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Example: A car of mass 1500 kg travels on a banked curve of radius 50 m. The road is banked at an angle of 15°. Find the speed at which the car can take the curve without relying on friction. Step 1: Draw forces. The weight (mg) acts downwards. The normal force (N) acts perpendicular to the road surface. Step 2: Resolve N into two components: N cosθ balances mg, and N sinθ provides the required centripetal force. Step 3: From vertical balance: N cosθ = mg → N = mg / cosθ. Step 4: Centripetal force: N sinθ = m v² / r. Step 5: Substitute N from step 3: (mg / cosθ) sinθ = m v² / r. Step 6: Simplify: g tanθ = v² / r → v² = g r tanθ. Step 7: Plug numbers: g = 9.8 m/s², r = 50 m, tan15° ≈ 0.268. v² = 9.8 × 50 × 0.268 ≈ 131.3 → v ≈ √131.3 ≈ 11.5 m/s. Answer: The car can safely negotiate the curve at about 11.5 m/s (≈ 41 km/h) without friction.