Net potential energy change from weight difference and pulley displacement

Steps:

• Convert 60° to radians: θ = π/3 rad.
• Vertical displacement: h = r θ = 0.40 × (π/3) m ≈ 0.419 m.
• Heavier weight (20 N) rises, lighter (15 N) falls, so net ΔPE = (20 - 15) × h = 5h.
• Calculate: 5 × 0.419 ≈ 2.1 J.

Why C is correct:

• Gravitational PE change equals weight difference times displacement height, per ΔPE = mgh formula applied to net system.

Why the others are wrong:

• A: Likely misuses sin(60°) for arc length, giving h ≈ 0.346 m, then 5 × 0.066 ≈ 0.33 J (incorrect conversion).
• B: Approximates π/3 as 1 rad, yielding 5 × 0.40 × 1 = 2.0 J (ignores precise angle).
• D: Uses single weight (15 N) times approximate h, ignoring difference (15 × 0.40 × π/3 / something, but mismatched).

Final answer: C