理论力学第十一章 英文.ppt

Chapter 12: Theorem of Momentum §12.1 The Center of Mass of a System of Particles §12.2 Momentum and Impulse §12.3 Theorem of momentum §12.4 Theorem of motion of the center of mass 3 According to the theorem of motion of the center of mass we have The dynamic reaction caused by the deviation from the center is a periodic function of time. There is a floating hoisting boat of weight P1=200kN with the jib of weight P2=10kN and length l=8m, The weight of the lifted load P3=20kN. Assume that at the initial moment the whole system at rest and the angle between the jib OA and the vertical was ?1=60o, Neglecting the resistance of the water determine the displacement of the boat at the instant when the jib OA makes an angle ?2 =30o to the vertical. Example 1 Choose the system consisting of the hoisting boat with the jib and the load as the object under study. 2 The analysis of the force is shown in the figure. and because the whole system was initially at rest the coordinate of the center of mass of the whole system will remain at rest. Solution: The displacement of the boat is ?x１. The displacement of the jib is The displacement of the weight is The negative sign shows that the boat moves to the left. * §12.4 Theorem of motion of the center of mass §12.1 The center of mass of a system of particles §12.2 Momentum and impulse §12.3 Theorem of momentum The center of mass. The center of mass of a system of particles is called center of mass. It is an important concept representing the distribution of mass in any system of particles. The position of the center of mass c is External forces are the forces exerted on the members of a system by particles or bodies not belonging to the given system Internal forces are the forces of interaction between the members of the same system. As far as the whole system of particles is concerned, the geometrical sum (the principal vector) of all the internal forces of a system is zero. The sum of the mo