Answer:
The kinetic energy lost in the collision is 48 J
Explanation:
Given;
mass of the first ball, m₁ = 2.0 kg
mass of the second ball, m₂ = 6.0 kg
initial speed of the first ball, u₁ = 12 m/s
initial speed of the second ball, u₂ = 4 m/s
let v be the final velocity of the two balls after the inelastic collision
Apply the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
2 x 12 + 6 x 4 = v(2 + 6)
48 = 8v
48 / 8 = v
v = 6 m/s
The initial kinetic energy of the balls is calculated as;
K.E₁ = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.E₁ = ¹/₂(2)(12²) + ¹/₂(6)(4)²
K.E₁ = 144 + 48
K.E₁ = 192 J
The final kinetic of the balls is calculated as;
K.E₂ = ¹/₂(m₁ + m₂)(v²)
K.E₂ = ¹/₂(2 + 6)(6²)
K.E₂ = ¹/₂(8)(6²)
K.E₂ = 144 J
The lost in kinetic energy of the balls is K.E₂ - K.E₁ = 144 J - 192 J = -48 J
Therefore, the kinetic energy lost in the collision is 48 J
