INSTITUTE OF AERONAUTICAL ENGINEERING

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1 Department Course Code Course Title INSTITUTE OF AERONAUTICAL ENGINEERING Course Category Course Structure : Course Coordinator Team of Instructors Dundigal, Hyderabad MECHANICAL ENGINEERING TUTORIAL QUESTION BANK : MECHANICAL ENGINEERING : A030 : ENGINEERING MECHANICS : CORE Lectures Tutorials Practical s Credits 5-6 : BDY Sunil, Assistant Professor : BDY Sunil, Assistant Professor Course Objectives: I Students should develop the ability to work comfortably with basic engineering mechanics concepts required for analyzing static structures II Identify an appropriate structural system to studying a given problem and isolate it from its environment, model the problem using good free-body diagrams and accurate equilibrium equations III Identify and model various types of loading and support conditions that act on structural systems, apply pertinent mathematical, physical and engineering mechanical principles to the system to solve and analyze the problem IV Understand the meaning of centre of gravity (mass/centroid and moment of Inertia using integration methods and method of moments V To solve the problem of equilibrium by using the principle of work and energy, impulse momentum and vibrations for preparing the students for higher level courses such as,mechanics of Solids, Mechanics of Fluids, Mechanical Design and Structural etc Short Answer Type S No Question UNIT-I Blooms Taxonomy Level Program Outcome State and explain newtons law of gravitation a,e,k,l Explain the terms - concurrent and non concurrent force system : a,e,k,l planar and non planar system of forces 3 Define the term resultant and equilibrant j,d 4 Define the term moment of a force d,j 5 Explain the procedure to find the resultant of several forces acting at d,j a point 6 What is a couple? State its characteristics a,e,d,j 7 Explain the terms unit vector position vector 8 Explain dot product of vectors d,j 9 Explain the characteristics of the cross products d,j 0 Define the moment of a force about a point write an expression in a,e

2 the vector form Define parallelogram law of forces and give mathematical formulae a,e,k,l Explain in brief free body diagrams a,e,k,l 3 State triangle law and explain Lami s theorem j,d 4 Define the law of polygon of forces d,j 5 Define moment of a couple Give at least five examples where effect d,j of couple is realized 6 Define equilibrium of a body and give conditions of equilibrium a,e,k,l when subjected to forces 7 Two coplanar forces act towards a point with an angle of 45 0 a,e,k,l between them If their resultant is 00kN and one of the forces is 0kN calculate the other force 8 Two forces act at an angle of 0 0 The bigger forces is 60N and the j,d resultant is perpendicular to the smaller one Find the smaller force 9 Two equal forces 0N each act at right angles to each other Find d,j the magnitude and direction of the resultant if that produces the same effect as the two forces 0 A Single force of 0 N is resolved into two concurrent forces of 6 N each Find the angle between them d,j Essay Questions a Define Lami s theorem l,k 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 a Derive an equation for resultant using parallelogram law of d,j,l forces b Find the magnitude of the two forces such that if they act at a,e,l right angles their resultant is sq root 0N But if they act at 60 degrees their resultant is sq root 3N 3 a Explain the different types supports and support reactions d,j b A beam AB is supported and loaded as shown in fig Find the reactions at the supports l,k 4 a State and explain the theorem of Varignon a,e,k b Two spheres, of each of weight 000 N and radius of 5 cm rest in horizontal channel of width 90 cm as shown in fig Find the reactions on the points of contact A, B and D

3 5 a Write the equations of equilibrium when the body is in space d,j,l b A ball of weight Q = N rests in a right - angled trough, as shown in fig Determine the forces exerted on the sides ofthe trough at D (R D and E (R E if all surfaces are perfectly smooth e,d,l 6 a State and explain the laws of forces: (ilaw of parallelogram of forces (ii Law of triangle of forces, (iii Law of polygon of forces b A rigid bar is subjected to a system of parallel forces as shown in Fig 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 l,k a,e 7 a Draw different types of supports and corresponding reactions b A system of connected flexible cables as shown in figure issupporting two vertical forces 40 N and 300 N at points B and D Determine the forces in various segments of the cable

