A 20.0 kg body is moving in the positive x direction with a speed of 200m/s, whe

Question

A 20.0 kg body is moving in the positive x direction with a speed of 200m/s, when owing to an internal explosion, it breaks into three parts. one part with a mass of 10.0 kg, moves away from the point of explosion with a speed of 100m/s in the positive y direction. a second fragment with a mass of 4.0 kg, moves in the negative x direction with a speed of 500m/s. (a) what is the velocity of the third (6.00kg) fragment? (b) how much energy is released in the explosion? ignore effects due to gravitiational force.

Explanation / Answer

A 24 kg body is moving through space in the positive direction of an x axis with a speed of 150 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 6.2 kg, moves away from the point of explosion with a speed of 200 m/s in the positive y direction. A second part, with a mass of 6.5 kg, moves in the negative x direction with a speed of 480 m/s. What are the (a)x-component and (b)y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force. his is actually a conservation of momentum problem...since the explosion is an internal force to the system...the momentum of the system is not changed (this is the meaning of the statement to ignore gravitational effects...this tells you there are no external forces) so, prior to the explosion, the momentum was 24kg*150m/s in the +x direction...so this must be the total momentum after explosion thus, the total y momentum after collision must be zero (since there was no y momentum prior to collision) you are told that one part carries 6.2kg*200m/s in the +y direction, so you know that the third mass(whose mass is 24-6.2-6.5=11.3kg) must have a component of velocity of 109.7m/s in the negative y direction to offset the y momentum of the 6.2 kg piece now, we can find the x component of the 11.3kg mass we know that its x momentum must be such that 3600kgm/s = -6.5kg*480m/s + 11.3 Vx where Vx is its velocity in the x direction, or Vx=3090m/s to find the energy release, compare the initial kinetic energy (1/2mv^2 = 1/2 * 24kg* 150m/s^2) or initial KE = 270,000J find the final KE by computing the KE for each fragment and summing them, remembering that the total speed for the third fragment is v^2=vx^2+vy^2

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