#### Transcript Lecture 8 - Center for Solar-Terrestrial Research

Physics 111: Elementary Mechanics – Lecture 8 Carsten Denker NJIT Physics Department Center 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, 2006 Center 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. xcom m1 x1 m2 x2 m1 m2 2 bodies, 1 dimension n bodies, 3 dimensions 1 n 1 xcom mi xi , ycom M i 1 M rcom 1 M n m r i 1 October 24, 2006 i i n m y i 1 i i and zcom 1 M n m z i 1 i i n bodies, 3 dimensions, vector equation Center for Solar-Terrestrial Research Center of Mass for a Solid Body xcom 1 M xdm, ycom 1 M ydm and zcom 1 M zdm Differential mass element dm Uniform density dm M dV V xcom 1 1 1 xdV , ycom ydV and zcom zdV V V V October 24, 2006 Center for Solar-Terrestrial Research Newton’s 2nd Law for a System of Particles System of particles Fnet Macom A firework rocket explodes A grand jeté October 24, 2006 Center for Solar-Terrestrial Research Linear Momentum Particle p mv System dp Fnet dt P Mvcom dP Fnet dt Conservation of Linear Momentum P const. Pi Pf 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, 2006 Center for Solar-Terrestrial Research Impulse and Linear Momentum Definition of Impulse dp F t dt pf pi Collision of two particle-like bodies dp F t dt tf ti J F t dt tf ti Impulse–Linear Momentum Theorem p f pi p J Steady stream of projectiles October 24, 2006 Center 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 P of the system cannot change, whether the collision is elastic or inelastic. October 24, 2006 Center for Solar-Terrestrial Research Inelastic Collisions in 1D Conservation of Linear Momentum p1i p2 f p1 f p2 f Completely Inelastic Collision m1v1i m1 m2 v m1 v vi m1 m2 Velocity of Center of Mass P Mvcom m1 m2 vcom vcom p p2 i P 1i m1 m2 m1 m2 October 24, 2006 Center for Solar-Terrestrial Research Elastic Collisions in 1D In an elastic collision, the kinetic energy of each colliding body may change, but the total kinetic energy of the system does not change. Stationary Target m1v1i m1v1 f m2 v2 f 1 1 1 m1v12i m1v12f m2 v22 f 2 2 2 m m2 v1 f 1 v1i m1 m2 v2 f 2m1 v1i m1 m2 October 24, 2006 Moving Target m1v1i m2v2i m1v1 f m2v2 f 1 1 1 1 m1v12i m2 v22i m1v12f m2 v22 f 2 2 2 2 m m2 2m2 v1 f 1 v1i v2i m1 m2 m1 m2 v2 f 2m1 m m1 v1i 2 v2i m1 m2 m1 m2 Center for Solar-Terrestrial Research