4 8 a Explain the classification of different system of forces 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 9 a Define free body diagram, Transmissibility of a force and resultant of a force 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 0 a Two identical rollers, each of weight 00 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 b Determine the magnitude and direction of the resultant force as shown in fig

5 a Write the Equilibrium equations for concurrent force system in space b A force 00 N is directed from A (, 0, 4 to B (3, 3, 5 What is the moment of force about the origin? A horizontal line ABCD measuring 9m is acted upon by forces of magnitude 400,600,400 and 00N at points A, B, C and D respectively with downward direction These points are so located that AB=BC=CD=3m The line of action of the forces and inclined at 90 0, 60 0, 45 0 and 30 0 respectively with AB Make calculations for the magnitude, position and direction of the resultant 3 a Derive an equation for resultant using parallelogram law of forces b Two equal forces act on a particle such that the square of their resultant is equal is equal to the three times of their product Find the angle between the forces 4 The resultant of two forces acting at a point is 65kN It is observed that one force is double than the other and if the direction of one of them is reversed the resultant becomes 45 kn Find the magnitudes of forces and the angle between them 5 Find the magnitude of two forces such that if they act at right angle, their resultant is 0, but they act at 60 0 their resultant is 3 6 A particle is acted upon by forces equal to P, P, 3 3P and 4P The angle between the first and second, the second and third and fourth are 60 0, 90 0 and 50 0 respectively Find the magnitude and direction of the resultant force 7 The five forces 0N, 30N, 40N, 50N and 60N are acting at one of the angular points of a regular hexagon, towards the other five angular points taken in order Find the direction and magnitude of the resultant force 8 The following forces act at a point a 30kN inclined at 35 0 towards North to East b kn towards North c 30kN inclined at 30 0 towards North to West d 35kN inclined at 5 0 towards South to West Find the magnitude and direction of the resultant force 9 Three forces acting at a point have a resultant of 00N towards north-east One of the forces is of 50 N towards the east The next force act towards 30 0 north of west and has a magnitude of 40N Determine third force in magnitude and l,k d,j,l a,e,l d,j l,k a,e,k d,j

6 direction 0 a Explain different conditions of equilibrium l,k b A lamp weighign 5 N is suspended from the ceiling by means a,e,k of a wire It is pulled to one side by a horizontal cord, until the wire makes an angle of 60 0 with the ceiling Find the tension in the wire and cord UNIT-II Short Answer Type SNo Question Blooms Taxonomy Level Program Outcomes Explain the types of friction with examples? Define the following i Friction ii Angle of friction iii Limiting friction 3 Define the following (iangle of Repose (iicoefficient of frictions 4 Differentiate between static and dynamic friction? 5 State laws of solid friction 6 Distinguish between quarter turn and compound belt drive 7 What is meant by cross belt drive? Explain 8 Define coefficient of friction and limiting friction 9 Distinguish between initial tension and centrifugal tension 0 Write down the conditions for transmission of maximum power Define friction and how can we appreciate the use of friction in practice? What are the effects of friction? 3 State the laws of solid friction 4 Define coefficient of friction and angle of friction How these are related to each other? 5 What do you understand by the limiting friction? And define angle of repose 6 Derive the least inclined force required to drag body resting on a horizontal plane in terms of weight of the dody, angle of the inclined force and angle of friction 7 What is the principle of a screw jack? 8 Derive an expression for the effort required to move a body up an inclined plane when the effort is parallel to the plane 9 Draw a neat sketch of a screw jack and mark salient parts on it 0 Derive the expression for efficiency of screw jack Essay Questions S No Question Blooms Taxonomy Program Level Outcomes a Obtain an equation for the length of the belt in an open belt drive b A ladder 6m long and with 300N weight is resting against a wall at an angle of 60 0 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 a Derive a relation for the efficiency of a screw jack, taking friction into account

