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Acceleration of a Block on an Incline

Mediuminclinefriction
A block slides down a 30° incline with a coefficient of kinetic friction of 0.20. Its acceleration down the slope is most nearly:
  1. A3.92 m/s²
  2. B4.91 m/s²
  3. C3.21 m/s²
  4. D7.51 m/s²
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Answer: C. 3.21 m/s²

Equation: along the slope, ma = mg sin θ − μk mg cos θ, so a = g(sin θ − μk cos θ). Values: θ = 30°, μk = 0.20, g = 9.81 m/s². Step 1: sin 30° = 0.500, cos 30° = 0.866. Step 2: a = 9.81(0.500 − 0.20 × 0.866) = 9.81 × 0.327 = 3.21 m/s². 4.91 m/s² ignores friction; 3.92 m/s² uses sin for the normal force; 7.51 m/s² swaps sin and cos.
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