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 1100 gm=and 2400 g,m=the initial velocities in the S frame are i1()4.0m/sxv=+and i21.0m/s.xvFigures (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, () 4.0m/sxv=and () 1.0m/s.xv=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/s3.0 m/s
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