Determine the work of the force directed horizontally if a body with a mass of 3 kg traveled a path

Determine the work of the force directed horizontally if a body with a mass of 3 kg traveled a path of 2 m and acquired a speed of 18 km / h. The coefficient of friction against the table surface is 0.01.

m = 3 kg.

g = 10 m / s ^ 2.

S = 2 m.

V0 = 0 m / s.

V = 18 km / h = 5 m / s.

μ = 0.01.

A -?

The work of force A is determined by the formula: A = F * S, where F is the force, S is the displacement under the action of this force.

Let us write Newton’s 2 law for a body of projections of forces on the horizontal axis: m * a = F – Ffr, where m is the mass of the body, a is the acceleration of the body, F is the force with which the body is pulled, Ffr is the friction force.

F = m * a + Ftr.

The friction force Ffr is determined by the formula: Ffr = μ * m * g, where μ is the coefficient of friction, g is the acceleration of gravity.

a = V ^ 2/2 * S.

F = m * V ^ 2/2 * S + μ * m * g = m * (V ^ 2/2 * S + μ * g).

A = m * S * (V ^ 2/2 * S + μ * g).

A = 3 kg * 2 m * ((5 m / s) ^ 2/2 * 2 m + 0.01 * 10 m / s ^ 2) = 3.75 J.

Answer: the force does the work A = 3.75 J.