7 b An open belt running over two pulleys 00 mm and 500 mm diameters connects two parallel shafts 4000 mm a part The maximum tension in the belt is 830 N Coefficient of friction between the belt and the pulley is 03The driven pulley of 00 mm diameter runs at 00 rpm Determine : a Power transmitted b torque on each of two shafts 3 a Derive an expression for length of crossed belt drive b A ladder 5m long weighing 00N leans against a smooth vertical wall at an angle of 60 0 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 4 a Draw a neat sketch of simple screw jack and derive an expression for minimum effort required to raise a load b Find the effort required at the end of the lever 300mm long of a screw jack, the mean diameter of the screw is 6mm, load acting is 0KN, helical angle is 5 0, and coefficient of friction between screw and nut is 0 5 a What is angle of repose? Prove that angle of repose is equal to the angle of friction b A shaft running at 00 rpm drives another shaft at 00 rpm and transmits kw The belt is 00 mm wide and mm thick and coefficient of friction is 05 the distance between the shaft is 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 6 a Explain the difference between coefficient of friction and angle of friction b A body weighing 50N is just pulled upon inclined plane of 30 0 by a force of 40N applied at 30 0 above the plane Find the coefficient of friction 7 a What is a wedge? Explain how wedge is used to raise the heavy load b A block over lying a 0 0 wedge on a horizontal floor and leaning against a vertical wall and weighing 500N is to be raised by applying horizontal force to the wedge Assume the coefficient of friction between all the surfaces in contact to be 03 Determine the minimum horizontal force to be applied to raise the block 8 a Derive an expression for the velocity ratio of a belt drive considering the thickness of the belt b A leather belt is required to transmit 9KW from a pulley 00mm in diameter running at 00rpm The angle embraced is 65 0 and coefficient of friction between leather belt and pulley is 03 If the safe working stress for the leather belt is 4N/mm, the mass of the leather is 00Kg/m 3 and the thickness of the belt is 0mm, determine the width of the belt taking the centrifugal tension in to the account 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 b An open belt drive connects two pulleys 00mm and 500mm diameter on parallel shafts 4m apart The maximum tension in

8 the belt is 830N The coefficient of friction is 03 The driven pulley of 00mm diameter runs at 00rpm Calculate (a power transmitted (b torque on each of two shafts 0 a Draw a neat sketch of differential screw jack and explain its working b The following are the specifications for a differential screw jack: i Pitch of the smaller screw is 5mm ii Pitch of the larger screw is 0mm iii Lever arm length from center of screw is 500mm The screw jack raises a load of 5KN with an effort of 85N Determine the efficiency of the differential screw jack at this load A weight 500N just starts moving down a rough inclined plane support by a force of 00N acting parallel to the plane and it is at the point of moving up the plane when pulled by a force of 300N parallel to the plane Find the inclination of the plane and the coefficient of friction between the inclined plane and the weight A cord connects two bodies A and B of weights 450 N and 900N The two bodies are laced on an inclined plane and cord is parallel to inclined plane The coefficient of friction for body A is 06 and that for B is 04 Determine the inclination of the plane to the horizontal and tension in the cord when motion is about to take place down the plane 3 A belt is running over a pulley of diameter 800mm at 40 rpm The angle of contact is 65 0 and coefficient of friction between the belt and pulley is 05 if the maximum permissible tension in the belt is 5 kn Find the power transmitted by the belt 4 The initial tension in an open flat belt is 000 N The angle of contact of smaller pulley is 35 0 and μ is 05 The smaller pulleys diameter is 36cm and rotates at 300 rpm Find the power transmitted by the belt 5 A flat belt transmits 5000 W from a shaft running at 300 rpm to another parallel shaft running at the same rpm The maximum permissible tension in the belt is 3kN Find the radius of the pulley consider μ=05 6 Two pulleys, one having diameter 450 mm and other having diameter 00 mm are mounted on parallel shaft and are 000 mm apart For open-belt arrangement, find power transmitted if larger pulley rotates at 50 rpm and μ=03 and maximum tension in the belt is 5kN 7 A belt of density 5 gm/cm 3 has a maximum permissible stress of 300 N/cm Determine the maximum power that can be transmitted by a belt of 5 cm x 5 cm if the ratio of the tension is 5 8 For an open-belt drive transmitting 4kW, the distance between the centre of pulley A and the centre of pulley B is 00cm diameters of pulleys A and B are 30cm and 0cm respectively The coefficient of friction between belt and pulley is 0 The pulley A is rotating at 00rpm If the permissible tensile force per cm width of belt is 80N, determine the width of the belt necessary

