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Tham khảo tài liệu 'principles of engineering mechanics (2nd edition) episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 96 Energy 7.8 The power equation If the work-energy relationship is written for a small time interval Az then we have ATT A k.e. V A losses Dividing by Ar and going to the limt Az o leads to a k.e. V losses 7.30 dz dr dz or power input equals the time rate of change of the internal energy plus power lost . Let us consider a simple case of a single particle acted upon by an external force p and also under the influence of gravity then d ri P-V ztnv-v tngz mv a mg z If the motion is planar V xi zk a xi zk and P Pxi Pzk so that Pxx Pz z tn xx zz tngz If z X tan a Fig. 7.14 then dividing by X gives Px P2tana mtan2 a i z mg tan a Hence z may be found without considering the workless constraints. z are not apparent but the reader is asked to be patient as later examples will show some of its rewards. A virtual displacement is defined as any small displacement which is possible subject to the constraints. The word virtual is used because the displacement can be any displacement and not necessarily an actual displacement which may occur during some specific time interval. The notation used for a virtual displacement of some co-ordinate say u is 8u. This form of delta is the same as is used in mathematics to signify a variation of u indeed the concepts are closely related. The work performed by the forces in the system over this displacement is the virtual work and is given the notation ỖW. Conditions for equilibrium Let us first consider a single particle which is free to move in a vertical plane subject to the action of two springs as shown in Fig. 7.15. Figure 7.15 From the free-body diagram Fig. 7.16 the condition for equilibrium is liP P1 P2 w o or p2cosa2-PỵCOsaỵ 0 7.31 and Pi sin a J p2sin a2 - mg 0 7.32 Z it Figure 7.14 7.9 Virtual work The concept of virtual work is one which saves a considerable amount of labour when dealing with complex structures since there is no need to dismember the structure and draw free-body diagrams. Basically we shall be using the method
