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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.
Original kinetic energy= 1/2mv2 = 16JEnergy imparted due to explosion = 16JTotal energy = 32J ½ m1v12 + 1/2 m2v22 = 32J2 v12 + 2v22 = 32Jv12 + v22 = 16J Also m1v1 + m2v2 = mv (conservation of linear momentum)4v1 + 4v2 = 8 x 2v1 + v2 = 4(v1 + v2 )2= 16i.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.
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