# lecture28 - Collisions(II Momentum and Kinetic Energy in...

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1 Physics 1D03 2 Serway 9.3, 9.4 Collisions (II) • Momentum and Kinetic Energy in Collisions For practice: Chapter 9, problems 19, 23, 27, 67, Physics 1D03 3 Elastic Collisions In one dimension (all motion along the x-axis): 1) Momentum is conserved: f f i i 2 2 1 1 2 2 1 1 v m v m v m v m + = + 2 2 2 2 1 2 1 1 2 1 2 2 2 2 1 2 1 1 2 1 f f i i v m v m v m v m + = + In one dimension, the velocities are represented by positive or negative numbers to indicate direction. 2) Kinetic Energy is conserved: We can solve for two variables if the other four are known.

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2 Physics 1D03 5 1) The magnitude of the relative velocity is the same before and after the collision: |v 1,i v 2,i | = | v 1,f v 2,f | (True for elastic collisions in 2 and 3 dimensions as well). For example, we can work through the algebra to get the following results for elastic collisions: 2) For a particle directed at a stationary target ( v 2,i = 0, v 1,i = v 0 ) : , 2 0 2 1 1 2 v m m m v f + = 0 2 1 2 1 1 v m m m m v f + - = Physics 1D03 6 Particle directed at a stationary target ( v 2,i = 0): • Equal masses: If
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