OBF Practice Questions - OBF - Olimpíada Brasileira de Física Exam - OBF Practice Questions - OBF

Question 1

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

Question 2

A uniform solid cylinder of mass M and radius R rolls without slipping down an incline of angle θ. What is the linear acceleration of the cylinder's center of mass and the minimum coefficient of static friction μ_s required to prevent slipping?

a = (1/2) g sin θ and μ_s = (1/2) tan θ a = (2/3) g sin θ and μ_s = (1/3) tan θ a = (3/4) g sin θ and μ_s = (1/4) tan θ a = (5/7) g sin θ and μ_s = (2/7) tan θ

Correct Answer:

a = (2/3) g sin θ and μ_s = (1/3) tan θ

Question 3

A small block of mass m rests on top of a frictionless sphere of radius R fixed to the ground. The block is given a tiny push so that it slides down the surface. At what vertical height h above the ground (measured from the base of the sphere) does the block lose contact with the sphere?

h = (4/3) R h = (3/2) R h = (5/3) R h = (7/5) R

Correct Answer:

h = (5/3) R

Question 4

A projectile is launched from the ground on a flat horizontal plane with initial speed v₀ at an angle α above the horizontal. Air resistance is negligible. If the projectile's maximum height equals its horizontal range (H = R), what is the launch angle α?

α = arctan(2) ≈ 63.4° α = arctan(1) = 45.0° α = arctan(3) ≈ 71.6° α = arctan(4) ≈ 76.0°

Correct Answer:

α = arctan(4) ≈ 76.0°

Question 5

A satellite of mass m is in a circular orbit of radius r around a planet of mass M. To transfer the satellite to a higher circular orbit of radius 2r using a standard Hohmann transfer orbit, what is the total speed change Δv_total = Δv₁ + Δv₂ required from the thrusters?

Δv_total = √(GM/r) [√(3/2) - 1 + 1/√2] Δv_total = √(GM/r) [√(4/3) - 1 + 1/√2 - √(1/3)] Δv_total = √(GM/r) [2 - √2] Δv_total = √(GM/r) [√(2) - 1]

Correct Answer:

Δv_total = √(GM/r) [√(4/3) - 1 + 1/√2 - √(1/3)]

Question 1

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Prepare with the OBF Practice Questions - OBF - Olimpíada Brasileira de Física Exam practice quiz. This question bank includes 100 questions covering mass, radius, uniform, field, and magnetic. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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OBF Practice Questions - OBF - Olimpíada Brasileira de Física Exam

This practice set contains 100 questions from the matching question bank and focuses on mass, radius, uniform, field, and magnetic. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

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OBF Practice Questions - OBF - Olimpíada Brasileira de Física Exam

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