This is related to law of conservation of energy. It says that the energy is neither created nor destroyed.
So When the explosion takes place the energy released due to the explosion will be transferred to kinetic energy of the two pieces.
Let us say the mass of small peice is m and its velocity is v1.
Then the mass of bigger particle will be 1.5m and let us take the velocity of the bigger particle as v2.
Using momentum conservation;
Initial momentum = 0 (no movement before explosion)
Final momentum = `mv1+1.5mv2`
`0 = mv1+1.5mv2`
`v2 = -v1/1.5`
The (-) reveals that the parts were left apart from each other.
Using energy conservation;
Explosion energy `=` kinetic energy of two parts
`7400 = 1/2*m*(v1)^2+1/2*1.5m*(v2)^2`
`7400 = 1/2*m*(v1)^2+1/2*1.5m*((v1)/1.5)^2`
`7400 = 1/2*m*(v1)^2(1+1.5/1.5^2)`
` 4440 = 1/2*m*(v1)^2`
Kinetic energy of small piece `= 1/2*m*(v1)^2 = 4440 J`
Kinetic energy of bigger piece `= 1/2*1.5m*((v1)/1.5)^2 = 2960 J`
- All the energy of the explosion transferred as kinetic energy of the two pieces and no any pieces formed.
- There is no loss of energy due to heat, sound or vibration.
- The two pieces travelled opposite directions in a straight line