tailieunhanh - Principles of Engineering Mechanics (2nd Edition) Episode 7

Tham khảo tài liệu 'principles of engineering mechanics (2nd edition) episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 116 Momentum and impulse Figure taken for slipping to cease. b Show that the energy lost is VI 2 Solution The horizontal and vertical forces acting on the system are shown in the free-body diagrams Fig. but are not relevant to this problem since they do not appear in the axial moment equations. Figure While the clutch is slipping the couple it transmits is 2o and when slipping ceases the shafts will have a common angular velocity say toC. The directions for 2o are marked on the free-body diagrams on the assumption that to to2. Shaft AB AfG IG to Qo idtoAB d Ổodí Z dtoAB Zj toC toj i Jo J CU Shaft BC AfG ZGto Qo I2 r at Ỡodí z toac Z2 toC toz ii Jo J 02 Adding equations i and ii we obtain Zj Z2 toc Zjto1 Z2to2 0 and we note that for this case there is no change in moment of momentum. The final angular velocity is toC Zjtoj Z2to2 Z1 Z2 iii Until time t when slipping ceases the transmitted couple 2o is constant so that j2odt 0oi iv J 0 Combining equations iii and iv with either i or ii we find Z1Z2 to1 M2 Ô0Ơ1 4 and note that since we have already assumed toj to2 the time taken is positive The energy change final energy minus initial energy is Ỉ Z1 2 c2 2Z1W 2 2I2 ữỉ which after substitution of MC from equation iii and some manipulation is equal to V1 2 toj - M2 2 Example Figure shows a box of mass m on a roller conveyor which is inclined at angle a to the horizontal. The conveyor consists of a set of rollers 1 2 3 . . . each of radius r and axial moment of inertia z and spaced a distance apart. The box is slightly longer than 31. Figure If a 30 r 50 mm z kg m2 m and m 30 kg and if the box is released from rest with the leading edge just in contact with roller 4 a determine the velocity of the box just after the first impulsive reaction with roller 6 takes place and b show that if the conveyor is sufficiently long the box will eventually acquire a mean velocity of m s. Assume that the box makes proper contact with each .

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