A 33 kg body is moving through space in the positive direction of an x axis with

Question

A 33 kg body is moving through space in the positive direction of an x axis with a speed of 310 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 7.0 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 7.1 kg, moves in the negative x direction with a speed of 460 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=33 kg, v=310i where i and j are unit vectors in direction x and y.

m1=7kg, v1=170j

m2=7.1kg, v2=-460i

m3=m-m1-m2=18.9kg, v3=xi+yj

From conservation of linear momentum in x direction,

mv=m1*0+m2v2+m3x

=>33*310=-7.1*460+18.9*x

=>x=714.07

From conservation of linear momentum in y direction,

m*0=m1v1+m2*0+m3y

=>0=7*170+18.9y

=>y=-62.96

a)x-component of velocity of 3rd part=714.07 m/s (i.e. in +ve x direction)

b)y-component of velocity of 3rd part=-62.96 m/s (i.e. in -ve y direction)

c)Energy released=initial kinetic energy-final kinetic energy

=0.5[mv^2-m1v1^2-m2v2^2-m3v3^2]

=0.5[33*310^2-7*170^2-7.1*460^2-18.9*(714.07^2+62.96^2)]

=-4122.66 kJ

So 4122.66 kJ of energy is released in the explosion

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