be exposed to application of free body diagrams. Solution to problems using graphical methods and law of triangle of forces. Free Body Diagrams, Equations of Equilibrium of Co-planer Systems:

1. A Sphere of weight 100N is tied to a smooth wall by a string as shown in figure. Find the

tension T in the string and reaction R of the wall.

2. A circular roller of radius 5cm and of weight 100N rests on a smooth horizontal surface and is held in position by an inclined bar AB of length 10cm as shown in figure. A horizontal force of 200N is acting at B. Find the tension in the bar AB and the vertical reaction at C.

3. An electric light fixture of weight Q=178N is supported as shown in figure. Determine the tensile forces s1 and s2 in the wires BA and BC if their angles of inclination are as shown

150

450

600

A

200 N B



4. A body weighing 600N is lifted by two ropes passing over a smooth pulley as shown in figure. Determine F1 and F2 .

5. A system of connected flexible cables shown in figure is supporting two vertical forces 200N and 250N at points B and D. Determine the forces in various segments of the cable.

6. A cylinder of weight (W) rests in a trough as shown in figure. Determine the reactions at contact points A and B.

300

600 450

200N

250N

300 600



7. Two cylinders of diameters 30cm and 80cm weighing 60N and 220N respectively are

placed as shown in figure, assuming all the contact surfaces to be smooth. Find the reactions?

8. Three cylinders weighing 100n each and of 80mm diameter are placed in a channel of 180m width as shown in figure. Determine the pressure exerted by (i) the cylinder A on B at the point of contact (ii) the cylinder B on the base and (iii) the cylinder B on the wall

9. Two identical rollers, each of weight 80N are supported by an inclined plane and a vertical wall as shown in the fig..Determine the reactions at the points of supports A,B and C assuming all the surfaces to be smooth. Also find the reaction forces between the spheres?



10. Two rollers of weights P and Q are connected by a flexible string AB. The rollers rest on two mutually perpendicular planeside and EF as shown in figure. Find the tension in the string and the angle θ that it makes with the horizontal when the system is in equilibrium.

11. Three bars, hinged at A and D and pinned at B and C as shown in fig.7 form a four-linked mechanism. Determine the value of P that will prevent movement of bars

Spatial equilibrium

12. Find the force in the string PS, PQ and PR shown

P

Q

D

E

F



13. A tripod is acted upon by forces at ‘P’ as shown in the fig.10 Determine the forces in the

legs of tripod if the legs rest on ground at A, B and C whose coordinates with respect to O are as shown in the Fig.8 The height of ‘P’ above the origin is 10 m.



UNIT – III: CENTROID AND CENTRE OF GRAVITY

Objectives: The students are to be exposed to concepts of centre of gravity. Derivations for rectangle, triangle, circle, semi-circle, circle etc….

1. a) Define centriod and centre of gravity, with examples?

b) Locate the centroid of I section as shown in figure?

2. Locate the centroid of L section as shown in figure?



3. Determine the centriod of the shaded area as shown in figure?

4. a) Define centriod and centre of gravity, with examples?

b) Determine the centriod of the shaded area as shown in figure?

5. a) Differentiate the Centroid and Center of Gravity?


6. a) Differentiate the Centroid and Center of Gravity?




7. Locate the centriod for the shaded area as shown in figure?

8. Determine the centroid of the shaded area shown in the figure?

9. Locate the centroid for the shaded area shown in the figure?



10. Derive an expressions for the centriod of semicircle about base and diametric axis?

11. Find the centriod of the shaded area shown in figure?

12.

13.



14. a) Differentiate between centroid and center of gravity?

b) Find the centriod of the shaded area shown in figure?

15. state and derive pappus and guldnius theorems



UNIT IV : AREA MOMENTS OF INERTIA AND MASS MOMENT OF INERTIA

Objective: The students are to be exposed to concepts of moment of inertia and polar moment of inertia including transfer methods and their applications. Area Moment of Inertia

1. Find the moment of Inertia of the following

2.

3.



4.

Mass Moment of Inertia

5. Find the mass moment of inertia



UNIT – V Objectives: The students are to be exposed to motion in straight line and in curvilinear

paths, its velocity and acceleration computation and methods of representing plane motion.

Equation of Motion in a Straight line

1. An electric train starting from rest attains a max speed of 100kmph in 20 sec. Determine i. Its acceleration assuming in to be uniform ii. Distance covered during time period iii. Its velocity 15 sec after starting from rest

2. A particle under a constant deceleration is moving in a straight and covering a distance of 20mts in 2 sec and 40 m in the 5 sec. Calculate the distance it covers in the subsequent 3 sec and the total distance covered before it comes to rest.

3. A car is tested for acceleration and breaking. In the street start acceleration test the elapsed time 8sec for a velocity increase from 8 kmph to 80 kmph. In the breaking test the distance travelled is 40mts during breaking to stop from 80 kmph. Assuming constant values of acceleration and deceleration. Determine

i. The acceleration during street start test ii. The deceleration during breaking test

Acceleration due to Gravity 4. A small steel ball is shot vertically upward from the top of a building 25mts above the

ground with an initial velocity of 18m/sec i. In what time it will reach the max height ii. How height above the building will the ball rise iii. Compute the velocity with which it will strike the ground and the total time it is in

motion. 5. A stone is dropped into a well hear to the strike the water in 4sec. Find the depth of the well

assuming the velocity of sound to be 335m/sec. 6. The motion of particle is defined by relation x=6t4-8t3-14t2-10t+16 where ‘x’ and ‘t’ are

expressed in meters and sec respectively. Determine the position, velocity and acceleration of particle when t=3sec.

