Physics 111: Elementary Mechanics – Lecture 8 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

October 24, 2006Center for Solar-Terrestrial Research Introduction  Collisions  Impulse and Linear Momentum Single Collision Series of Collisions  Momentum and Kinetic Energy  Inelastic Collisions in One Dimension One-Dimensional Collision Completely Inelastic Collision  Elastic Collisions in One Dimension  Collisions in Two Dimensions

October 24, 2006Center for Solar-Terrestrial Research Center of Mass for a System of Particles The center of mass of a body or a system of bodies moves as though all of the mass were concentrated there and all external forces were applied there. 2 bodies, 1 dimension n bodies, 3 dimensions n bodies, 3 dimensions, vector equation

October 24, 2006Center for Solar-Terrestrial Research Center of Mass for a Solid Body Differential mass element dm Uniform density

October 24, 2006Center for Solar-Terrestrial Research Newton’s 2 nd Law for a System of Particles A firework rocket explodes A grand jeté System of particles

October 24, 2006Center for Solar-Terrestrial Research Linear Momentum ParticleSystem Conservation of Linear Momentum If no net external force acts on a system of particles, the total linear momentum P of the system cannot change. If the component of the net external force on a closed system is zero along an axis, then the component of the linear momentum along that axis cannot change.

October 24, 2006Center for Solar-Terrestrial Research Impulse and Linear Momentum Definition of Impulse Impulse–Linear Momentum Theorem Collision of two particle-like bodies Steady stream of projectiles

October 24, 2006Center for Solar-Terrestrial Research Momentum and Kinetic Energy  Closed system (no mass enters or leaves)  Isolated system (no external net force)  Elastic collision (kinetic energy conserved)  Inelastic collision (kinetic energy not conserved)  Completely inelastic collision (bodies always stick together). In a closed, isolated system containing a collision, the linear momentum of each colliding body may change but the total momentum of the system cannot change, whether the collision is elastic or inelastic.

October 24, 2006Center for Solar-Terrestrial Research Inelastic Collisions in 1D Conservation of Linear Momentum Completely Inelastic Collision Velocity of Center of Mass

October 24, 2006Center for Solar-Terrestrial Research Elastic Collisions in 1D Stationary TargetMoving Target In an elastic collision, the kinetic energy of each colliding body may change, but the total kinetic energy of the system does not change.