A body of mass m located on a horizontal plane is acted upon by F (force)

A body of mass m located on a horizontal plane is acted upon by F (force) directed downward at an angle α, the coefficient of friction against the plane = µ. Find the acceleration of the body.

Let us write Newton’s 2 law in vector form: m * a = F + m * g + N + Ftr, where F is the force with which the load is pulled, m * g is the force of gravity, N is the surface reaction force, Ftr is the friction force.

For projections onto coordinate axes 2, Newton’s law will have the form:

ОХ: m * a = F * cosα – Ftr.

OU: 0 = – F * sinα – m * g + N.

a = (F * cosα – Ftr) / m.

N = m * g + F * sinα.

The friction force Ffr is determined by the formula: Ffr = μ * N = μ * (m * g + F * sinα).

The acceleration of the body a will be determined by the formula: a = (F * cosα – μ * (m * g + F * sinα)) / m.