7. A bullet moving at the rate of 250m/sec is fired into a long of wood. The bullet penetrates to a depth of 40cms. If the bullet moving with the same velocity is fired into a similar piece of wood 20cms thick, with what velocity wood is emerged. Resistance to be uniform in both the cases.

Motion with varying Acceleration 8. A particle moves along a straight line its motion is represented by the equation s=16t+4t2-3t2-

3t3 where s is a meters and t in sec. Determine



i. Displacement, velocity and acceleration 2 sec after start ii. Displacement and acceleration when velocity is zero iii. Displacement and velocity hen acceleration is zero

9. The motion of particle is defined by the relation x=6t4-8t3-14t2-10t+16 where x and t are expressed in meters and sec respectively. Determine position, velocity and acceleration of particle when t=3sec.

10. The velocity particle moving in a straight line is given by the expression v=t3-t2-2t+2. The particle is found to be at the distance 4mts from station A after 2 sec. Determine i. Acceleration and displacement after 4sec ii. Max or min acceleration

Curvilinear Motion; Projectile Motion 11. A pilot flying his bomber at a height of 200m with a uniform horizontal velocity of 600kmph

wants to strike a target. At what distance from the target, he should release the bomb. 12. A projectile is aimed at a target on the horizontal plane and falls 12m short when the angle of

projection is 15o, while it overshoots by 24m when the angle is 45o. Find the angle of projection to hit the target.

13. The horizontal component of the velocity of a projectile is twice its initial component. Find the range on the horizontal plane, if the projectile passes through a point 18m horizontally and 3m vertically above the point of projection.

Rigid Bodies 14. A wheel is rotating about a fixed axis at 20 revolutions per minute is uniformly accelerated

for 70 sec during which it makes 50 revolutions. Find the (i) angular velocity at the end of this interval (ii) Time required for the velocity to reach 100 revolutions per minute

Kinetics

1. A block of 25kg mass at rest on an inclined plane is pulled up by a force of 175N magnitude acting parallel to the pulled up by a force of 175N magnitude acting parallel to the inclined plane. Determine the acceleration of the bloc, if the coefficient of kinetic friction between the block and the plane is 0.3.

2. A body weighing 196.3 N slides up a 30o inclined plane under the action of an applied force 300N acting parallel to the inclined plane. The coefficient of friction is 0.2. The body moves from rest. Determine acceleration of the body.

3. A body weighing 120N rests on a rough plane inclined at 12o to the horizontal. It is pulled up the plane by means of a light flexible rope running parallel to the plane and passing over a light frictionless pulley at the top of the plane as shown in fig. The portion of the rope



beyond the pulley hangs vertically down and carries a weight of 800N at its ends. If the coefficient of friction for the plane and the body is 0.2, find

i. Tension in the rope ii. Acceleration with which the body moves up the plane iii. The distance moved by the body in 3sec after starting from rest

4. For the system of connected bodies shown in fig. Determine the velocity and distance moved

by each block 8 sec after release from rest and the tension in the string. Block A and B are 150N and 200N respectively. The coefficient of friction between block A and the contact surface is 0.26 Feb 2016

5. Two rough planes inclined at 30o and 60o to horizontal are placed back to back as shown in

fig. The blocks of weights 50N and 100N are placed on the faces and are connected by a string running parallel to planes and passing over a frictionless pulley. If the coefficient of friction between planes and blocks is 1/3, find the resulting acceleration and tension in the string.



6. Determine the time required for the weights shown in Fig.3 to attain a velocity of 9.81m/sec.

What is tension in the chord? Take μ=0.2 for both planes. Assume the pulleys as frictionless.

7. Two bodies weighing 300N and 450N are hung to the ends of a rope passing over an ideal

pulley as shown in fig. with what acceleration the heavier body comes down? What is the tension in the string?

8. Determine the tension in the string and acceleration of blocks A and B weighing 1500N and 500N connected by an inextensible string as shown in fig. Assume pulleys are frictionless and weightless.



9. Determine the tension in the string and acceleration of blocks A and B weighing 1500N and 500N connected by an inextensible string as shown in fig. Assume pulleys are functionless and weightless.



UNIT-6

Work -Energy

1. Define (i) coefficient of restitution (ii) work-energy principle for the body under translation and rotational

2. Determine the constant force P that will give the system of bodies shown in Fig.8 a velocityof 3m/sec after moving 4.5 m from rest. Coefficient of friction between the blocks and the plane is 0.3. Pulleys are smooth.

3. A block and pulley system is shown in the figure.3. The pulley is friction less. Find the tension in the cable and the velocity of 50kg block after it has moved a distance of 1.5m when the system starts from rest. Neglect the mass of the pulley. Take the coefficient of kinetic friction between the blocks and plane as 0.25. Use the principle of work and energy

Impulse-Momentum

4. (a)State the impulse momentum principle. Write its equation. (b) A body weighing 196.2N slides up a 60o and a force of 400N acting parallel to the inclined plane. The coefficient of friction is equal to 0.2. body moves from rest. Determine (i) Acceleration of the body (ii) Distance travelled by the body in 5 seconds (iii) Work done by the body in 5 seconds. (iv) Momentum of the body after 5 seconds.



5. Determine the tension in the strings and the velocity of 1500n block shown in figure 5 seconds after starting from (a) rest (b) starting with download velocity of 3 m/sec. assume pulleys as weightless and frictionless.

l t p c i year - ii semester 4 0 3 enigineering mechanics

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