2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system.

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1 Code No: R21031 R10 SET - 1 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) How do you resolve a force into a force couple system about another point? Explain. b) The parallel force system of five forces of magnitudes 12 kn, 15 kn, 24 kn, 30 kn, and 20 kn is shown in the Figure1. Reduce them to a force and couple at the point P. 2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system. b) Determine the reactions at all the supports of the beam / structure shown in Figure a) What is centroid? Derive an expression for the centroid of a sector of a circle. b) Find the centroid of the shaded plane area shown in the Figure 3. (7M+8M) 1 of 3 ''' ' '' '' ''

2 Code No: R21031 R10 SET a) State and prove the Parallel axis theorem to find the M.I. of a plane area w.r.t. any reference axis in its plane. b) The shaded area shown in the Figure 4 is 125 cm 2. If I xx = 35,000 cm 4, I x'x' = 70,000 cm 4, and d 2 = 7.5 cm, determine the distance d 1 and the M.I. of the area w.r.t. the centroidal axis parallel to the axis x x. (5M+10M) 5. a) Explain the procedure to determine the forces in the members of a perfect frame by the method of joints. b) Determine the forces induced in the members of the pin jointed truss shown in the Figure 5. Show the values on a neat diagram of the truss, and mention clearly the nature of the force (tension or compression) in each member. 6. a) Derive the expressions for the magnitude and direction of the rectangular component of acceleration of a particle moving along a curved path. b) The motion of a particle in rectilinear motion is defined by the relation : s = 2t 3 9t t 10, where s is expressed in meters and t in seconds. Determine: i) The acceleration of the particle when the velocity is zero. ii) The position and total distance travelled by the particle when the acceleration is zero. 2 of 3

3 Code No: R21031 R10 SET a) State and prove the Work Energy principle. b) A 200 N block is originally at rest on a horizontal surface, for which the coefficient static friction is 0.6 and the coefficient of kinetic friction is 0.5. If a horizontal force is applied such that it varies with time as shown in the Figure 6, determine the speed of the block in 10 seconds. F(N) F 200 o 5 10 t (s) Figure 6 8. a) State the Coulomb s laws of friction. Also explain the terms Dry friction and Cone of friction. b) The mean diameter of threads of a square threaded screw is 50 mm. The pitch of the thread is 6 mm. The coefficient of friction is What force must be applied at the end of a 600 mm lever, which is perpendicular to the longitudinal axis of the screw to raise a load of 17.5 kn, and to lower the same load? 3 of 3

4 Code No: R21031 R10 SET - 2 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) State and prove (i) Varignon s theorem, and (ii) Law of Parallelogram of forces. b) The four forces shown in the Figure 1 are to be replaced by one force and moment about A. Find the magnitudes of this force and moment. 2. a) Explain the equilibrium of i) Collinear force system, and ii) Parallel force system. b) Determine the reactions at all the supports of the beam / structure shown in Figure 2. 1 of 3

5 Code No: R21031 R10 SET a) State and prove the first and second Pappus Guldinus theorems. b) A composite solid built by a cone, cylinder, and hemisphere is shown in the Figure 3. Locate the centroid w.r.t. the origin. (8M+7M) 4. a) Describe the procedure to find the mass moment of inertia of a thin circular ring. b) ABC is an isosceles triangle of base 100 mm and height 90 mm. A square of side a, with its geometric center at a distance of 30 mm from the base of the triangle, is removed from the triangular lamina. If the M.I of the net figure is 80 % of that of the original triangle, find the size of the square. 5. a) In a cantilever truss, support reactions are not required for the analysis of truss Justify and explain this statement with a suitable example. b) Find the force in the member AD of the plane truss shown in Figure 4. by the method of sections. 2 of 3

6 Code No: R21031 R10 SET a) Draw the acceleration time (a t) curve for rectilinear motion of a particle. How do you find the displacement and the change in velocity of the particle from the a t curve? b) In curvilinear motion, a particle P moves along the fixed path given by 9y = x 2, where x and y are expressed in cm. At any instant t, the x coordinate of P is given by x = t 2 14 t. Determine the y component of the velocity and acceleration of P when t = 15 seconds. 7. a) Distinguish between centroidal rotation and non centroidal rotation of a rigid body about a fixed axis. b) A spring mass system has a mass m attached to a spring from the ceiling. When the mass hangs freely, it stretches the spring by a distance C. Show that, if the mass is suddenly released, the spring stretches a distance of 2C before the mass starts to return upward. 8. a) Distinguish between static friction, limiting friction, and kinetic friction. b) Two rectangular blocks of weights W 1 = 150 N, and W 2 = 100 N are connected by a string, and rest on a horizontal surface and on an inclined plane, as shown in Figure 4. The coefficient of friction for all the contiguous surfaces is 0.2. Find the magnitude and direction of the least force P at which the motion of the blocks will impend. 3 of 3

