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A 2 kg block on rough incline at 45° with μ = 0.3. Determine if it stays at rest (g = 10, sin 45° = cos 45° = 1/√2 ≈ 0.707):
AStays at rest (μ ≥ tan 45° = 1 required, false)
BSlides down (tan 45° = 1 > μ = 0.3)
CSlides up
DFloats
Answer & Solution
Correct answer: B. Slides down (tan 45° = 1 > μ = 0.3)
For rest: μ ≥ tan θ. tan 45° = 1. Since μ = 0.3 < 1, friction can't hold — block slides down. (Body slides; calculate acceleration: a = g(sin45 - 0.3·cos45) = 10 × 0.707 × 0.7 = 4.95 m/s².)
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