Determine the acceleration of a body sliding along an inclined plane if the angle of inclination

Determine the acceleration of a body sliding along an inclined plane if the angle of inclination of the plane is 30 degrees and the coefficient of friction is 0.5.

The body is acted upon by gravity, friction, and the reaction force of the support. If we project the forces on the X-axis at an angle of inclination of 30º, and on the rest of the Y-axis a component with the X-axis at 90º:
X: ma = m * g * sin 30º – Ftr, where Ftr = μN (μ = 0.5), g – gravitational acceleration (g = 10 m / s²).
Y: 0 = N – m * g * cos 30º, N = m * g * cos 30º.
ma = m * g * sin 30º – μN = m * g * sin 30º – μ * m * g * cos 30º.
a = g * (sin 30º – μ * cos 30º) = 10 * (0.5 – 0.5 * 0.866) = 0.67 m / s².
Answer: The acceleration of the body is 0.67 m / s².



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