(5pts) Two pieces of clay in outer space drift toward each other, collide, and s

Question

1. (5pts) Two pieces of clay in outer space drift toward each other, collide, and stick together. The ?rst piece of clay has a mass of 45 grams and a velocity of < 4,?3,7 > m/s just before the collision. The second piece has a mass of 52 grams and a velocity of < 3,?1,?7 > m/s just before the collision.
   1. What is the velocity of the stuck-together lump just after the collision? Start from a fundamental principle and show all work clearly. Your answer must be a 3-component vector.
   2. What is the vector change in momentum of the 45-gram piece of clay alone?
   3. What is the unit vector that points in the direction of the net force on the 45-gram piece of clay during the collision?

Explanation / Answer

1. by conservation of momentum ,
45 * 4 + 52 *3 = (45 + 52) * V
V = 3.46391 m/s
45 * -3 + (52 * -1) = (45 + 52) * V
v=-1.9278
(45* 7) + (52*-7) = (45 + 52) * V
v=-0.505
< 3.46391, -1.9278, -0.505> is the velocity of lump.
2. change in momentum for 45 gm = 0.045 * < (3.46391 - 4), (-1.9278 + 3) , (-0.505 -7) > = < -0.02412, 0.0482, -0.3377 >
3. unit vector that points in the direction of the net force = unit vector of change in momentum
magnitude = sqrt ( (-0.02412)^2 + (0.0482)^2 + (-0.3377)^2) = 0.34197
so unit vector = < -0.02412/0.34197, 0.0482/0.34197, -0.3377/0.34197 > = < -0.0705, 0.140948, -0.9875 >
unit vector that points in the direction of the net force = < -0.0705, 0.140948, -0.9875 > is the answer

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