Incline 53°, friction 0.5: acceleration

A block slides down an inclined plane with an angle of 53 degrees, the coefficient of kinetic friction between the block and the incline is 0.5, take g = 10 m/s². Find the acceleration of the block sliding down and determine whether the block will slide.

Step-by-step

1. Gravity component factor sin53 = 0.8
   The tendency to slide comes from the component of gravity along the slope (factor sinθ)
2. Friction factor μ·cos53 = 0.3
   The friction limit comes from the normal force and the friction coefficient (factor μcosθ)
3. a = g(sinθ − μcosθ) = 10×(0.8 − 0.3) = 5
   Component exceeds friction → it slides

Why it works

The method for inclined plane problems is to decompose gravity into components parallel and perpendicular to the incline, writing force equations for each direction. The sliding component and normal force are both determined by the angle; the normal force is used to calculate friction. To judge whether it will slide, compare the sliding component with the maximum static friction. Only checking if acceleration is positive merely indicates accelerating downward and cannot replace this judgment.

Common mistakes

• Swapped sine and cosine for the angle, writing the sliding component as gravity times cosine.
• Calculated friction using the sliding component times the coefficient of friction instead of the normal force times the coefficient of friction.
• Only reported acceleration without answering the simultaneous question of whether it will slide.

Related

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