PHY183-Lecture24 - Physics for Scientists & Engineers 1...

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February 24, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 24
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February 24, 2006 Physics for Scientists&Engineers 1 2 Totally Elastic Collisions in 2d or 3d Totally Elastic Collisions in 2d or 3d General considerations: 1d: p f ,1 and p f ,2 are 2 unknowns; momentum conservation and kinetic energy conservation provide 2 equations 2d: each final momentum vector has 2 components => 4 unknowns; momentum conservation (x and y component) and kinetic energy conservation only provide 3 equations 3d: each final momentum vector has 3 components => 6 unknown; momentum conservation (x, y, z component) and kinetic energy conservation only provide 4 equations  More information needed! Makes billiards interesting! (Need information on where exactly balls touch)
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February 24, 2006 Physics for Scientists&Engineers 1 3 Elastic Collision with Wall, 2d Elastic Collision with Wall, 2d Momentum component parallel to wall remains the same, Momentum component perpendicular to wall changes sign, Angle of incidence = angle of reflection, Absolute value of momentum stays the same Same for light as for bouncing balls r p f , = r p i , r p f , ! = " r p i , ! r p i r p i , r p i , ! ! i r p f r p f , ! r p f , f f = i Normal force, N
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February 24, 2006 Physics for Scientists&Engineers 1 4 Elastic Collision with Wall, 3d Elastic Collision with Wall, 3d In 3d there is still one momentum component perpendicular to the wall. It changes sign. Now there are 2 momentum components parallel to wall. They stay the same. Still true: angle of reflection = angle of incidence Still true: absolute value of momentum vector stay the same. r N
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February 24, 2006 Physics for Scientists&Engineers 1 5 Elastic Collision of Elastic Collision of Equal-Mass Objects, 2d, 3d Equal-Mass Objects, 2d, 3d Situation in billiards: shoot one ball so that it collides with another ball, which is initially at rest
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PHY183-Lecture24 - Physics for Scientists & Engineers 1...

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