9 9 A leather belt of cm thick and 5cm width drives a pulley of 0cm diameter at 80rpm The angle of lap is 90 0 The density of belt material is 5gm/cm 3 If the stress in the belt is limited to 00N/cm, determine (a power transmitted neglecting centrifugal tension and (b considering centrifugal tension Take =03 0 What maximum power is transmitted if the cross section of the belt is 0cm and maximum stress is limited to 400N/cm Density of the belt material =5 cm 3 The ratio of effective tension= UNIT-III Short Answer Type SNo Question Blooms Taxonomy Level Program Outcomes Define and Explain centre of gravity and Distinguish between centre of gravity and centroid b,d,j,l Derive an expression for the centre of gravity of a plane area using method of moments 3 Describe the various methods of finding the centre of gravity of a body 4 What do you understand by axes of reference? Explain Prove that the first moment of area wrt the centroidal axis is zero 5 Explain the difference between the centre of gravity and centre of mass 6 Explain the difference between the centre of gravity and centre of mass 7 How would you find out the centre of gravity of a section, with a cut out hole? 8 State and prove first theorem of Pappus 9 State and prove second theorem of Pappus 0 Where does the centre of gravity of the following section lies (isemi circle, (iitrapezium, (iiihemisphere, (ivright circular solid cone Define CG and moment of inertia b,d,j,l Illustrate the centre of gravity of hemisphere 3 Define a Radius of gyration and b Perpendicular axis theorem 4 Write the moment of inertias of the following plane figures a Hollow rectangle b Semi-circle and c Quadrant 5 Derive an equation for M I of a rectangular section of height h and width b about its centroidal axis 6 Define radius of gyration and express it mathematically 7 State parallel axis theorem with a line diagram 8 Find the CG of a channel section 00 mm x 50 mm x 5mm 9 What is the built-up section? 0 Give the expression for finding centroid Essay Questions S Question Blooms Program

10 No a Find the centroid of a semi circular lamina of radius R from its base 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 Taxonomy Level Outcomes b Find the moment of inertia of the shaded area shown in fig about its centroidal axis parallel to X-axis 3 a Find the centre of gravity of the T lamina as shown in figure All dimensions are in mm 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

11 4 a afind the centroid of the plane lamina shown in _Figure b Find the centroid of the plane lamina shown in _gure 5 a Find the centroid of the shaded plane area shown in figure b Uniform lamina shown in fig consists of rectangle, a semi circle and a triangle Find the centre of gravity 6 a State and prove parallel axis theorem of area moment of inertia b Find the moment of inertia for the shaded area parallel to x axis As shown in the Figure

12 7 a State and prove perpendicular axis theorem b Find the moment of inertia of the area in the given figure about the axis AB 8 Determine the moment of Inertia of a triangle with respect to its centroidal x axis parallel to the base 9 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 0 a Find the moment of inertia about the horizontal centroidal axis of shaded portion for the Figure 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

