9 Linear Momentum - 1 Chapter 9 Linear Momentum and...

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2 Chapter 9 Linear Momentum and Collisions
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3 Conserved Quantities Conservation of energy is one of the important conservation laws. Among some others are: linear momentum angular momentum electric charge. This chapter uses conservation of linear momentum and energy to analyze collisions.
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4 9-1 Momentum and its Relation to Force Linear momentum of an object is defined: P = m v In SI its units are: kg m/s. Momentum is a vector. The rate of change of momentum of an object is equal to the net force applied to it. Σ F = d p dt .
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5 Momentum and the Second Law Consistent Σ F = = = m = m a [constant m ] What is an example of a non constant m ? How would this equation change? d p d ( m v ) d v dt dt dt
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6 Example 9-1 Washing a Car: Momentum Change and Force. Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it. (That is, we ignore an splashing back.) What is the force exerted by the water on the car?
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8 Conceptual Example 9-2 Water Splashes Back. What if the water splashes back from the car in example 9-1? Would the force on the car be greater or less?
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9 Response If the water splashes back from the car, the change in momentum will be greater in magnitude, and so will the force on the car be greater in magnitude. Note that p final will now point in the negative x direction. So the result for F will be minus something of magnitude more than 30 N (i.e., -35 to -40 N, depending on the water’s rebound speed.). To put it simply, the car exerts not only a force to stop the water, but also an additional force to give it momentum in the opposite direction.
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12 7-2 Conservation of Momentum Assume the net external force on this system of two balls is zero—that is, the only significant forces are those that each ball exerts on the other during the collision. Then: momentum before = momentum after m 1 v 1 + m 2 v 2 = m 1 1 + m 2 2 p 1 + p 2 = 1 + 2 This is the law of conservation of momentum.
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13 Conservation of Momentum The law of conservation of momentum was found experimentally, however it can be derived from Newton’s laws. Although the law of conservation of momentum was derived from Newton’s laws (second and third), it is more general than Newton’s laws. It holds ever where for all processes where no net external force is present. For example, it holds at the microscopic level where Newton’s laws do not.
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15 External Forces = F ext d P dt • If F ext = 0 then the total momentum remains constant. The total momentum of an isolated system remains constant
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17 Example 7-3 Railroad cars collide: momentum conserved. A 10,000-kg railroad car traveling at a speed of 24.0
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This note was uploaded on 09/10/2009 for the course PHY 76875 taught by Professor Turner during the Summer '09 term at University of Texas.

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9 Linear Momentum - 1 Chapter 9 Linear Momentum and...

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