A 35.0-kg body is moving in the direction of the positive x axis with a speed of
ID: 1962497 • Letter: A
Question
A 35.0-kg body is moving in the direction of the positive x axis with a speed of 400 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 5.5 kg, moves away from the point of explosion with a speed of 396 m/s along the positive y axis. A second fragment, whose mass is 2.5 kg, moves away from the point of explosion with a speed of 323 m/s along the negative x axis. (A)What is the speed of the third fragment? Ignore effects due to gravity.(B)How much energy was released in the explosion?
Explanation / Answer
Total mass M = 35 kg Initial speed U = 400 i Total initial kinetic energy E = ( 1/ 2) MU 2 = 2.8 x 10 6 J Masses of pieces m = 5.5 kg m ' = 2.5 kg m " = M - ( m+ m') = 27 kg Speeds of the pieces u = 396 j u ' = 323 (-i) u " = ? Where i , j are the unit vectors along positve x and y axis respectively. From law of conservation of momentum , total momentum before explosion = total momentum after explosion MU = mu + m' u ' + m " u " 14000 i = 2178 j - 807.5 i + 27 u " 27 u" = 14807.5 i + 2178 j u " = 548.42 i + 80.666 j Speed of third fragment u " = [ 548.42 2 + 80.666 2 ] = 554.32 m / s Total kinetic energy after explosion E ' = ( 1/ 2) m u 2 + ( 1/ 2) m' u ' 2 + ( 1/ 2) m" u" 2 = 4.709 x 10 6 J Energy was released in the explosion = E'- E = 1.909 x 10 6 JRelated Questions
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