PAP111_Lecture10 - Three identical balls are thrown from...

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Unformatted text preview: 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 Active figure 1 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 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 = = = , , Original and General Form of Newtons Second Law Newtons 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 Two Particles Interaction in an Isolated System 12 21 = + F F ( 29 ( 29 2 2 1 1 = + dt m d dt m d v v ( 29 2 2 1 1 = + v v m m dt d By Newtons Third Law: By Newtons Second Law: ( 29 2 1 = + p p dt d Then, Note: c is a constant c tot = + = 2 1 p p p (10.3) 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) 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 = = = , , The Concept of Impulse The concept of Impulse relates to a net force F that may vary with time....
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PAP111_Lecture10 - Three identical balls are thrown from...

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