In Chapters 4 and 5, efforts were directed toward analyzing the transient response and parametric relationships of a dynamic system under impact and/or excitation conditions. The basis for modeling such a dynamic system is Newton’s Second Law. In this chapter, the principle of impulse and momentum and the principle of energy derived from Newton’s Second Law are utilized to solve impulsive loading problems. The solutions to such dynamic problems do not directly involve the time variable. On the subject of impulse and momentum, the basic principles are reviewed first. This is followed by the application of the CG (center of. | CHAPTER 6 IMPULSE MOMENTUM AND ENERGY INTRODUCTION In Chapters 4 and 5 efforts were directed toward analyzing the transient response and parametric relationships of a dynamic system under impact and or excitation conditions. The basis for modeling such a dynamic system is Newton s Second Law. In this chapter the principle of impulse and momentum and the principle of energy derived from Newton s Second Law are utilized to solve impulsive loading problems. The solutions to such dynamic problems do not directly involve the time variable. On the subject of impulse and momentum the basic principles are reviewed first. This is followed by the application of the CG center of gravity motion theorem in an analysis of multiple vehicle collisions and the circle of constant acceleration COCA for the g-loading of vehicles. Impulsive loading can be concentrated or distributed. The distributed loading can be analyzed because the superposition method is applicable to linear systems. Specific design analysis such as the selection of a location for an air bag crash sensor is presented. In the analysis of vehicle occupant collisions without using time as a reference variable it is imperative that both principles be used. This is because collisions between multiple objects involve energy loss and the principle of impulse and momentum provides information about the kinetic and the absorbed structural energies being transferred. In modeling component tests the parametric relationships among the effective weight of the energy absorber the mass ratio and the coefficient of the restitution are presented. Methods of determining vehicle inertia properties such as the CG height and moment of inertia of a vehicle are covered. The formulations of critical sliding velocity CSV rollover dynamics and detection of an incipient rollover using a simple vehicle model are introduced. Extending the local coordinate based COCA method a vector operation in a global coordinate system is used to analyze
