The body rises up the inclined plane according to the equation s = 1.6t / 2 + 0.8t. The coefficient of friction

The body rises up the inclined plane according to the equation s = 1.6t / 2 + 0.8t. The coefficient of friction against the surface is 0.15. determine the magnitude of the driving force, if the angle of inclination is 30 °, and the weight is 735N.

s = 1.6 * t / 2 + 0.8 * t.

μ = 0.15.

∠α = 30 °.

P = 735 N.

F -?

s = 1.6 * t / 2 + 0.8 * t = 0.8 * t + 0.8 * t = 1.6 * t.

From the dependence we see that this is a uniform motion with a constant speed V = 1.6 m / s.

Let’s write 2 Newton’s law in projections on the axis:

F = Ftr + m * g * sinα;

N = m * g * cosα.

N is the reaction force of the support.

According to Newton’s 3 law: the reaction force of the support N is equal to the weight of the body P: N = P.

m * g = P / cosα.

Ftr = μ * N = μ * Р.

F = μ * P + m * g * sinα.

F = μ * P + P * sinα / cosα.

F = 0.15 * 735 N + 735 N * sin30 ° / cos30 ° = 537.5 N.

Answer: a driving force F = 537.5 N. acts on the body.