A car moves around a circular banked track of radius 50 m at speed 10 m s⁻¹. For minimum tyre friction/wear, find bank angle θ, using g = 10 m s⁻².
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Question

A car moves around a circular banked track of radius 50 m at speed 10 m s⁻¹. For minimum tyre friction/wear, find bank angle θ, using g = 10 m s⁻².

G1 Physics · Accepted Answer

Step 1: At design speed, tyre friction is not needed; the horizontal component of normal force provides centripetal acceleration. Step 2: Vertical balance gives Ncosθ = mg. Step 3: Horizontal balance gives Nsinθ = mv²/r. Step 4: Divide the second equation by the first: tanθ = v²/(rg). Step 5: tanθ = 10²/(50 × 10) = 100/500 = 1/5. Final answer: θ = tan⁻¹(1/5) (Option A).