f_momentum - PHYS 81 GY 1st Sem 2009-2010 AKGTapia Momentum...

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PHYS 81 GY 1st Sem 2009-2010 AKGTapia 1 Systems of Particles and Systems of Particles and Conservation of Momentum Conservation of Momentum Momentum of an Object • Momentum ( p ) is defined as the product of its mass and velocity. – Measure of the difficulty of bringing a particle to rest. v p m = Unit: 1 kg•m/s = 1 N•s m v Problem on Linear Momentum • A 0.100-kg ball is thrown straight up into the air with an initial speed of 15.0 m/s. Find the momentum of the ball (a) at its maximum height and (b) halfway up to its maximum height. Original statement of Newton’s Second Law v p Δ = Δ m t t m m Δ Δ = Δ Δ = = p v a F net The net force acting on a particle equals the time rate of change of the particle’s linear momentum. For systems of particles, = = i CM i i MV v m P Infinitesimally, dt dP F net = The net force acting on a particle equals the time rate of change of the particle’s linear momentum. Original statement of Newton’s Second Law The wrestling entertainment ring was designed to cushion the fall of wrestlers. This will lessen the impact force by increasing the change in time.
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PHYS 81 GY 1st Sem 2009-2010 AKGTapia 2 Conservation of Linear Momentum • If the net external force on a system is zero, the velocity of the center of mass of the system is constant and the total momentum of system is conserved; the is, it remains constant. = f i p p = = = i i i CM v m MV P constant Note: Can be applied in isolated system where there are no external forces. Problem on Cons. of Linear Momentum : A man of mass 70 kg and a boy of mass 35 kg are standing together on a smooth ice surface for which friction is negligible. If they push each other apart and the man moves away with speed of 0.3 m/s relative to the ice, how far apart are they after 5 s? Questions : 1. If the kinetic energy of a particle is zero, what is its linear momentum? 2. As a pendulum bob swings. Is the momentum conserved? Why? 3. If the speed of a particle is doubled, by what factor is its momentum changed? By what factor is its kinetic energy changed? Collisions An isolated event where bodies exert a relatively great amount of force to each other over a short period of time. M 1 M 2 v 1 v 2 System boundary Particles before collision Particles after collision Collision event Elastic Collisions The momenta and kinetic energies of the bodies may change but the total momentum and the total kinetic energies are constant . = f i p p = f KE KE i e.g. (billiards, collision of particles,…) System boundary Particles before collision Particles after collision Collision event Note: Kinetic energy is not dissipated. Note: For elastic collisions, the relative speed of
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f_momentum - PHYS 81 GY 1st Sem 2009-2010 AKGTapia Momentum...

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