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A physics professor uses an air-track cart of mass m to compress a spring of constant k by an amount x from its equilibrium length. The air-track has negligible friction. When she lets go, the spring launches the cart. What cart velocity should she expect after it is launched by the spring

Respuesta :

Answer:

        v = √k/m    x

Explanation:

We can solve this exercise using the energy conservation relationships

starting point. Fully compressed spring

        Em₀ = [tex]K_{e}[/tex] = ½ k x²

final point. Cart after leaving the spring

        [tex]Em_{f}[/tex] = K = ½ m v²

        Em₀ = Em_{f}

        ½ k x² = ½ m v²

        v = √k/m    x

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