The body evenly slides along an inclined plane with an angle of inclination of 30 to the horizon

The body evenly slides along an inclined plane with an angle of inclination of 30 to the horizon. if the angle of inclination is increased to 45, then the body will move with acceleration.

Task data: α1 (initial angle of inclination of the plane) = 30º; α2 (final tilt angle) = 45º.

Constants: g (acceleration due to gravity) = 9.81 m / s2.

1) Projection of forces on the plane at α1 = 30º: m * a = 0 = Fт * sinα1 – Fтр; Ft * sinα1 = Ftr; m * g * sinα1 = μ * m * g * cosα1; μ = sinα1 / cosα1 = tan 30º = √3 / 3.

2) Projection of forces onto the plane at α1 = 45º: m * a = Fт * sinα2 – Fтр = m * g * sinα2 – μ * m * g * cosα2, whence a = g * sinα2 – μ * g * cosα2 = 9, 81 * sin 45º – √3 / 3 * 9.81 * cos 45º = 2.93 m / s2.

Answer: After increasing the angle of inclination to 45º, the body will acquire an acceleration of 2.93 m / s2.