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# 598 Class Note for PHYS 211 at PSU

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
21
WORDS
KARMA
25 ?

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This 21 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 45 views.

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Date Created: 02/06/15
SYSTEMS OF PARTICLES AND MOMENTUM Center of mass Linear Momentum Newton s Laws for a System Conservation of Momentum Impulse Collisions and Recoil DEFINITION OF CENTER OF MASS The center of mass is that point for a mass or collection of masses where the total mass may be considered to be concentrated for the purpose of describing the motion of the object or objects Center of Mass Consider a system of n particles Each particle is located 739 from the origin Each particle is moving with a velocity17i Center of Mass defining i equations x x y 777 7lt 0 r 73 7 r 40 kg 2 pin 73 72 71 I 2 3 4 5 71 40 kg 2 0 1gt E4 3 a T 3 2 1 Terminology System the collection of particles to be analyzed isolated from its surroundings Internal Forces forces solely between particles of the system External Forces forces that have their origin outside the defined system Definition of Momentum gt gt Linear momentum p mv Momentum is a vector Momentum must obey the rules of vector algebra Units are kg ms Acceleration and Newton s V Second Law 13 2 m7 v 05 dm 7 dt dt If mass is constant 13 11 dt mc i Velocity and Momentum of a V System of Particles dr j v1 dt 1 7 1 17 m CM M i1 I l WCM m Relation between I Momentum and Force F M 67 net for cm proof see blackboard 6115 d I7 4 M for i dt dt M 5239 lot cm proof see blackboard Internal and External Forces P1 mlvl ext quot392 p mzvz Illustrating Internal Forces which are action reaction pairs i1 ext LAW OF CONSERVATION OF MOMENTUM If there are no external forces on the system of objects No net force on the center of mass of the system then the momentum of the system is conserved a d Fm 7 O gt PCM const Inelastic Collisions Two objects collide and stick together Momentum must be conserved Befo r e c o l s I on 071 p1ip2ipf a mlvll 77121722 2 m1 m2vf After collision 00 ml 7712 b Example Inelastic Collision Ballistic Pendulum V Inelastic Collision BC lb rC o In 1 wt 9 P rojec Li IE r39if39te r xample 9 8 Ballistic Pendulumn Elastic Collisions 1 D Belcure collision lcr collision quot quotquot quotII a 7 12 b p1ip2i 2191f p2f K1iK2i KlfK2f Elastic Collisions Two objects collide and rebound Momentum must be conserved Kinetic Energy is also conserved Baum Iquot gt 2 0 4 0 x m m Prujm n Ir l 39nrgc 39 339 I gt lt quot A V I 2 fun gt gt 9quot o o A 7 Example 9 10 Using Energy and Momentum conservation 5 Elastic Collisions 771 U sin 9 i 11 56 l Putlitre Ilu relMirian 1 192139 h AXI39Irl 11111 ulliniun p1fp2f K1fK2f Collision Phys Lab

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