The body moves down an inclined rough plane, which forms an angle of 40 ° with the horizon.

The body moves down an inclined rough plane, which forms an angle of 40 ° with the horizon. Determine the acceleration of the body if the coefficient of sliding friction f = 0.3

To find the acceleration of a given body on a rough plane, we project all the forces onto the axis of the direction of motion: m * a = Ft * sinα – Ftr = m * g * sinα – μ * m * g * cosα = m * g * (sinα – μ * cosα), whence we express: a = g * (sinα – μ * cosα).

Constants and variables: g – gravitational acceleration (g = 9.81 m / s2); α is the angle of inclination of this rough plane (α = 40º); μ – coefficient of sliding friction (μ = 0.3).

Let’s perform the calculation: a = g * (sinα – μ * cosα) = 9.81 * (sin 40º – 0.3 * cos 40º) = 4.05 m / s2.

Answer: The body moved along this rough plane with an acceleration of 4.05 m / s2.