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Lecture214Week6 - Momentum What happens when a force acts...

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05/06/09 Physics 214 Fall 2008 1 Momentum What happens when a force acts on an object We know v = v 0 + at So that mv – mv o = mat mv – mv o = Ft The quantity mv is known as the momentum p and it is a vector quantity in the same direction as the velocity. The result of applying a force for a time t results in a change of momentum. So a body moving with velocity v has kinetic energy = 1/2mv 2 and momentum = mv F
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05/06/09 Physics 214 Fall 2008 2 Conservation of Momentum F 1 F 2 For a short interval of time t we have mv – mv o = F t and p = F t This is the impulse equation If we have a collision between two objects then in general the velocity of each object changes and kinetic energy is lost in the form of heat, sound or in a permanent deformation of the bodies.
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05/06/09 Physics 214 Fall 2008 3 Isolated systems anim0010.mov http://www.physics.purdue.edu/academic_programs/courses/phys214/lectures/anim0010.mov
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05/06/09 Physics 214 Fall 2008 4 Momentum conservation The conservation of momentum also is connected to the fundamental physical laws The laws of physics do not change under translation or rotation in space
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05/06/09 Physics 214 Fall 2008 5 Impulse We have seen that a force F acting for a time Δt changes momentum FΔt = Δp. FΔt is called an impulse There are many situations where it is more useful to use the impulse when two objects collide than equating the change in momentum of each. In the case shown below the momentum of the earth changes but that is too difficult to calculate. It is better to use the fact that the earth exerts a force for a short time.
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05/06/09 Physics 214 Fall 2008 6 Collisions Collisions In a closed, isolated system containing a collision, the linear momentum of each colliding object can change but the total momentum of the system is a constant . This statement is true even if energy is lost by the colliding bodies
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05/06/09 Physics 214 Fall 2008 7 Types of collision Elastic - no energy is lost Inelastic - Energy is lost (transformed) Perfectly inelastic – objects stick together In two dimensions momentum is conserved along the x and y axes separately y x
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05/06/09 Physics 214 Fall 2008 8 Perfectly Inelastic Let initial velocity be v i and the mass of a car be m. Then mv i = 3mv final and v final = v i /3
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05/06/09 Physics 214 Fall 2008 9 Head on Elastic collisions Pool ball collisions are close to being elastic v v Pool balls v Bowling ball hits tennis ball Tennis ball hits bowling ball http://www.physics.purdue.edu/class/applets/phe/collision.htm
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05/06/09 Physics 214 Fall 2008 10 Collisions of Particles Both energy and momentum and charge are conserved in elementary particle interactions and are a powerful tool in analyzing the fundamental physics.
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