Dos carritos se colocan en una mesa sobre la que pueden moverse sin rozamiento y se sujetan comprimiendo un resorte entre ellos. El carrito 1 tiene doble masa que el 2. De pronto se sueltan. A) Compara las velocidades, cantidades de movimiento y energías cinéticas que adquieren, b) ¿Cómo serían las respuestas si la masa del carrito 1 fuese mucho mayor que la del 2?

a)  v₁ = - ½ v₂,  K₁ / K ₂ = ½,)

Explanation:

A) Let's use the conservation of the moment, for this we define the system formed by the spring and the two cars, so the force during the separation is internal, therefore the moment is conserved

initial instant. Before releasing the carts

         p₀ = 0

final instant. After jumping the cars

         p_f = M v₁ + m v₂₂

how the moment was preserved

        p₀ = p_f

        0 = M v₁ + m v₂

        v₁ = - m / M v₂

indicate that M = 2m

        v₁ = - ½ v₂

the kinetic energy of each car is

        K₁ = ½ M v₁²

        K₁ = ½ 2m (v₂/ 2) ²

        K₁ = m ₂v₂² / 4

        K₂ = ½ m v₂²

the relationship between the kinetic energies is

         K₁ / K₂ = ½

B) If the much greater than the mass of car 1 is mass of car 2

        v = - m / M v₂

         In this case, the speed of car 1 is very small, so the car 1 practitioner does not backtrack and car 2 leaves with a lot of speed.

The energy is still conserved, where almost all the energy has it is car 2

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