UNIT-1 DEPARTMENT OF MECHANICAL ENGINEERING SUBJECT: ENGINEERING MECHANICS (ME101ME/201) Q.1. Q.2. D E. C 1.5m. 60 o A B.

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1 UNIT-1 DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101ME/201) Mr.Nurul Hassan Q.1. Q.2. D E 2 D 1.5m 1 1m 60 o 120mm Radius of ball 1=100mm and ball 2=50mm ; Weight of ball 1=2000N and ball 2 =800N Determine reactions at,,, D Q.3. is hinge joint ylinder 1m diameter and 10kg mass is lodged between cross pieces that makes an angle of 60 0 with each other s shown in Fig. above. Determine the Tension in the horizontal rope DE. P Q S 30 o R Three uniform, homogeneous and smooth spheres, & weighing 300N, 600N & 300N respectively and having diameters 800mm, 1200mm & 800mm respectively are placed in a trench as shown in Fig. above. Determine the reactions at the contact points P, Q, R and S Q.4. rigid circular roller of weight 5000N rest on a smooth inclined plane and is held in position by a chord as shown in Fig below. Find the tension in the chord if there is a horizontal force of magnitude 1000N acting at. 30 o 1000N 20 o

2 Q.5. DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101/201)) UNIT:1 20KN/m Mr.Nurul Hassan 5m 3m D 5m 60 o 30 o E Determine the magnitude of pin reaction at on the horizontal member D. The smooth surface on which the structure rests is horizontal Q.6.. The horizontal force 200N in Fig is applied to the slopping member D whose bottom rests on a smooth horizontal plane. Its upper end is pinned at to the horizontal member. What couple must be applied to the member to hold the system in equilibrium? What is the magnitude of the pin reaction at 16m M 60 o 8m 200N 4m Q.7. 6m 2m D 600N/m D E F 3000Nm 3m 1m 50 o Determine the tension in the wire which is horizontal.

3 SUPPORT RETIONS Q.8.Find support reactions at,e,& D DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101/201) Mr.Nurul Hassan 1m 20KN 3m 1KN 40KN E 45 o.5m D F 60 o.5m 1m 1m 1m 20KN 1KN 1m Q.9. Find resultant reaction at and. 1kN/m 1m 5KN 10KNm 3m 2KN/m 2m 3KN/m 1m 1m 50N 12m 100N Q.10. 3m x Find x to keep the bar in equilibrium. 30 o 45 ns:6.91m

4 DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101/201) Mr.Nurul Hassan Q.1. Determine the magnitude and direction of the resultant of the following set of forces acting on a body. (i) 200N inclined 30 degree with east towards north (ii) 250N towards the north (iii) 300N towards North West (iv) 350N inclined at 40 degree with west towards south. What will be the equilibrant of the force system? (ns: R=456N, 47.7 degree with X-axis in negative direction) Q.2.. Find the resultant of forces 2, 3, 4, 5, 6 N that act at an angular point of a regular hexagon towards the other angular points taken in order. Q.3. uniform wheel of 50cm diameter and 1kN weight rest against a rigid rectangular block of thickness 20 cm as shown in Fig.1. onsidering all surfaces smooth, determine P θ 20cm (a) Least Pull to be applied through the centre of wheel to just turn it over the corner of the block. (b) Reaction of the block Q.4. 1kN force has been resolved into components along and directions in the x-y plane as shown in Fig.2.specified by the angles α and β as shown in Fig. If the component along is 2kN and along is 1.6kN, determine the angles α and β Q.15.Fig below shows a sphere resting in a smooth V shaped groove and subjected to a spring force. The spring is compressed to a length of 100mm from its free Length of 150mm. If the stiffness of spring is 2KN/mm. β Determine the contact reactions at and 100mm k=2kn/mm α 30 o 1kN 40N 30 o 60 o

5 DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101/201) Mr.Nurul Hassan Q.5.Determine the resultant of the forces acting tangential to the circle of radius 3m as shown in Fig given below. What will be its location with respect to the centre of the circle? 150N N 80N 100N Q.6. rigid bar is subjected to a system of parallel forces as shown in Fig given below. Reduce this system to (i) single force (ii) a single force moment system at (iii) single force-moment system at 50N 0.2m 100N 0.15m 70N 0.25m 80N D Q.7.Forces equal to P, 2P, 3P and 4P act along the sides,,d and D of a square D. Find the magnitude, direction and line of action of the resultant. 3P D 4P 2P P Q.8.Three forces equal to 1kn, 2kN and 3kN are respectively acting in order along the three sides of an equilateral triangle. Make calculation for the magnitude, direction and position of their resultant.

