How Is Kinetic Energy Distributed in an Explosion with Unequal Mass Fragments?

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The discussion focuses on calculating the distribution of kinetic energy between two fragments resulting from an explosion, where one fragment has 1.5 times the mass of the other. The total energy released in the explosion is 7400 J, which is converted into kinetic energy. The conservation of linear momentum is applied, leading to the equation m1v1 + m2v2 = 0, with m1 being 1.5 times m2. By solving the kinetic energy equation 0.5m1v1^2 + 0.5m2v2^2 = 7400 J, the velocities of the fragments can be determined. Ultimately, the kinetic energy for each piece can be calculated based on their respective masses and velocities.
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Homework Statement


An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. If 7400 J were released in the explosion, how much kinetic energy did each piece acquire?


Homework Equations


Momentum?
Kinetic Energy?


The Attempt at a Solution


I used all types of formulas having to do with energies and momentum and nothing gave me an answer.
 
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Use conservation of linear momentum along the horizontal since all the forces are internal (the energy that the explosion released was stored inside the projectile/object).

You know that m1v1+m2v2=0. And are given that m1=1.5m2.
Also, the total energy released in the explosion is converted into kinetic energy (you have to assume that), so 0.5m_1v_1^2+ 0.5m_2v_2^2=7500. Solve for v1/v2 and find the KE of each piece.
 

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