1. Conservation of Momentum
The principle of conservation of momentum states that in a closed system, the total momentum before a collision or explosion is equal to the total momentum after.
* Initial Momentum: Before the explosion, the bomb is at rest, so its initial momentum is 0.
* Final Momentum: After the explosion, the two pieces have their own momenta.
2. Setting up the Equation
Let:
* m₁ = 4 kg (mass of the first piece)
* v₁ = 6 m/s (velocity of the first piece)
* m₂ = 8 kg (mass of the second piece)
* v₂ = ? (velocity of the second piece)
The conservation of momentum equation is:
0 (initial momentum) = m₁v₁ + m₂v₂
3. Solving for the Velocity of the Second Piece
* 0 = (4 kg)(6 m/s) + (8 kg)v₂
* 0 = 24 kg⋅m/s + 8 kg⋅v₂
* -24 kg⋅m/s = 8 kg⋅v₂
* v₂ = -3 m/s (The negative sign indicates the second piece moves in the opposite direction to the first)
4. Calculating the Kinetic Energy of the Second Piece
Kinetic energy (KE) is calculated using the formula:
KE = (1/2)mv²
KE₂ = (1/2)(8 kg)(-3 m/s)²
KE₂ = 36 J (Joules)
Therefore, the kinetic energy of the 8 kg piece is 36 Joules.