6 DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (EME101/201) Mr.Nurul Hassan Q.9.The frictional less pulley shown in Fig is supported by two bars and which are hinged at and to a vertical wall. The flexible cable DG hinged at D goes over the pulley and supports a load of 20KN at G. The angles between various members are shown in Fig. Determine the forces in and. Neglect the size of pulley 60 o G D 30 o 30 o 20KN Q.10. One end of a split horizontal beam is fixed into wall and the other end rests on a roller support. hinge is at point. crane of weight 50KN is mounted on the beam and is lifting a load of 10KN at the end L. The.G of the crane acts along the vertical line D and KL=4m.Neglect the weight of the beam, find the reaction / moments at &. 4m L D W 10KN 1m 1m 4m 8m

7 Q.11. The cross-section of a block is an equilateral triangle. It is hinged at and rests on a rollerat. It is pulled by means of a string attached at. If the weight of the block is Mg and the string is horizontal, determine the force P which should be applied through string to just lift the block off the roller. P 2a a Mg Q m boom weighs 1KN, the distance of the centre of gravity G being 6m from. For the position shown, determine the tension T in the cable and the reaction at 15 o 2.5KN 30 o G Q.13. cylinder of weight 1000N and radius 40cm is in equilibrium as shown in Fig. Find the tension in the rope. Length of is 2m 90 o 60 o

8 UNIT-2 DEPRTMENT OF MEHNIL ENGINEERING SUJET: ENGINEERING MEHNIS (ME101/201) FRITION Mr.Nurul Hassan Q.1. body of weight 100N rest on a rough horizontal surface (µ=03) and is acted upon by a force applied at an angle of 30 degree to the horizontal. (a)what force is required to just cause the body to slide over the surface? (29.53N) (b) Proceed to determine the inclination and magnitude of minimum force required to set the block in to impending motion (28.73N, angle=16.7 degree) Q.2. wooden block of weight 50N rest on a horizontal plane. Determine the force required to just (a) pull it and (b) push it. Take µ=04 between the mating surface. omment on the result (It is easier to pull the block than push it) Q.3. body resting on a rough horizontal plane required a pull of 24N inclined at 30 degree to the plane just to move it. It was also found that a push of 30N at 30 degree to the plane just enough to cause motion to impend. Make calculation for the weight of the body and the co-efficient of friction. (120.25N, 0.192) Q.4.Two blocks & of weight 4kN and 2 kn Respectively are in equilibrium as shown in Fig.1. Presuming that co-efficient of friction between the blocks as well as between block and floor is 0.25, make calculation for the force P required to move the block (P=1.874N) P 30 o Q.5. alculate the force P required to move the lower block and tension in the cable. Take coefficient of friction at all the contact surfaces to be 0.3( P=521.4N, T=147.15N) P cable 50 kg 80kg 30 o

9 Q.6. State whether is stationary with respect to ground and or is stationary with respect to. Determine the minimum value of weight W in the pan so that motion starts.coefficient of friction between ground and block is 0.1 and between block and is 0.28 ( ) 50N 30 o W () 80N Q.7.What should be the value of θ in Fig given below which will make the motion of 900N block down the plane to impend? oefficient of friction all contact surfaces is 1/3 (29.05 degree) 300N 900N Θ Q.8. weight 500 N just starts moving down a rough inclined plane supported by a force of 200N 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? (30degree, ) P Q N 30 degree 750N 60 degree What is the value of P in the system as shown in Fig to cause the motion to impend? ssume the pulley is smooth and coefficient of friction between the other contact surfaces is 0.2 (853.52N) Q N block is placed on an inclined plane as shown in Fig. find the maximum value of W for equilibrium if tipping does not occur. ssume coefficient of friction as 0.2. ( N) 3000N 30 degree W

