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PAP111_Lecture10 - ,allwith thesameinitialspeed...

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Three identical balls are thrown from the top of a building, all with  the same initial speed.  A: horizontally, B: inclined upwards, C: inclined downwards Rank the speeds of the balls at the instant each hits the ground. 1 2 3 4 5 6 0% 0% 0% 0% 0% 0% 1. A, B, C 2. A, C, B 3. B, A, C 4. C, B, A 5. C, A, B 6. B, C, A
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PAP 111  Mechanics and Relativity  Lecture 10 Linear Momentum The Conservation of Linear Momentum Impulse and Momentum The Collision Problem Center of Mass and the Motion of a System of Particles Rocket Propulsion
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Linear Momentum v p m = 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:  (10.1) Remarks:  The SI units of momentum are kg ∙ m / s .  Momentum can be expressed in component form as follows: z z y y x x mv p mv p mv p = = = , ,
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Original and General Form of  Newton’s Second Law Newton’s Second Law states that: ( 29 dt d dt m d p v F = = The time rate of change of the linear momentum of  a particle is equal to the net force acting on the  particle: (10.2) Remarks: This general formulation allows for mass change, and is more powerful  when applies to a system of particles. When the mass is constant, Eq. (10.2) reduces to Newton called  m v , the quantity of motion. = = . / a v F m dt md
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Two Particles Interaction in an  Isolated System 0 12 21 = + F F ( 29 ( 29 0 2 2 1 1 = + dt m d dt m d v v ( 29 0 2 2 1 1 = + v v m m dt d By Newton’s Third Law: By Newton’s Second Law: ( 29 0 2 1 = + p p dt d Then, Note:  c  is a constant c tot = + = 2 1 p p p (10.3)
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Conservation of Linear  Momentum Equation (10.3) tells us that the total momentum of  an isolated system is constant    Law of Conservation of Linear Momentum f f i i 2 1 2 1 p p p p + = + Whenever two or more particles in an isolated system  interact, the total momentum of the system remains  constant. (10.4)
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Remarks on Conservation of  Linear Momentum The momentum of the system is conserved, not  necessary the individual particles. The total momentum of an isolated system at all  times equal its initial momentum. Conservation of momentum applies to systems with  any number of particles. In component form, the total momenta in each  direction are independently conserved: fz iz fy iy fx ix p p p p p p = = = , ,
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The Concept of Impulse The concept of Impulse relates to a net force  F  that may vary with time.
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