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Unformatted text preview: 1 Chapter 9 Chapter 9 Linear Momentum and Collisions Linear Momentum and Collisions Linear Momentum Linear Momentum • The The linear momentum linear momentum of a particle or an object that can be modeled as of a particle or an object that can be modeled as a particle of mass a particle of mass m moving with a velocity moving with a velocity v is defined to be the product is defined to be the product of the mass and velocity: of the mass and velocity: The terms momentum and linear momentum will be used The terms momentum and linear momentum will be used interchangeably in the text interchangeably in the text v m p a a = • Linear momentum is a vector quantity Linear momentum is a vector quantity – Its direction is the same as the direction of Its direction is the same as the direction of v • The dimensions of momentum are The dimensions of momentum are ML/T ML/T • The The SI SI units of momentum are units of momentum are kg kg ¡ m / s m / s • Momentum can be expressed in component form: Momentum can be expressed in component form: p x = = m v m v x p y = = m m v y p z = = m v m v z 2 Newton Newton ’s Second Law s Second Law • The time rate of change of the linear momentum of a particle is The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle equal to the net force acting on the particle – This is the form in which Newton presented the Second Law This is the form in which Newton presented the Second Law – It is a more general form than the one we used previously It is a more general form than the one we used previously – This form also allows for mass changes This form also allows for mass changes • Newton Newton ’s Second Law can be used to relate the momentum of a s Second Law can be used to relate the momentum of a particle to the resultant force acting on it particle to the resultant force acting on it with constant mass with constant mass ( ) d m d d m m dt dt dt Σ = = = = v v p F a Conservation of Linear Momentum Conservation of Linear Momentum • Whenever two or more particles in an isolated system interact, Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant the total momentum of the system remains constant – The momentum of the The momentum of the system system is conserved, not necessarily is conserved, not necessarily the momentum of an individual particle the momentum of an individual particle – This also tells us that the total momentum of an isolated This also tells us that the total momentum of an isolated system equals its initial momentum system equals its initial momentum • Conservation of momentum can be expressed mathematically in Conservation of momentum can be expressed mathematically in various ways various ways p total total = p = p 1 + p + p 2 = constant = constant p 1i 1i + p + p 2i 2i = p = p 1f 1f + p + p 2f 2f • In component form, the total momenta in each direction are...
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 Spring '08
 bose
 Physics, Kinetic Energy, Mass, Momentum

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