Knight Ch 9 - impulse and momentum - Impulse and Collisions...

Knight Ch 9 - impulse and momentum
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Impulse and Collisions – Ch 9 Male rams butt heads at high speeds in a ritual to assert their dominance. How can the force of this collision be minimized so as to avoid damage to their brains?
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Linear Momentum Momentum is a vector; there is a direction and magnitude. Momentum = mass x velocity p = m v In general, we must worry about the x, y, and z components of momentum If the particle is moving with in an arbitrary direction then p must have three components which are equivalent to the component equations: p x = mv x p y = mv y p z = mv z Newton called m v the quality of motion .
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v v v A block and a ball of the same mass and downward speed v hit the floor. The block falls and “sticks” to the floor. x y The ball rebounds with the same velocity it hit the floor with. Change in Momentum
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v x y Change in Momentum We only have to consider the momentum in the y direction. Block p y = p y,f – p y,i = 0 – m(-v) = mv The change in momentum is mv upward. Ball p y = p y,f – p y,I = mv – m(-v) = 2mv The change in momentum is 2mv upward. Be careful about the vector nature of momentum!!!
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Linear Momentum Newton's Second Law, which we have written as F = m a can also be written in terms of momentum, F = m a = m (d v /dt) = d(m v )/dt F = d p /dt The force acting on an object equals the time rate of change of the momentum of that object.
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Conservation of Momentum Consider two objects that "interact" or collide or have some effect on each other (billiard balls). From Newton's Third Law of motion, we know F 12 = - F 21 Where F 12 is the force exerted by particle 1 on particle 2 and F 21 is the force exerted by particle 2 on particle 1. In terms of momentum, this means d p 1 /dt = - d p 2 /dt d p 1 /dt + d p 2 /dt = 0 d ( p 1 + p 2 ) /dt = 0 d p Tot /dt = 0; p Tot = p 1 + p 2
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Conservation of Momentum Lets look at that again! d p Tot /dt = 0 where p Tot = Σ p = p 1 + p 2 = const This statement may also be written as p 1i + p 2i = p 1f + p 2f Since the time derivative of the momentum is zero, the total momentum of the system remains constant . This is Conservation of Momentum Conservation of Momentum is essentially a restatement of Newton's Third Law of Motion.
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Conservation of Momentum We have said that if the particle is moving with in an arbitrary direction then p must have three components which are equivalent to the component equations. This allows us to rewrite the conservation of momentum as = = = system zf system zi system yf system yi system xf system xi p p p p p p Conservation of momentum: Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.
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1-D inelastic collisions Perfectly inelastic collisions are those in which the two objects stick together. Consider a mass m
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