Question

An air-track cart with mass m1=0.30kg and initial speed v0=0.95m/s collides with and sticks to a second cart that is at rest initially.

Part A

If the mass of the second cart is m2=0.44kg, how much kinetic energy is lost as a result of the collision?

Express your answer to two significant figures and include appropriate units.

Answer 1

Mass of the first cart = m₁ = 0.3 kg

Mass of the second cart = m₂ = 0.44 kg

Velocity of the first car before the collision = V₁ = 0.95 m/s

Velocity of the second car before the collision = V₂ = 0 m/s

Velocity of the carts after the collision = V₃

By conservation of linear momentum,

m₁V₁ + m₂V₂ = (m₁ + m₂)V₃

(0.3)(0.95) + (0.44)(0) = (0.3 + 0.44)V₃

V₃ = 0.385 m/s

Kinetic energy of the system before the collision = E₁

E₁ = m₁V₁²/2

E₁ = (0.3)(0.95)²/2

E₁ = 0.1354 J

Kinetic energy of the system after the collision = E₂

E₂ = (m₁ + m₂)V₃²/2

E₂ = (0.3 + 0.44)(0.385)²/2

E₂ = 0.0548 J

Kinetic energy lost in the collision = E

E = E₁ - E₂

E = 0.1354 - 0.0548

E = 0.0806 J

Converting to two significant figures,

E = 8.1 x 10^-2 J

Kinetic energy lost as a result of the collision = 8.1 x 10^-2 J