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POKHARA UNIVERSITY Level: Bachelor Programme: BE Semester – Spring Course: Applied Mechanics II Year : 2010 Full Marks : 100 Pass Mark : 45 Time : 3 hrs Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks. Attempt all the questions. 1. a. A stone is thrown vertically upward from a point on a bridge 7 located 40 m above the water and that it strikes the water 4 sec after release. Determine (a) speed with which the stone was thrown upward (b) the speed with which the stone strikes the water. b. Car A and B are travelling in adjacent highway lanes and t = 0 8 have the positions and speed shown knowing that car A has a constant acceleration of 0.6 m/s2 and that B has a constant deceleration of 0.4 m/s2. Determine (a) when and where A will overtake B, (b) the speed of each car at that time. A 2. B The 3 kg collar was moving down the rod with a velocity of 3 m/s 15 when a force F was applied to the horizontal cable. Assuming a coefficient of friction 0.2 between the collar and rod. Determine the magnitude of force F if the collar stopped after moving 1 m more down the rod. 1 F 300 3. A spring is used to stop a 75 kg package which is moving down a 15 20° incline. The spring has a constant K = 25 kN/m, and is held by cables so that it is initially compressed 100 mm. The velocity of the package is 6 m/s. When it is 10 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest. Assume μ =0.2. 6 m /s 75 10 kg m Cable 20° 4. A 240 kg space vehicle travelling with velocity VO = 500 k m/s 15 passes through the origin O at t = 0. Explosive charges then separate the vehicle into three parts A, B and C, of mass 40 kg, 80 kg and 120 kg respectively. Knowing that at t = 3 s the positions of three parts are, respectively, A (150, 150, 1350), B (375, 825, 2075) and C (-300, -600, 1200), where the coordinates are expressed in meters, that the velocity of C is VC = -100 i -200 j + 400k m/s, and that the y component of the velocity of B is + 350 m/s. Determine the velocity of part A. 5. A 120 × 180 cm2 rectangle plate weighting 100 N is suspended from 15 two pins A and B. If pin B is suddenly removed, determine angular 2 acceleration of plate. B A 120 cm 180 cm 6. 7. The pulleys shown has a mass moment of inertia of 20 kg m2 and is 15 initially at rest. The outside radius is 0.4 m and the inner radius is 0.2 m. Determine (a) the angular acceleration of each pulley, (b) the angular velocity of each pulley after point A on the cord has moved 3 m. Write short notes on any two: a. Projectile b. Newton’s Second law of motion c. Translation 3 2×5