The body slides down an inclined plane with an angle of inclination to the horizon of 30, the coefficient of friction

The body slides down an inclined plane with an angle of inclination to the horizon of 30, the coefficient of friction between the body and the plane is 0.2. Find the acceleration of the body.

To calculate the acceleration with which the taken body will slide along the inclined plane, we will make the projection of the acting forces on the axis located along the plane: m * a = Ft * sinα – Ftr; m * a = m * g * sinα – μ * N; m * a = m * g * sinα – μ * m * g * cosα; a = (sinα – μ * cosα) * g.

Variables and constants: g – gravitational acceleration (g = 9.81 m / s2); α – angle of inclination of the used plane (α = 30º); μ – coefficient of friction (μ = 0.2).

Calculation: a = (sinα – μ * cosα) * g = (sin 30º – 0.2 * cos 30º) * 9.81 = 3.2 m / s2.

Answer: The acceleration of the body during sliding is 3.2 m / s2.