With what acceleration does the bar slide along an inclined plane with an angle of inclination

With what acceleration does the bar slide along an inclined plane with an angle of inclination of 30 degrees to the horizon with a friction coefficient of 0.2.

∠α = 30 “.

μ = 0.2.

g = 9.8 m / s ^ 2.

but – ?

Let’s write Newton’s 2 law for projections onto an inclined plane and a perpendicular to it.

m * a = m * g * sinα – Ftr.

N = m * g * cosα.

The friction force Ffr is determined by the formula: Ffr = μ * N = μ * m * g * cosα.

m * a = m * g * sinα – μ * m * g * cosα.

a = g * sinα – μ * g * cosα.

a = g * (sinα – μ * cosα).

a = 9.8 m / s ^ 2 * (sin30 “- 0.2 * cos30”) = 3.2 m / s ^ 2.

Answer: the acceleration of the bar is a = 3.2 m / s ^ 2.