13 Derive an expression for the moment of inertia of a circular ring of uniform cross section of radius R about its diametrical axis Derive an expression for the moment of inertia of a circular plate of radius R and thickness t about its centroidal axis 3 Determine the moment of inertia of a solid sphere of radius R about its diametrical axis 4 Find the Mass moment of inertia of a rectangular plate of size a x b and thickness t about its centroidal axis 5 Find the Mass moment of inertia of a solid cone of height H and base radius R about axis of rotation an axis through the vertex mormal to the axis of rotation 6 Derive an expression for centroid of triangular area 7 Derive an expression for centroid of sector of a circle 8 Determine the Centroid of the parabolic spandrel as shown in figure 9 a State and prove Pappus-Guldinus First theorem b State and prove Pappus-Guldinus Second theorem 0 Give the expressions for centroid and moment of inertia of any five basic geometrical shapes with figures and details UNIT IV Short Answer Type S N o 3 4 Question Blooms Taxonomy Level Program Outcomes Define the terms velocity and acceleration Define angular displacement angular velocity angular acceleration A stone is thrown vertically upwards and returns in 5secHow high does it go A body falling freely under the action of gravity passes two points 9m apart vertically 0secfrom what height above the higher point did it start to fall?

14 Explain the term recoil of gun How will you find the velocity of the bullet? Explain types of motion and distinguish between uniform motion and accelerated motion A car weighing 8kn rounds a curve of 60mts radius banked at an angle of 30 0 find the frictional force acting on the tires when the is travelling at 9654kmphthe coefficient of friction between tires and road is 06 Derive a relation for the distance travelled by a body in the n th second Define the terms i velocity of projection ii angle of projection iii time of flight iv range of a projectile Obtain an equation for the trajectory of a projectile and show that it is a parabola Explain law of conservation energy Explain D Alembert s principle A force of 0 N acts on a body continuously for 0 seconds and causes it to describe 0m in that line Find the mass (Use s ut gt and F=ma, where u=0 Derive the equation for distance travelled in n th term A ball is thrown vertically upwards with a velocity of 40m/sec Find the position after 5 seconds A shot is fired horizontally from a gun at a height of 9m from the ground Find the initial velocity of shot, if it strikes the ground at a horizontal distance of 000m Explain projectile & trajectory and give examples The horizontal range of projectile is 4 3time its maximum height Find the angle of projection Prove that the equation of the path of projectile is a parabola Show that horizontal range of projectile in u sin g (Where, u=initial velocity of projection Essay Questions S Question Blooms Program

15 N o Taxonomy Level Outcomes The motion of a particle in rectilinear motion is defined by the relation 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 a,b,d,e,j,k,l An auto is accelerated from rest to a speed of 00kmph and then immediately decelerated to a stop If the total elapsed time is 0sec, determine the distance covered The acceleration and deceleration are both constant but not necessarily of the same magnitude 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 6kmph/s until the speed is reduced of 4kmph It is then travels at a constant speed for 400m and then accelerates at 08kmph/s until its speed is once more 90kmph Find the delay period a,b,d,e,j,k,l 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 a,b,d,e,j,k,l 5 A stone is thrown vertically upwards with a velocity of 96m/s from the top of a tower 45m 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 a,b,d,e,j,k,l 6 An aircraft is moving at a speed of 50kmph 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 a,b,d,e,j,k,l a Two bodies of weight 0N and 0N are connected to ends of a 7 light in extensible spring passing over a smooth pulley The weight of 0N is placed on a horizontal surface while the weight of 0N is hanging free in air The horizontal surface is a,b,d,e,j,k,l a rough one, having coefficient of friction between the weight 0N and the plane surface equal to 03 Determine a the acceleration of the system b The tension in the string b Explain the terms momentum of a body and angular momentum of a body a,b,d,e,j,k,l 8 a Two bodies of weights 40N and 5N 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 5N is hanging free in air The a,b,d,e,j,k,l angle of plane is 5 0 Determine a the acceleration of the system b The tension (µ=0 in the string C The distance moved by the weight 5N in 3 seconds starting from rest b State D Alemberts Principle Explain it for a rigid body in plane motion giving equations a,b,d,e,j,k,l 9 a Explain the laws of motion for a body in rotational motion a,b,d,e,j,k,l

