As the drawing illustrates, two disks with masses m1 and m2 are moving horizonta

Question

As the drawing illustrates, two disks with masses m1 and m2 are moving horizontally to the right at a speed of v0. They are on an air-hockey table, which supports them with an essentially frictionless cushion of air. They move as a unit, with a compressed spring between them, which has a negligible mass. Then the spring is released and allowed to push the disks outward. Consider the situation where disk 1 comes to a momentary halt shortly after the spring is released. Assuming that m1 = 1.8 kg, m2 = 2.8 kg, and v0 = 4.5 m/s, find the velocity of disk 2 at that moment.

Explanation / Answer

First we want to think about what type of collision (explosion) this is. Whenever two objects stick together or come apart kinetic energy is not conserved. There is no friction on the table, so momentum is conserved. Before the spring shot them apart the momentum was (m1 + m2) v0 Since momentum is conserved, after they separate the momentum must be the same, but mass 1 is motionless so all the momentum must come from mass 2, so m2 vf Set this equal to the initial momentum m2 vf = (m1 + m2) v0 solve for final velocity vf = (m1 + m2) v0 / m2 = 4.6 (4.5) / 2.8 in meters per second velocity will be in the same direction as starting velocity

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