Engineering Mechanics-Pune-Summer-2016
PUNE UNIVERSITY
B.E. Second Semester
All Branches (C.B.S.)
Time: 2 hours
Maximum marks: 50
Notes :
1. Attempt Q. No. 1 or Q. No. 2, Q. No. 3 or Q. No. 4 and Q. No. 5 or Q. No. 6.
2. Neat diagram must be drawn wherever necessary.
3. Figures to the right indicate full marks.
4. Assume suitable data, if necessary and clearly state.
5. Use of cell phone is prohibited in the examination hall.
6. Use of electronic pocket calculator is allowed.
1. (a) The post is to be pulled out of the ground using two ropes A and B as shown in Fig. 1 (a). Rope A is subjected to a force of 600 N and is directed at 60° from the horizontal. If the resultant force acting on the post is be 1200 N vertically upward, determine the force T in rope B and the corresponding angle θ. [4M]
(b) If a block A of the pulley system is moving downward at 2 m/s while block C is moving down at 6 m/s, determine the relative velocity of block B with respect to C. Refer Fig. 1 (b). [4M]
(c) Water flows from a drain spout with an initial velocity of 0.75 m/s at an angle of 75° with the vertical as shown in Fig. 1(c). Determine the range of values of the distance d for which the water will enter the trough BC. [4M]
(d) Block A has a weight of 300 N and block B has a weight of 50 N. Determine the speed of block A after it moves 1.5 m above the plane, starting from rest by work energy principle. Neglect the friction and mass of the pulleys. Refer Fig, 1 (d). [4M]
OR
2. (a) A slender rod is welded into the shape as shown in Fig. 2(a) Locate the position of centroid of the rod with respect to origin 0 if AO = BO = CO = 50 mm : [4M]
(b) Block B rest on smooth surface. If the coefficient of static and kinetic friction between A and B are μs = 0.4 and μk = 0.3 respectively, determine the acceleration of each block if a block A is push with a force F : [4M]
(a) 30 N
(5) 250 N. Refer Fig. 2 (5)
(c) The man has a mass of 80 kg and sits 3 m from the center of the rotating platform. Due to the rotation his speed is increased from rest by 0.4 m/s2. If the coefficient of static friction between his clothes and the platform is μs = 0.3, determine the time required to cause him to slip. Refer Fig. 2 (c). [4M]
(d) Each of the cable can sustain a maximum tension of 25 kN. If the uniform beam has a weight of 25 kN, determine the shortest time possible to lift the beam with a speed of 3 m/s starting from rest by impulse momentum principle. Refer Fig. 2 (d). [4M]
3. (a) The boom is intended to support two vertical loads, F1 and F2 as shown in Fig. 3 (a). If the cable CE can sustain a maximum load of 1500 N before it fails, determine the critical loads F1 and F2 if F1 = 2F2. Also determine the reaction at A : [6M]
(b) There parallel bolting forces act on the rim of the circular cover plate as shown in Fig. 3 (b). Determine the magnitude, nature and point of application of the resultant force with respect to origin O. [6M]
(c) Determine reaction at A and B for the beam loaded and supported as shown in Fig. 3 (c). [5M]
OR
4. (a) The 30 kg pipe is supported at A by a system of five cords as shown in Fig. 4 (a). Determine the force in each cord for equilibrium. [6M]
(b) A 90 N load is supported from the hook shown in Fig. 4 (b). The load is supported by two cable and a spring having stiffness k = 500 N/m. Determine the force in the cables and the stretch of the spring for equilibrium cable AD lies in the x-y plane and cable AC lies in the x-z plane : [6M]
(c) A simply supported beam loaded and supported is as shown in Fig. 4 (c). If the reaction at supports are equal in magnitude, determine the overhang a. [5M]
5. (a) A uniform hoop of weight W is suspended from the peg at A and a horizontal force P is slowly applied at B as shown in Fig. 5 (a). If the hoop begins to slip at A when θ = 30°, determine the coefficient of static friction between the hoop and the peg. [6M]
(b) Determine the force in each member of the truss as shown in Fig. 5 (b) and tabulate the result with magnitude and nature of force in the members. [6M]
(c) Determine the horizontal and vertical component of reactions at A and B for the frame loaded and supported as shown in Fig. 5 (c). [5M]
OR
6. (a) The uniform pole of length l and mass m is leaned against the vertical wall as shown in Fig. 6 (a). If the coefficient of static friction between supporting surfaces and the ends of the pole is 0.25, calculate the maximum angle θ at which the pole may place before it starts to slip. [6M]
(b) Cable ABCD supports the 4 kg block E and 6 kg block F as shown in Fig. 6 (b). Determine the maximum tension in the cable and the sag of point B. [6M]
(c) The homogeneous semi-cylinder has a mass m and mass center at G as shown in Fig. 6 (c). Determine the largest angle θ of the inclined plane which it rest so that it does not slip down the plane. The coefficient of static friction between the plane and the cylinder is 0.3. [5M]
