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Grade upto college level Mechanics

A body of mass 8.0 kg is traveling at 2.0 m/s under the influence of no external force. At a certain instant an internal explosion occurs, splitting the body into two chunks of 4.0 kg mass each; 16 J of translational kinetic energy are imparted to the two-chunk system by the explosion. Neither chunk leaves the line of the original motion. Determine the speed and direction of motion of each of the chunks after the explosion.

Profile image of Shane Macguire
11 Years agoGrade upto college level
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1 Answer

Profile image of Hasan Naqvi
11 Years ago
Original kinetic energy= 1/2mv2 =  16J
Energy imparted due to explosion = 16J
Total energy = 32J
 
½ m1v12 + 1/2 m2v22  = 32J
2 v12 + 2v2= 32J
v12 + v2= 16J
 
Also m1v1 + m2v= mv (conservation of linear momentum)
4v1 + 4v2 = 8 x 2
v+ v2 = 4
(v+ v2 )2= 16
i.e. v1v2 = 0
 
So one of the chunk stops at rest, while the other chunk moves with a velocity 4m/s in the same direction.