Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Important Reminders Last Lecture Power 2D collisions Pset # 8 due this Friday. Today Power is change in energy per unit time: Power, Impulse, Center of Mass Problem Solving session in class this Friday. Experiment #5 MasteringPhysics due next Monday. Important Concepts Momentum changes due to external forces acting over a period of time (called impulse). Power is change in energy over time. Center of mass and momentum are closely related. 8.01L Fall 2005 11/15/2005 Impulse Just the change in momentum: Note the vectors! ! ! !pTot = " Fdt The change in momentum can be used to find information about the force if the time is known. Power = My apologies for the confusion i nadvertently caused by posting the next MasteringPhysics assignment early. NOTE: Class grading guidelines clearly allow discussion of MasterPhysics problems but also clearly prohibit directly working together or copying the answers of other students. 8.01L Fall 2005 11/15/2005 ! RC.M . = 1 ! 11/15/2005 ! ! Power = Fiv 8.01L Fall 2005 M TOT d ! d ! RC.M . = 1 m r M TOT ! i dt i dt ! ! = 1 mv = 1 p M TOT ! i i M TOT ! i Definition: vC.M . = i i As with all vectors, components are the only way to do a quantitative calculation: xC.M . = 1 ! mi xi 8.01L Fall 2005 11/15/2005 ! !m r The positions, velocities, and accelerations, as well ! ! as F = Ma and other equations we have been studying up to now apply exactly to the center of mass of an extended object. 8.01L Fall 2005 One interesting result: Power delivered by a given force increases with velocity in the force direction Center of Mass Velocity M TOT If force and time are known, the change in momentum can be calculated. A concept that has enormous technological impact but very little utility in solving problems. Center of Mass Definition: dE dt 11/15/2005 ! Connection to momentum: M TOT vC.M . = ! !p i ! = pTOT So, if momentum is conserved, the velocity of the center of mass is constant. 8.01L Fall 2005 11/15/2005 1