What minimum speed must a mass m have when entering the bottom of a vertical loop of radius R so that it can complete the loop (string/track contact maintained)?
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What minimum speed must a mass m have when entering the bottom of a vertical loop of radius R so that it can complete the loop (string/track contact maintained)?

G1 Physics · Accepted Answer

Step 1 — Principle: For a vertical loop, combine energy conservation with the minimum contact condition at the top. Step 2 — Working: At the top, minimum contact requires N = 0 and mvₜ²/R = mg, hence vₜ² = gR. Step 3 — Working: The top is 2R above the bottom, so conservation of energy gives ½mvᵦ² = ½mvₜ² + 2mgR = ½mgR + 2mgR. Step 4 — Working: Thus vᵦ² = 5gR and vᵦ = √(5gR). Correct answer: C — √(5gR).