tutorial_6 - Mechanics tutorial_6 1 The diagram shows the...

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Mechanics tutorial_6.doc 1 1. The diagram shows the plan and elevation of a pluck resting on ice. The pluck receives an offset horizontal blow P as shown. The blow is of short duration and the horizontal component of contact force with the ice is negligible compared with P. Immediately after the impact, the magnitude of V G , the velocity of the centre of mass G, is V o . If the mass of the pluck is m and the moment of inertia about the vertical axis through G is I, determine the angular velocity after impact. x y a P P G G ans: (mV o a/I)k 2. Two rotors, A and B, having moments of inertia 2.1 and 1.26 kg m 2 respectively, are mounted on coaxial shafts that are connected by a friction clutch. Before clutch engagement, A rotates at 2000rev/min and B rotates at 1000 rev/min in the opposite direction. During engagement of the clutches, the developed friction couple increases from zero uniformly with time, and slipping ceases after 7s. Determine the final speeds of the shafts and the angular displacement of A during the period of clutch slip. ans: 875 rev/min, 1194 rad 3. A uniform pole AB of length l and with end A resting on the ground rotates in a vertical plane about A and strikes a fixed object at point P, where AP=b. Assuming there is no bounce, show that the minimum length b such that the blow halts the pole with no further rotation is b=2l/3. 4. The open-linked chain shown below is prevented from moving by the forked rod R at A. The coefficient of friction between the chain and the horizontal surface AB is 0.5 and the surface BC may be taken to be a smooth circular arc of small radius. If the rod R is removed, determine the speed of the chain when the end D has dropped 1m. Neglect the motion of the chain inside the pile at A and assume that there are some links left in the pile. Also assume that the chain does not loose contact with the surface BC. R A B C D 2m 2m ans: 2.316 m/s
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Mechanics tutorial_6.doc 2 5. A roundabout can rotate freely about its vertical axis and a child of mass m is standing on the roundabout at radius R from the axis. The axial moment of inertia of the roundabout is I A . When the angular velocity is o the child leaps off and lands on the ground with no horizontal component of velocity. What is the angular velocity of the roundabout just after the child jumps? ans:
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tutorial_6 - Mechanics tutorial_6 1 The diagram shows the...

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