10 Q.1.Find whether block is moving up or down the plane in Fig. for the data given below. Weight of block and are 300N and 600N respectively. oefficient of friction between plane and block is 0.2.oefficient of friction between plane and block is 0.25.ssume the pulley is smooth. (lock moves up) 60 o 40 o Q.2.Two identical blocks and are connected by a rod and they rest against vertical and horizontal planes respectively as shown in Fig. If sliding impends when θ=45 degree, determine the coefficient of friction, assuming it to be the same for both floor and wall. 45 o Q.3. What is the least value of P to cause motion to impend? ssume the coefficient of friction to be 0.20 (P=162N, o ) 100N θ 150N 60 o Q.4. lock of mass 12kg and block of mass 6kg are connected by a string passing over a smooth pulley. If µ =0.12 at all surfaces P

11 of contact find smallest value of P force to maintain equilibrium.(163.5n) Q. 5. Two blocks are separated by a uniform strut attached to each block. lock weighs 400N, block weighs 300N and strut weighs 200N.I f µ =0.25, find coefficient of friction under to prevent motion 30 o 60 o P θ Q.6. Two block havimg weights W1 and W2 are connected by W1 string and rest on horizontal plane as shown in Fig. If the angle of friction for each block is φ, find magnitude and direction of least force P [Pmin=(W1+W2) sinθ] θ 1 W2 Q.7...two blocks and each of mass 100N are connected by P slender bar of negligible weight. If coefficient of friction at all ontact surfaces is 0.3, determine the largest value of P to maintain Equilibrium. (26.37N) 30 o Q.8. Find whether a cylinder of 800N will slip or not under the action of a tangential force of 200N as shown in Fig. Take µ=0.5 at all contact surfaces.

12 Q.9.Two blocks connected by a horizontal link are supported on two rough planes as shown in Fig. The coefficient of friction for the block on the horizontal plane is 0.4. the limiting angle of friction for block on the inclined plane is 20 degree. What is the smallest weight W of the block for which equilibrium of the system can exist if weight of block is 5kN. (10.49N) 30 o Q.10. Two blocks and each weighing 1500N are connected by a uniform horizontal bar which weighs 1000N.If the angle of limiting friction under each block is 15 degree, find the force P directed parallel to the 60 degree plane that will cause motion impending to the right. (P= N) P 30 o 60 o

13 ELT FRITION Q.11. The mass of is 23 kg and the mass of is 36kg.The coefficient of friction are 0.6 between &,0.2 between and the plane and 0.3 between the rope and fixed drum. Determine the maximum mass of M before motion impends M Q.12.Determine the force P to cause motion to impend.µ=0.25 at all contact contact surfaces. The pulley is frictionless.(p=6.6n) P 9kg 30 o 4.5kg Q.13. Determine the coefficient of friction between the rope and pulley if the coefficient of friction between the block and the plane is N 4 52N

14 TRUSS 20kN Q.1. Find the forces in members, & 60 o 30 o 5m Q.2. Find the forces in members D,,,D &D 30 o 60 o 30 o D 1kN Q.3. Find forces in all members. 10kN D 12kN E o 60 o 30 o

15 Q4. Find the forces in all members? D E F θ θ θ θ θ 4m G H 3m 3m 3m 9kN 12kN Q.5. Find the forces in all members?=d=d=3m 4kN 4kN D E D E 6m Q.6.Find forces in all members? 1kN G D 2.25m 1m E 1m F 1m H 1m

16 Q7. Find forces along all members. Q.8. Find forces along all members. 1kN 1kN D 2m 2m 3m D 4m 1kN E Q.9. Find forces along all members. 12kN D 1.5m 2m 18kN 2m Q.10 Find forces along all members. D E 8kN 1.5m F G 4m 3kN 4m 6kN 4m

17 Q.1.Determine the forces in members,g, EG & GD of the truss shown in Fig below? Roller E 30kN/m G Roller 3m 20kN NS: =21.33(T), G=36.66(T), GD=26.67(T), D EG=50.66() 4m 4m 4m 2. 50N 100N The Pulley is frictionless and fixed at one end and a load of 50N acting on other end.find forces in all member of the truss. Q.3. Find forces in D,DF and GF members. D E 8kN 1.5m F G

