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Lectures 19-22 - Momentum & Center of Mass

Lectures 19-22 - Momentum & Center of Mass -...

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    Linear Momentum and  Collisions Chapter 9
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    Linear Momentum The  linear momentum  of a particle or  an object that can be modeled as a  particle of mass  m  moving with a  velocity  v  is defined to be the product of  the mass and velocity: p  =  m   v The terms momentum and linear momentum  will be used interchangeably
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    CPS Question
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    Linear Momentum Linear momentum is a vector quantity Its direction is the same as the direction of  v The dimensions of momentum are ML/T The SI units of momentum are kg ∙ m / s Momentum can be expressed in component  form: p x  =  m v x   p y  =  m v y p z  =  m v z
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    Newton and Momentum Newton called the product  m v  the  quantity of motion  of the particle Newton’s Second Law can be used to  relate the momentum of a particle to the  resultant force acting on it with constant  mass F = μ α= μ δ ω δτ = δ μ ω ( 29 δτ = δ π δτ
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    CPS Question
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    Newton’s Second Law The time rate of change of the linear  momentum of a particle is equal to the net  force acting on the particle This is the form in which Newton presented the  Second Law It is a more general form than the one we used  previously This form also allows for mass changes Applications to systems of particles are  particularly powerful
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    Conservation of Linear  Momentum Whenever two or more particles in an  isolated system interact, the total  momentum of the system remains  constant The momentum of the  system  is  conserved, not necessarily the momentum  of an individual particle This also tells us that the total momentum  of an isolated system equals its initial  momentum
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    Conservation of Momentum Conservation of momentum can be  expressed mathematically in various ways p total  =  p 1  +  p 2  =  constant p 1i  +  p 2i = p 1f  +  p 2f In component form, the total momenta in  each direction are independently conserved p ix  =  p fx p iy  =  p fy p iz  =  p fz Conservation of momentum can be applied to  systems with any number of particles
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    Conservation of Momentum,  Archer Example The archer is standing on a  frictionless surface (ice) Approaches: Newton’s Second Law – no,  no information about  F  or  a Energy approach – no, no  information about work or  energy Momentum – yes
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    Archer Example Let the system be the archer with bow  (particle 1) and the arrow (particle 2) There are no external forces in the  x -
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