CalcElfCalcElf › 37° incline, μ = 0.75: does it move?
37° incline, μ = 0.75: does it move?
A block is released from rest at the top of an incline of angle 37°; the coefficient of kinetic friction between the block and the incline is 0.75 (g = 10 m/s²). Find the acceleration of the block and say whether it slides.
Answer
It does not slide (at rest), acceleration 0 m/s²
Step-by-step
- Gravity component factor sin37 = 0.6The tendency to slide comes from the component of gravity along the slope (factor sinθ)
- Friction factor μ·cos37 = 0.6The friction limit comes from the normal force and the friction coefficient (factor μcosθ)
- a = g(sinθ − μcosθ) = 10×(0.6 − 0.6) = 0Friction exceeds the component → it stays at rest
Why it works
Whether a block stays put on a slope is decided by comparing tanθ with μ: when μ = tanθ the downhill component of gravity exactly equals the friction limit, so the block is on the verge of sliding.
Common mistakes
- Forcing a negative acceleration onto the block even though it cannot slide uphill by itself.
- Using μ = sinθ (comparing 0.75 with 0.6) instead of the correct condition μ = tanθ.