18 4m 3kN 4m 6kN 4m Q4. Find forces in DE,E and members. 10kN D 12kN E 60 o 60 o 30 o UNIT-3 1. What do you mean by centre of gravity? Differentiate between centroid, centre of gravity and centre of mass. 2. Explain different methods to determine centroid. 3. Determine centroid of a rectangle and a triangle. 4. Determine centroid of semicircle and quadrant of acircle. 5. Determine centroid of a semicircular arc of radius R. 6. Determine centroid of a circular sector. 7. Find centroid of the given section. 40mm 30mm 10mm

19 8.Find centroid of the given section. 80mm 12mm 12mm 128mm 120mm 10mm 100mm 9.Determine centroid of T-section 20mm 80mm 20mm

20 10.Determine by calculation the position of.g.of the section shown in Fig.2 100mm 25mm 50mm 25mm 50mm 25mm 11.Find the centre of gravity of the shaded section from the Fig given below. D is a square of side equal to radius of the circle D a

21 160mm 12.Find the centroid of Z section as shown in Fig. 30mm 40mm 400mm 40mm 300mm 13.From a circular plate of diameter 100mm, a circular part is cut whose diameter is 50mm. Find the centroid of the remainder. 14. Deternine the centroid of the section given below. 30mm 40mm 10mm

22 40mm 15.Find centroid of shaded area. 10mm 4mm 3mm 16.Find centroid of shaded area. 6mm 4mm 3mm 2mm 2mm

23 17.Find centroid of area remaining after removing a triangle from a circle of diameter 9cm. 6cm 18. semicircle of diameter 100mm has been removed from a trapezium. Determine centroid of the remaining portion 100mm 150mm 200mm

24 19. Determine the ratio a/b for which the centroid will be located at point O for a wire bent as shown in Fig. b b a a 20.Find the centroid of area bounded by x=a, and y=kx n x=a y=kx n 21..Determine area moment of inertia of the given T section about x and y axis x 100mm 20mm 80mm 20mm

25 22.Find area moment of inertia of given I section about x and y axis x 100mm 20mm 20mm 80mm 20mm y 40mm 23. Find area moment of inertia of the above I section about its centroid mm 40mm 10mm 40mm Find moment of inertia about x and y axis. 25. Determine area moment of inertia of the above L section about its.g

26 1. hole of diameter 2a has been removed from a circle of side 4a.find area moment of inertia about x-axis y 2a x 2a 2a 2a 2.Find moment of inertia of regular hexagon of side a about its centroidal x axis. 3. y 10mm x 4mm Find area moment of inertia of shaded area about x and y axis. 4.Determine moment of inertia of the shaded area about its entroid

27 5. Deternine the moment of inertia of the section given below. bout x and y axis y 30mm 40mm 10mm x 40mm 6.Determine the moment of inertia of the above E section about its centroid 7. y (a,b) x Find moment of inertia of the area bounded by y=kx 2 about x and y axis 8.. Determine MOI of the given section about x and y axis y 20mm 20mm x 20mm 20mm

28 UNIT-4& 5 1.What do you mean by plane motion? Explain types of plane motion. 2.Rotation of a flywheel is governed by the relation α=20t-t 2 rad/s 2.How many revolutions will it make before it comes to rest for a moment and starts reversing?ssuming w=0 at t=0 3.What do you mean by Instantaneous centre.write its properties. 4.Due to slipping points and on the rim of wheel of radius 0.8m have velocities as shown in Fig. Determine velocities of centre and point P Vb=8m/sec Ppppp 60 o p Va=5m/sec 5. Two automobile travelling in the same direction in adjacent lanes are stopped at a highway traffic signal. s the signal turns green, automobile accelerates at a constant rate of 1m/s2.Two seconds later automobile starts and accelerates at a constant rate of 1.3m/s2.Determine: 1. When and where will overtake 2. The speed of automobiles at that time 6. Determine the tension in the strings and acceleration of block and weighing 150N and 50N connected by a string and frictionless and weightless pulley as shown in Fig below

29 7. Find acceleration of bodies and tension in the string joining & shown in Fig below 5kg 10kg 15N 8. beam of span 10m carries two point loads as shown in Fig below. Determine the beam reaction by principle of Virtual work 15kN 20kN 4m 2m 10m 9.Find acceleration of the weights & tension in the thread using D lemberts principle Thread 200N 800N 10. The acceleration of a particle is given by m/sec 2 Particle starts with zero velocity at the origin. fter 5 second find out particle's position, displacement, distance travelled, velocity speed and acceleration. 11. The velocity of a particle moving along a space curve is m/sec 2 t the instant when the particle is at the point where the radius of curvature is 2m, find out the acceleration of the particle.

