An interior explosion division an object, at first at rest, into two pieces, among which has actually 1.6 time the fixed of the other.If 6300 JJ were released in the explosion, just how much kinetic energy did each piece acquire?

Express her answers utilizing two far-ranging figures. Go into your answers numerically be separated by a comma.

You are watching: An internal explosion breaks an object initially at rest into two pieces Let

m1, v1 be the mass and also speed that one piece,

m2, v2 it is in the mass and speed that the various other piece,

E = 6300 J be the complete energy,

E1 = m1v1²/2 it is in the power of the an initial piece,

E2 = m2v2²/2 it is in the power of the other piece,

r = m1/m2 = 1.6 be the ration in between the masses.

Then

m2 = m1/r

By conservation of momentum

m1v1 = m2v2

Therefore we deserve to write

v2 = m1v1/m2 = rv1

Therefore

E2 = (m1/r)(rv1)²/2 = rm1v1²/2 = rE1

By conservation of energy

E = E1 + E2 = E1 + rE1 = E1(1+r)

Therefore

E1 = E/(1+r)

Plugging in actual numbers

E1 = 6300/2.6 = 2423 J

E2 = E - E1 = 6300 - 2423 = 3877 J

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