A 18 kg body is moving through space in the positive direction of an x axis with

Question

A 18 kg body is moving through space in the positive direction of an x axis with a speed of 130 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 5.5 kg, moves away from the point of explosion with a speed of 170 m/s in the positive y direction. A second part, with a mass of 5.9 kg, moves in the negative x direction with a speed of 440 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

Explanation / Answer

M =18 kg , ux =130 m/s, uy =0

m1 =5.5 kg , v1x =0 ,v1y = 170 m/s

m2 = 5.9 kg , v2x = -440 m/s

m3 = M- m1-m2 = 18-5.5-5.9 =6.6 kg

(a) From conservation of momentum along x direction

Mux =m1v1x+m2v2x+m3v3x

18*130 = 0 - (5.9*440) + (6.6*v3x)

v3x = 747.9 m/s

(b) From conservation of momentum along y direction

Muy =m1v1y+m2v2y+m3v3y

0 = (5.5*170)+0+ (6.6*v3x)

v3x = -141.7 m/s

(c) Initial kinetic energy K.E1 = (1/2)Mu^2 = 0.5*18*130*130

K.E1 = 152100 J

final kinetic energy K.E2 =(1/2)m1v1^2 +(1/2)m2v2^2+(1/2)m3v3^2

K.E2 = (0.5*5.5*170*170) +(0.5*5.9*440*440) + (0.5*6.6*(747.9)^2+(141.7)^2)

K.E2 = 2562724 J

Energy released = 2562724 - 152100 =2410624 J

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