A box of mass m = 6 kg slides with speed v = 4m/s across a frictionless floor. It suddenly explodes into two places. One piece, with mass m1= 2kg moves in same direction with speed vi= 8 m/s. the velocity of the second piece is:
Correct answer: D. 2m/sec
- A. 6m/sec
- B. 3m/sec
- C. 1m/sec
- D. 2m/sec
- E. 4m/sec
Explanation
Before the explosion: Total momentum = (mass of box) * (initial velocity of box) = m * v After the explosion: Total momentum = (mass of piece 1) * (velocity of piece 1) + (mass of piece 2) * (velocity of piece 2) We are given the following information: mass of box (m) = 6 kg initial velocity of box (v) = 4 m/s mass of piece 1 (m1) = 2 kg velocity of piece 1 (v1 )= 8 m/smass of 2nd piece should be 4 m/sSo, mv = m1v1 + m2v26(4) = 2(8) + 4v224 = 16 + 4v224 - 16 = 4v28 = 4v2v2 = 2 m/s
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