Esys W Q psys Fnet t Lsys nett Real vs. Point Particle System July 13 2010 Chapter 9, Section 4-6 Real vs. Point: A cow M = mass of cow co2calculator.files.wordpress.com/2008/09/grazing-cow-1b.jpg Real System Use the actual physical shape of the object Contains all forms of energy in the system Translational, Rotational, Vibrational, Potential, Chemical, … Can have multi-object systems Point Particle System The system is a single point Located at Center of Mass Everything else is surroundings System only has Translational KE Work is done on the point f K W F dr F r trans net cm net i Real vs. Point In both cases 1 K Mv2 trans 2 cm This is the same Kinetic Energy A real system will have additional behavior due to location of forces Example: The Jumper F = mg Normal Normal Force Force F = mg Clicker Question #1 What force(s) contribute to total work in the Real System? F = mg A) Normal Force only Normal Force B) Normal Force and Gravity C) Gravity only D) None, the feet never leave the ground so there is no work done Normal Force and Work Does not do work in real system A contact force Only exists when 2 objects touch Forces point of contact never moves Can do work in point system Can act on the COM over a distance Force is in contact at the COM, which moves Example: The Jumper Normal Force does not do work in real system FN Esys Ktrans EChem Ethermal mgh Normal Force does work in Point system Ktrans (FN mg)h Echem Etherm FN h Energy was used Example: Stretching a Spring Real System: Work done by each force separately Espring Wtot Fl *rl Fr *rr Point System Work done by net force only Ktrans W Fnet *r 00 Why Use Point Particles Reduction in complexity Fewer forms of energy to worry about Allows easier calculation of vcm Can make difficult problems simpler Limits of Point Particle Does not take into account all forms of energy Can’t give information about rotation, vibration, etc. Not Physical Does not indicate if the system is changing shape Example: Yo-Yo The hand moves up a distance d The Yo-Yo moves down a distance h Esys Ktrans Krot Whand WEarth Use point particle to find Ktrans Then find Krot Yo-Yo –Point Particle System: yo-yo Surroundings Earth, Hand Ktrans W Fnet ycm ycm h Fnet Fhand mg Ktrans (mg Fhand )h Yo-Yo –Real System System: yo-yo Surroundings Earth, Hand Esys Ktrans Krot Whand WEarth Ktrans Krot Fhand d (mg)(h) Ktrans (mg Fhand )h Krot Fhand (d h) Remember Point particles Have all of the forces acting on the object at the center of mass Only have Ktrans Work done by net force Real system More general/physical Can have all available forms of energy Work done by individual forces.