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