A body weighing 1 kg moves on a horizontal surface under the action of two forces. The force f1 = 10H

A body weighing 1 kg moves on a horizontal surface under the action of two forces. The force f1 = 10H and is directed at an angle of 30 to the horizon, and f2 = 20H and is directed horizontally. Determine the acceleration of the body if the coefficient of friction is 0.1

To calculate the acceleration of a given body, we project all the forces onto the OX axis: m * a = F1 * cosα + F2 – Ftr = F1 * cosα + F2 – μ * N = F1 * cosα + F2 – μ * (Ft – F1 * sinα) = F1 * cosα + F2 – μ * (m * g – F1 * sinα), whence we express: a = (F1 * cosα + F2 – μ * (m * g – F1 * sinα)) / m.

Variables and constants: F1 – the first force (F1 = 10 N); α – the angle between the direction of the first force and the horizon (α = 30º); F2 – second force (F2 = 20 N); μ – coefficient of friction (μ = 0.1); m – body weight (m = 1 kg); g – acceleration due to gravity (g ≈ 10 m / s2).

Calculation: a = (F1 * cosα + F2 – μ * (m * g – F1 * sinα)) / m = (10 * cos 30º + 20 – 0.1 * (1 * 10 – 10 * sin 30º)) / 1 = 28.16 m / s2.

Answer: Acceleration is equal to 28.16 m / s2.