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10_P58InstructorSolution - 10.58 Model Model the balls as...

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10.58. Model: Model the balls as particles. We will use the Galilean transformation of velocities (Equation 10.44) to analyze the problem of elastic collisions. We will transform velocities from the lab frame S to a frame S in which one ball is at rest. This allows us to apply Equations 10.43 to a perfectly elastic collision in S . After finding the final velocities of the balls in S , we can then transform these velocities back to the lab frame S. Visualize: Let S be the frame of the 400 g ball. Denoting masses as 1 100 g m = and 2 400 g, m = the initial velocities in the S frame are i1 () 4 . 0 m / s x v =+ and i2 1 . 0 m / s . x v Figures (a) and (b) show the before-collision situations in frames S and S, respectively. The after-collision velocities in S are shown in figure (c). Figure (d) indicates velocities in S after they have been transformed to S from S . Solve: In frame S, () 4 . 0 m / s x v = and () 1 . 0 m / s . x v = Because S is the reference frame of the 400 g ball, 1.0 m/s. V = The velocities of the two balls in this frame can be obtained using the Galilean transformation of velocities . vvV =− So, ( ) ( ) 4.0 m/s 1.0 m/s 3.0 m/s
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