Question

A mass of 3 kg is initially moving in the +x direction and collides inelastically with a mass of 10 kg moving in the -x direction at 2 m/s. After the collision, both masses move in the +x direction at 4 m/s. How much kinetic energy is lost in the collision in Joules? Answer is positive

Answer 1

Mass of object 1 = m₁ = 3 kg

Mass of object 2 = m₂ = 10 kg

Velocity of object 1 before the collision = V₁

Velocity of object 2 before the collision = V₂ = -2 m/s (Negative sign as it is directed in the negative X direction)

Velocity of both the objects after the collision = V₃ = 4 m/s

By conservation of momentum,

m₁V₁ + m₂V₂ = (m₁ + m₂)V₃

3V₁ + (10)(-2) = (3 + 10)(4)

V₁ = 24 m/s

Kinetic energy of the system before the collision = KE₁

KE₁ = m₁V₁²/2 + m₂V₂²/2

KE₁ = (3)(24²)/2 + (10)(-2)²/2

KE₁ = 884 J

Kinetic energy of the system after the collision = KE₂

KE₂ = (m₁ + m₂)V₃²/2

KE₂ = (3 + 10)(4²)/2

KE₂ = 104 J

Kinetic energy lost in the collision = KE_lost

KE_lost = KE₁ - KE₂

KE_lost = 884 - 104

KE_lost = 780 J

Kinetic energy lost in the collision is 780 J.