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Note for ENGINEERING MECHANICS - EM By gokul Nathan

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WWW.VIDYARTHIPLUS.COM ENGINEERING MECHANICS UNIT-I BASICS & STATICS OF PARTICLES 1. What is meant by mechanics? 2. What is meant by Engineering Mechanics? 3. State the different type of mechanics 4. Define Statics 5. Define Dynamics 6. Define Kinematics 7. Define Kinetics 8. What do you understand from the concept of “Law of dimensional homogeneity? 9. State Parallelogram law. 10. State triangle law. 11. Define Lami’s theorem 12. Define principle of transmissibility of forces 13. Define vectors 14. Define Unit vector. 15. The point of application of a force F = 5i + 10j – 15k is displaced from the point I + 3k to the point 3i – j – 6K. Find the work done by the force 16. Given A = 2i – 3j –k and B = I + 4j – 2k. Find A.B and A X B. 17. The following forces act at a point. Determine the resultant force. 18. Two forces F1 = 5i and F2 = 8.66j pass through a point whose coordinates are (2,1)m. Calculate the moment of the forces about the origin. 19. A couple of moment 60Nm acts in the plane of a paper. Indicate this couple with 30N forces. 20. A horizontal bar ABC is hinged at A and freely support over B. Calculate the reaction a B1 if a force of 6KN acts downwards at C. 21. A horizontal beam ABC is hinged at A and freely supported by B. Calculated the reaction at B due to clockwise moment of 12 Nm applied at C. 22. A force F has the components Fx = 50N, Fy = 75N and Fz = 100N. Find out the angles θx, θx, θx that forms with the x, y and z axes. 23. Find the moment of the force about A. If the forces are acting as shown in figure. Figure (Q & A 6) 24. State Varigon’s theorem 25. Define moment of a force about a point. 26. Define a couple. 27. State the conditions for the equilibrium of a two dimensional rigid body. Page 1 of 46 WWW.VIDYARTHIPLUS.COM

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WWW.VIDYARTHIPLUS.COM 28. State the analytical conditions for the equilibrium of coplanar forces in a plane. 29. What is meant by coplanar concurrent force systems? 30. What is the single force that replaces a system of coplanar concurrent forces? 31. Two forces act on a body as shown in fig. Calculate the magnitude of their resultant? Figure 32. How will you resolve a given force into a force and a couple? 33. Differentiate Resultant and equilibrant. 34. A force system has a resultant of 58 KN. The resultant acts at 360 with horizontal. What will be the direction and magnitude of equilibrant. 35. Determine the resultant of the body given below Figure 36. Replace the given system with a couple and force. 37. What is the value of R and S if the system is in equilibrium 38. Find the Value of x Figure 39. Following forces act a point P. a) F1 = 50i b) F2 = -30i -15j c) F3 = -25i -10j + 5k 40. Two forces F1 = 5i and F2 = 8.66j pass through a pint whose co ordinates are (2,1)m. Calculate the moment of the forces about the origin. 41. What are the conditions for the equilibrium of a particle in space? 42. A force 27N makes an angle 30, 45, 80 with x, y, z axes. Find the force vector. 43. A force R = 5i + 2j – 8k KN acts through origin. What is the magnitude of the force and angle it makes with x, y and z axis 44. Take two points (1,2,3), (4,5,6). If a force of 25N is applied between this pints. Find the force vector. 45. A force of 125N makes an angle of 30, 60 and 120 with X,Y and Z axis. Find the force vector. 46. What are fundamental and derived units? Give examples 47. Distinguish between Equal vectors and like vectors. 48. State the equations of equilibrium of a coplanar system of forces 49. Find the resultant of a n 800N force acting towards eastern direction and 500N force acting towards north eastern direction. 50. Distinguish the following types of forces with suitable sketch: a) Collinear and b) Co-planar forces 51. State and explain Lami’s theorem of triangle law of equilibrium. 52. A man has a mass of 72 Kg is standing on a board inclined 200 with the horizontal. Find the component of man’s weight. A) Perpendicular to the plane of the board b) Parallel to the plane of the board. 53. A force is represented by a vector form P = (10i – 8j +14k)N. Determine the projection of this force on a line which originates from (2, -5, 3) and passes through point (5,2,-4) 54. A force of magnitude 750N is directed along AB where A is (0.8, 0, 1.2)m and B is (1.4, 1.2,0) m. Write the vector form of the force. Page 2 of 46 WWW.VIDYARTHIPLUS.COM