16 b A wheel rotating about a fixed axis at 0rpm 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 00 revolutions per minute A stone is dropped into a well while splash is heard after 45 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 A particle starts moving along a straight line with initial velocity of 5m/s, from O under a uniform acceleration of - 5m/s Determine i Velocity, displacement and the distance travelled at t=5 sec ii How long the particle moves in the same direction? What are its velocity, displacement and distance covered then? iii The instantaneous velocity, displacement and the distance covered at t=5 sec, iv The time required to come back to O, velocity displacement and distance covered then and v Instantaneous velocity, displacement and distance covered at t=5 sec Two stations P and Q are 5km apart An automobile starts from rest from the station P and accelerates uniformly to attain a speed of 48 kmph in 30 seconds This speed is maintained until the brakes are applied The automobile comes to rest at the station Q with a uniform retardation of one metre per second Determine the total time required to cover the distance between these two stations A motorist is travelling at 90 kmph, when he observes a traffic light 50m ahead of him turns red The traffic light is timed to stay red for sec If the motorist wishes to pass the light without stopping, just as it turns green Determine (i The required uniform deceleration of motor and (ii The speed of the motor as it passes the traffic light Determine the time required for a car to travel km along a road if the car starts from rest, reaches a maximum speed at some intermediate point, and then stops at the end of the road The car can accelerate or decelerate at 5m/s The velocity of particle moving in a straight line is given by the expression v=t 3 -t -t+ The particle is found to be at a distance 4m from station A after seconds Determine : i Acceleration and displacement after 4 seconds and ii Maximum / Minimum acceleration A ball is thrown from horizontal level, such that it clears a wall 6m high, situated at a horizontal distance of 35m If the angle of projection is 60 0 with respect to the horizontal, what should be the minimum velocity of projection? A ball is thrown from top of building with speed m/s at angle of depression 30 0 with horizontal, strikes the ground 3 m horizontally from foot of the building Determine height of building a,b,d,e,j,k,l a,b,d,e,j,k,l

17 8 9 0 An aeroplane is flying in horizontal direction with a velocity of 540 km/hr and at a height of 00 m When it is vertically above the point A on the ground, a body is dropped from it The body strikes the ground at point B calculate the distance AB (ignore air resistance Also find velocity at B and time taken to reach B a A body is projected at an angle such that its horizontal range is 3 times the maximum height Find the angle of projection b A projectile is aimed at a target on the horizontal plane and falls m short when the angle of projection is 5 0, while it overshoots by 4m when the angle is 45 0 Find the, angle of projection to hit the target A particle projected from a point A, with the angle of projection equal to 5 0 falls short of a mark B on the horizontal plane through A by 5 and when the angle of projection is 45 0 if falls beyond B by same distance Show that for the particle to fall exactly at B, the angle of projection must be 3 sin, the velocity of projection being the same in all 4 the three cases Also determine the velocity of projection UNIT-V Short Answer Type S N Question o Define the following terms: (i Work (ii Energy (iii Impulse and momentum What are the units of work done? What is the relation between Blooms Taxonomy Level Program Outcomes work done and power? 3 Explain the principle of conservation of energy d,j 4 State law of conservation of momentum 5 Explain work-energy method and its applications 6 Explain the terms simple harmonic motion, amplitude, frequency, oscillation and period of simple harmonic motion 7 What are the important types of free vibrations? What type of stresses is 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 9 Define and explain the term torsional vibrations 0 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 Express the equations for the frictional losses interms of load and effort Define: i Machine ii Effort iii MA iv VR

18 v Efficiency vi Ideal machine How levers are classified? Explain them in brief with sketches and d,j give one example for each Explain with the aid of sketch how the speed reduction is achieved using worm and worm wheel Derive an expression for VR in worm & worm wheel What are the applications of screw jack? Explain the principles of screw jack Obtain the expression for the VR in a simple screw jack used to lift loads Given an expression for velocity ratio of rack and pinion In a simple lifting machine an effort of 400 N lifted a load of 0kN What is mechanical advantage? If the machine has an efficiency of 60% what is the VR? Essay Type Questions S N o a b Question Derive work energy equation for translation The bullet weighing 03 N and moving at 660m/s penetrates the 45 N body emerges with a velocity of 80m/s as shown How far and How long the body moves? Take coefficient of friction as 04 Blooms Taxonomy Level Program Outcomes 3 a b a b Derive an expression for kinetic energy of a body rotating about a fixed axis A bullet of mass 5gms 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 Prove that the work done by body is equal to change in its kinetic energy A hammer of mass 500Kg 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

