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Unformatted text preview: 1 PC1221 Fundamentals of Physics I Lectures 17 and 18 Linear Momentum and Collisions Dr Tay Seng Chuan 2 Ground Rules Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while lecture is going on No gossiping while the lecture is going on Raise your hand if you have question to ask Be on time for lecture Be on time to come back from the recess break to continue the lecture Bring your lecturenotes to lecture 3 Linear Momentum The linear momentum 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 in this course, ie, when we say momentum we also means linear momentum (which is in a straight line) 4 Linear Momentum, cont Linear momentum is a vector quantity Its direction is the same as the direction of v The dimensions of momentum (mass x velocity) are ML/T The SI units of momentum are kg m / s Momentum can be expressed in component form (small letter p ): p x = m v x p y = m v y p z = m v z Momentum in x direction Momentum in y direction Momentum in z direction 5 Newton and Momentum Newton called the product mv mv the quantity of motion quantity of motion of the particle Newtons Second Law can be used to relate the momentum of a particle to the resultant force acting on it with constant mass ( ) d m d d m m dt dt dt = = = = v v p F a 6 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 Momentum approach can be used to analyse the motion in a system of particles ( ) d m d d m m dt dt dt = = = = v v p F a 7 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, but the momentum of individual particle may not necessarily conserved. The total momentum of an isolated system equals its initial momentum 8 Conservation of Momentum, 2 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 for the various directions, the total momentum in each direction is independently 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 final Sum Initial Sum 9 Conservation of Momentum, Archer Example The archer is standing on a frictionless surface (ice)....
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 Spring '11
 Chiu
 Physics, Momentum

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