7 Code No: R21031 R10 SET - 3 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) Explain the procedure to find the resultant of : i) Concurrent force system ii) Parallel force system b) The resultant of four vertical forces is a couple of 300 N-m about the centre 0. Three of these forces are shown in the Figure 1. Determine the fourth force. (8M+7M) 2. a) State and prove Lami s theorem. What are its limitations? b) Determine the reactions at all the supports of the beam / structure shown in Figure a) Describe the procedure to locate the centroid of a composite area. b) Show that the coordinates of the centroid G of the area between aparabola y x2 a a 2a. and a straight line y = x (as shown in Figure) are given by : x =, y = 2 5 (5M+10M) 1 of 2

Code No: R21031 R10 SET - 3 4. a) How do you find the M.I. of a triangle about the centroidal axis parallel to the base? Describe the procedure, assuming the base equal to a and height equal to h.

8 Code No: R21031 R10 SET a) How do you find the M.I. of a triangle about the centroidal axis parallel to the base? Describe the procedure, assuming the base equal to a and height equal to h. b) Determine the M.I. of the shaded area shown in the Figure 3 about the centroidal x axis and the centroidal y axis. All dimensions in the figure are in cm. (8M+7M) 5. a) What is a perfect truss? Sketch at least four examples of perfect trusses, and show that they satisfy the relationship between the number of members, number of joints, and the number of support reaction components. b) For the truss loaded as shown in Figure 4, find the forces in the members CE and CF by the method of sections. (8M+7M) 6. a) Explain the curvilinear motion by the tangential and normal component method. b) Two trains P and Q start from the same station on parallel lines. The train P starts from rest with y uniform acceleration of 0.2 m / s 2, and attains a speed of 10 m / s. Further the speed is kept constant. The train Q leaves 30 seconds later with uniform acceleration of 0.5 m / s 2 from rest, and attains a maximum speed of 20 m / s. When will the train Q overtake P? 7. a) State and derive the Impulse Momentum principle. b) The armature of an electric motor comes to rest in x seconds after the power is cut off. If the armature speed was n rpm before the power was cut off, what is its angular deceleration, assuming it to be uniform? What are the number of revolutions made by the armature before stopping? 8. a) Derive the expression for screw friction. b) A person of weight W is ascending a 5 m ladder which is held against a smooth wall at an inclination of 40 0 with the horizontal ground. If the coefficient of friction between the ladder and ground is 0.3, how far up the ladder may the person climb before the sliding motion of the ladder takes place? 2 of 2

9 Code No: R21031 R10 SET - 4 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) Explain the composition of forces by the method of resolution. b) Determine the resultant force and moment acting on a body, whose centroid is (2,2,2) Due to the following forces / moments. M 1 = (12 i + 10 j + 8 k) kn-m at A (0,2,0) M 2 = (4 i + 10 j - 8 k) kn-m at B (2,1,2) M 3 = ( i + 2 j + 3 k) kn-m at D (2,4,3) F 1 = (4 i + 5 j - 6 k) kn-m at C (4,3,4) F 2 = (5 j - 5 k) kn-m at B (2,5,7) 2. a) Explain the types of supports, and indicate the unknown reactions they offer. b) Determine the reactions at all the supports of the beam / structure shown in Figure Prove that the centroid of the shaded area shown in the Fig.2 w.r.t. the x and y axes 2 3 r sin α 3 is given by : x = sin 2α. (15M) α 2 1 of 3

10 Code No: R21031 R10 SET a) State and prove the Perpendicular axis theorem to find the M.I. of a plane area. b) Find the M.I. of a section shown in the Fig3 about the : i) x axis ; ii) y axis ; iii) Parallel centroidal x axis ; and iv) Parallel centroidal y axis. (4M+11M) 5. a) State the assumptions for a perfect truss. b) A simple plane truss is shown in Figure 4. Two 1,000 N loads are acting on the pins at C and E. Determine the forces in all the members, using the method of joints. (5M+10M) 6. a) Derive the relation for the component of normal acceleration of a particle moving along a curved path. b) A particle under a constant deceleration is moving in a straight line, and covers a distance of 20 m in the first two seconds and 40 m in the next 5 seconds. Calculate the distance it covers in the subsequent 3 seconds, and the total distance covered before it comes to rest. 7. a) Explain the following terms : i) Impulse, ii) Impact, iii) Momentum, iv) Coefficient of restitution. b) A 50 gm golf ball is hit at an angle of 40 0 with the horizontal. The ball leaves the Tee, and lands at the same elevation 15 maway. Determine the impulse on the ball. (8M+7M) 2 of 3

11 Code No: R21031 R10 SET a) What is a wedge, and where is it used? Why is the coefficient of static friction greater than the coefficient of kinetic friction? b) In the Figure 5 shown below, the wedge is used to level the member. For the loading shown, determine the horizontal force P that must be applied to move the wedge to the right. The coefficient of static friction between the wedge and its surfaces of contact may be taken as 0.25.

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.