OBF Practice Questions - OBF - Olimpíada Brasileira De Física Exam

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A particle moves along the x-axis under a conservative force with potential energy U(x) = α x⁴ - β x², where α = 2.0 J/m⁴ and β = 8.0 J/m². The particle is released from rest with total mechanical energy E = 0 J. What are the positions of the stable equilibrium points and the maximum speed attained by the particle if its mass is m = 0.50 kg?

Stable equilibria at x = ±√2 m (≈ ±1.41 m) and maximum speed v_max = 4√2 m/s ≈ 5.66 m/s Stable equilibria at x = 0 m and maximum speed v_max = 2.0 m/s Stable equilibria at x = ±2.0 m and maximum speed v_max = 8.0 m/s Stable equilibria at x = ±1.0 m and maximum speed v_max = 4.0 m/s

Correct Answer:

Stable equilibria at x = ±√2 m (≈ ±1.41 m) and maximum speed v_max = 4√2 m/s ≈ 5.66 m/s

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