19 4 5 a b a b pile comes to rest after penetrating 5cms in to the ground Define the law of conservation of momentum and prove it A block of mass 5Kgs resting on a 30 0 inclined plane is released The block after travelling a distance of 05m along the inclined plane hits a spring of stiffness 5N/cm Find the maximum compression of the spring Assume coefficient of friction between the block and inclined plane is 0 What is a simple pendulum? Derive an equation for the time period 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 5m Assume the coefficient of friction between block A and the plane is 05, masses of A and B are 00Kgs and 300Kgs respectively a b a b a b a b Explain mathematically the effect of variations in g (acceleration due to gravity on the oscillations of a simple pendulum A flywheel 50KN and having radius of gyration m lost its speed from 400rpm to 80rpm in minutes Calculate (i torque acting on it (ii change in Kinetic Energy (iii change in angular momentum Derive the work energy equation for translation A man wishes to move a wooden box of m 3 to a distance of 5m with least amount of work If the block weighs KN and coefficient of friction is 03, find whether he should tip it of slide it? How a Torsional pendulum differs from simple pendulum? Derive an expression for the time period of a Torsional pendulum 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 Define the term coefficient of restitution State the principle of conservation of linear momentum of a particle Determine the velocity of block B shown in figure after 5s staring from rest

20 a b Define the following (i Kinetic Energy (ii Potential Energy Find the length of a seconds pendulum assuming the value of g as 98m/s A man wishes to move wooden box of metre cube to a distance of 5m with the least amount of work If the block weighs kn and the coefficient of friction is 03, find whether he should tip it or slide it A mass of 0kg is projected up an inclined of 6 0 with velocity of 4m/s If μ=0 i Find maximum distance that the package will move along the plane and ii What will be the velocity of the package when it comes back to initial position? A body weighing 300 N is pushed up a 30 0 plane by a 400 N force acting parallel to the plane If the initial velocity of the body is 5 m/sec and coefficient of kinetic friction is μ=0, what velocity will the body have after moving 6m? Find the power of a locomotive, drawing a train whose weight including that of engine is 40 kn up an incline in 0 at a steady speed of 56kmph, the frictional resistance being 5N/kN While the train is ascending the incline, the steam is shut off Find how far it will move before coming to rest, assuming that the resistance to motion remains the same Two particles of masses 0kg and 0kg are moving along a straight line towards each other at velocities of 4m/s and m/s respectively Determine the velocities of the particles immediately after their collision Also find the loss of kinetic energy A block weighing 500N rests on a level horizontal plane for which coefficient of friction is 00 This block is pulled by a force of 000N acting at an angle of 30 0 to the horizontal Find the velocity of the block after it moves 30m starting from rest If the force of 000 N is then removed, how much further will it move? Use work energy method A wagon weighing 500 kn starts from rest, runs 30 metre down one per cent grade and strikes the bumper post If the rolling resistance of the track is 5 N/kN, find the velocity of the wagon when it strikes the post If the bumper spring which compresses mm for every 5kN determine by how much this spring will be compressed

21 8 9 0 A 0,000 kn train is accelerated at a constant rate up a % grade The track resistance is constant at 9N/kN The velocity increases from 9m/sec to 8m/sec in a distance of 600 metres Determine the maximum power developed by the locomotive Find the power required to pull a train up an incline of in 00 at a speed of 36 kmph, if the weight of the train is 3000 kn and the track resistance is 5 N/kN Also determine the maximum speed with which the train moves up on incline of in 00 with the same power A mine cage weights kn and can carry a maximum load of 0kN The average frictional resistance of the side guides is 500N What constant cable tension is required to give a loaded cage an upward velocity of 3m/sec from rest in a distance of 3m? Prepared by: BDY Sunil Assistant Professor, MED, IARE HOD, MECHANICAL ENGINEERING