30 12. t a particular instant, the magnitude of the velocity of a particle moving along a space curve is 10 m/sec. Its acceleration is 1 m/sec 2 and it makes 30 0 with the direction of the velocity. Find out the radius of curvature of the space curve at the point where particle is at the moment. 13. particle is rotating in a plane with a constant angular velocity of 1 rad/sec 2. Simultaneously it moves towards center at a constant radial velocity of 10 cm/sec. t the instant when it is 2cm away from the center, find out its acceleration disk is rotating at an angular speed. particle starts in the y direction at an speed v. Find out the absolute acceleration of the particle when it reaches the periphery. 15. motor shaft attains a velocity of 1500 RPM in 3 seconds starting from rest. ssuming constant angular acceleration, find out the number of full revolution of the shaft during this period. 16. motor shaft attains a velocity of 1500 RPM. The angular acceleration of the shaft is highest when the motor attains the speed of 1500 RPM. In between 0 RPM and 1500 RPM, the angular acceleration is a linear function of speed. Find out the time to attain the full speed kg mass slides on a rough floor with a speed of 10 m/sec. 2 kg mass is resting on it. The coefficient of static friction between the 2 kg mass and 10 kg mass is 0.2. The coefficient of kinetic friction between the floor and 10 kg mass is 0.1. It is desired to stop the assembly by applying a horizontal force P, such that the entire assembly consisting of 10 kg and 2 kg mass stops in a minimum distance. However, during stopping 2 kg mass should not slip on 10 kg mass. Find out the maximum force P and minimum stopping distance.

31 18. mass of m kg is being pulled upward by a cable-pulley system. The cable is being pullled with a velocity of v downward. Find out the tension in the cable. 19.

20.Establish relation between linear velocity and angular velocity. 21.Establish the relation between linear acceleration and angular acceleration. 22.State and explain DÁlembert Principle. 23.

32 20.Establish relation between linear velocity and angular velocity. 21.Establish the relation between linear acceleration and angular acceleration. 22.State and explain DÁlembert Principle. 23.Prove that Impulse =hange in momentum 24.Prove work energy principle. 25.State and prove conservation of energy. 26. horizontal bar 1.5m long and of a small cross section rotates about vertical axis through one end. It accelerates uniformly from 1200rpm to 1500rpm in an interval of 5seconds.What is the linear velocity at the beginning and at the end of the interval? What are the normal and tangential components of acceleration of the midpoint of the bar after 5 seconds after the acceleration begins? 27. One ship is sailing south with velocity of 20km/h and another south east with a velocity of 10km/h. Find the velocity of second ship with respect to an observer on the first ship. 28. The acceleration of a particle moving along a straight line is given by the relation a=3(v) 2/3.When t=3sec,its displacement s=37.516m and velocity v=42.87m/s. Determine the displacement, velocity and acceleration when t=5sec 28. The disk has a mass of 100kg and is moving as shown. ompute the magnitude of its linear movement about the point O.

The sliding collar has a constant velocity of 20 m/s to the right at the

33 29. The cart has a mass 100kg and a mass centre at G. Determine its acceleration. 30. The sliding collar has a constant velocity of 20 m/s to the right at the instant shown. Determine the angular velocity of at this instant. 31.ompute the work done by the indicated force when block undergoes the specified displacement.

34 32.The disk has a mass of 100kg. If it rolls without slipping, determine its angular acceleration. For the solution sum moments about the ground point and use kinematics.

PART-A. 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.

PART-A. 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. V.S.. ENGINEERING OLLEGE, KRUR EPRTMENT OF MEHNIL ENGINEERING EMI YER: 2009-2010 (EVEN SEMESTER) ENGINEERING MEHNIS (MEH II SEM) QUESTION NK UNIT I PRT- EM QUESTION NK 1. efine Mechanics 2. What is meant