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WWW.VIDYARTHIPLUS.COM 55. A force (10i + 20j – 5k) N applied at A (3,0,2)m is moved to point B(6,3,1)m. Find the work done by the force. 56. How many equations of equilibrium are defined for a concurrent force system and coplanar force system? 57. A force F = 700i + 1500j is applied to a bolt A. Determine the magnitude of the force and the angle it forms with the horizontal. 58. Two forces of magnitude 20N and 40N are acting on a particle such that the angle between the two is 1350. If both these forces are acting away from the particle, calculate their resultant and find its direction. 59. A force of magnitude 700N is directed along PQ where P is (0.8,0,1.2)m and Q is (1.4,1.2,0)m. Write the vector form of the force. 60. Define equivalent system of forces. 61. A vector A is equal to 2i – 3j + 2k. Find the projection of this vector on the line joining the point P(-3,2,1) and Q(2,-2,-1) 62. The sum of two concurrent forces F1 and F2 is 300N and their resultant is 200N. The angle between the force F1 and resultant is 900. Find the magnitude of each force. 63. A 100N force acts at the origin in a direction defined by the angles θx = 750 and θy = 450. Determine θz and the component of the force in the z direction. 64. Find the magnitude and direction cosines of the resultant of two concurrent forces F1 = 4i + 8j – 8k and F2 = 5i – 5j + 4k 65. Using Lami’s theorem calculate the forces in the member CA and CB for the system shown in figure 66. A force F has the components Fx = 20N, Fy = -30N, Fz = 60 N. Find the angle θy it forms with the coordinates axes y. 67. What are the characteristics of forces. 68. Explain principles of transmissibility. 69. Define equilibrant. PART – B   1. Two forces F 1 = (-2.0i + 3.3j - 2.9 K) N and F 2 = (-i + 5.2j - 2.9 K) N are concurrent at the point (2,2,-5). Find the magnitude of the resultant of these forces and the angle it makes with positive x-axis.  2. A force is represented by a vector F = 8i - 6j N. Find magnitude of the force and the CCW angle that it makes with +ve x-axis. 3. A force of 200N is directed along the line drawn from the point A(8,2,3)m to the point B(2,4.4,7.8). Find the magnitude of moment of this force about z-axis. 4. A 50N force is directed along the line drawn from point whose x,y,z coordinates are (8,2,3)m to the point whose coordinates are (2,-6,5)m. Find the moment of this force about z axis. Page 3 of 46 WWW.VIDYARTHIPLUS.COM

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WWW.VIDYARTHIPLUS.COM   5. Two vectors A and B are given. Determine their cross product and the unit vector along it.   A = 2i + 3j +k and B = 3i – 3j + 4k. 6. Compute the moment of the 200N force about points A and B for the figure shown below.   , F 2 = −2i − j + 4k and 7. Determine the resultant of three forces F 1 = 3i + 2 j + 5k  F 3 = 7i − 3 j + 6k which are concurrent at the point (1, -6,5). The forces are in N and the distances are in metres.  8. A force F = 5i + 2 j + 4kis acting at a point A whose position vector is given by )4i + 2j – 3k). find the moment of the force about the origin. 9. The coordinates of the initial and terminal points of a vectors are (4,5,2) and (6, -3,9) respectively. Determine the components of the vector and its angles with the axes. 10. An inclined plane makes 45 0with the horizontal. A body of weight 1000N is acted by three forces such F = 150N, T =1300N and R = 500N as shown in figure. Find the resultant force acting on that body.      in terms of I, j, k and it magnitude. Take A =i-2j-3k; B =4i11. Find the vector 2A + 3B + 5C  3j+2k; C =0.5i +j-k      12. Find the vector (- -2 A B -3 C ) in terms of i,j,k and its magnitude. Take A =4i-3j+7k; B =3i 2j-5k; C = 2i-j-4k 13. Find the unit vector along the line which originates at the point (3,4, -3) and passes through the point (2,1,6). 14. Resolve the force 250N acting on the joint as shown in figure. Into components in the (a) x and y directions and (b) x 1 and y1 directions. Page 4 of 46 WWW.VIDYARTHIPLUS.COM

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