A 3.0-kg block is traveling in the -x direction at 5.0 m/s, and a1.0-kg block is

Question

A 3.0-kg block is traveling in the -x direction at 5.0 m/s, and a1.0-kg block is traveling in the +x direction at 3.0 m/s. (a)Find hte velocity Vcm of the center of mass. (b) Subtract Vcmfrom the velocity of each block to find the velocity of each blockin the center-of-mass reference frame. (c) After they make ahead-on elastic collision, the velocity of each block is reversed(in the center-of-mass frame). Find the velocity of eachblock in the center-of-mass frame after the collision. (d)Transform back into the original frame by adding Vcm to thevelocity of each block. (e) Check your result by finding theinitial and final kinetic energies of the blocks in the originalframe and comparing them.

Explanation / Answer

Given that m1 = 3 kg m2 = 1.0 kg v1 = - 5.0 m/s v2 = 3.0 m/s M = m1 + m2 = 4.0 kg (a) Vcm = [ m1v1 + m2v2 ] / M = [3 * -5 +1.0 * 3.0 ] / 4 = - 4 m/s (b) V1 = -5.0 - 4.0 = - 9.0 m/s        V2 = - 1 m/s (c) V1' = 9.0 m/s         V2' = 1 m/s d) v1' = 9.0 - 4.0 = 5.0 m/s       v2' = 1 - 4.0 = - 3.0 m/s e) KEini   = 0.5 * 3 * -5 *-5 + 0.5 * 1 * 3 * 3 = 42 J        KE fin = 0.5* 3 * 5 * 5 + 0.5 * 1 * -3 * -3 = 42 J      Therefore initial and final kineticenergies are equal.

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