Block on a rough slope: does it slide?

A block is released on a slope of angle 37° with friction coefficient 0.5 (g = 10). Find the acceleration 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 = 0.4
   The friction limit comes from the normal force and the friction coefficient (factor μcosθ)
3. a = g(sinθ − μcosθ) = 10×(0.6 − 0.4) = 2
   Component exceeds friction → it slides

Why it works

Compare the downhill component of gravity with the maximum friction. Textbooks use sin37° = 0.6 and cos37° = 0.8, so a = g(sinθ − μcosθ).

Common mistakes

• Using the exact trigonometric values instead of the textbook 0.6/0.8 for 37°.
• Forgetting to check the sign to decide whether it slides at all.

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