Question

An air-track cart with mass m1=0.30kg and initial speed v0=0.80m/s collides with and sticks to a second cart that is at rest initially. If the mass of the second cart is m2=0.46kg, how much kinetic energy is lost as a result of the collision?

Answer 1

Mass of the first cart = m₁ = 0.3 kg

Mass of the second cart = m₂ = 0.46 kg

Velocity of the first cart before the collision = V₁ = 0.8 m/s

Velocity of the second cart before the collision = V₂ = 0 m/s (At rest initially)

Velocity of the carts after the collision = V₃

By conservation of linear momentum,

m₁V₁ + m₂V₂ = (m₁ + m₂)V₃

(0.3)(0.8) + (0.46)(0) = (0.3 + 0.46)V₃

V₃ = 0.316 m/s

Kinetic energy of the system before the collision = KE₁

KE₁ = m₁V₁²/2

KE₁ = (0.3)(0.8)²/2

KE₁ = 0.096 J

Kinetic energy of the system after the collision = KE₂

KE₂ = (m₁ + m₂)V₃²/2

KE₂ = (0.3 + 0.46)(0.316)²/2

KE₂ = 0.0379 J

Kinetic energy lost in the collision = KE

KE = KE₂ - KE₁

KE = 0.0379 - 0.096

KE = -0.0581 J

Kinetic energy lost in the collision = -0.0581 J