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P161Sp08Chapter_09

P161Sp08Chapter_09 - Chapter 9 Impulse Momentum Linear...

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Chapter 9 Impulse & Momentum
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Linear Momentum n 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: n p = m v n The terms momentum and linear momentum will be used interchangeably in the text
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Linear Momentum, cont n Linear momentum is a vector quantity n Its direction is the same as the direction of v n The dimensions of momentum are ML/T n The SI units of momentum are kg m / s n Momentum can be expressed in component form: n p x = m v x p y = m v y p z = m v z
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Newton and Momentum n Newton called the product m v the quantity of motion of the particle n Newton’s Second Law with constant mass (i.e. dm/dt = 0) can be used to relate the momentum of a particle to the resultant force acting on it This is a generalization of Newton’s 2nd Law.
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Newton’s Second Law n The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle n This is the form in which Newton presented the Second Law n It is a more general form than the one we used previously n This form also allows for mass changes n Applications to systems of particles are particularly powerful
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Conservation of Linear Momentum n Whenever two or more particles in an isolated system , i.e no outside forces are present , interact the total momentum of the system remains constant n The momentum of the system is conserved, not necessarily the momentum of an individual particle n This also tells us that the total momentum of an isolated system equals its initial momentum
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Conservation of Momentum, 2 n Conservation of momentum can be expressed mathematically in various ways n p total = p 1 + p 2 = constant n p 1i + p 2i = p 1f + p 2f n In component form, the total momenta in each direction are independently conserved n p ix = p fx p iy = p fy p iz = p fz n Conservation of momentum can be applied to systems with any number of particles
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Conservation of Momentum, Archer Example n The archer is standing on a frictionless surface (ice) n Approaches: n Newton’s Second Law no, we have no information about F or a n Energy approach – no, no information about work or energy n Momentum – yes
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Archer Example, 2 n Let the system be the archer with bow (particle 1) and the arrow (particle 2) n There are no external forces in the x -direction, so it is isolated in terms of momentum in the x -direction n Total momentum before releasing the arrow is 0 n The total momentum after releasing the arrow is p 1f + p 2f = 0
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Archer Example, final n The archer will move in the opposite direction of the arrow after the release n Agrees with Newton’s Third Law n Because the archer is much more massive than the arrow, his acceleration and velocity will be much smaller than those of the arrow
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Conservation of Momentum, Kaon Example n The kaon decays into a positive p and a negative p particle n Total momentum before decay is zero n Therefore, the total momentum after the decay must equal zero n p + + p - = 0 or p + = -p -
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Momentum Conservation Demos n Gas powered Tricycle n Water Rocket n Ballistic Cannon
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