37° incline, μ = 0.25: will it slide?

A block starts from rest and slides down an incline of angle 37°; the coefficient of kinetic friction between the block and the incline is 0.25 (g = 10 m/s²). Find the acceleration of the block and say whether it slides.

Step-by-step

1. Gravity component factor sin37 = 0.6
   The tendency to slide comes from the component of gravity along the slope (factor sinθ)
2. Friction factor μ·cos37 = 0.2
   The friction limit comes from the normal force and the friction coefficient (factor μcosθ)
3. a = g(sinθ − μcosθ) = 10×(0.6 − 0.2) = 4
   Component exceeds friction → it slides

Why it works

On an incline, gravity pulls the block downhill with mg sinθ while friction can resist with at most μmg cosθ. Comparing those two decides whether the block moves, and when it does a = g(sinθ − μcosθ).

Common mistakes

• Using the weight mg as the normal force instead of mg cosθ.
• Swapping the textbook values sin37° = 0.6 and cos37° = 0.8.

Related

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