The power of the tractor is 80 kW. With what speed can he go uphill with a slope of 0.25, if his mass is 2.5 tons?

N = 80 kW = 80,000 W.

h / S = 0.25.

m = 2.5 t = 2500 kg.

g = 10 m / s2.

V -?

With uniform rectilinear motion, the power of the tractor N is expressed by the formula: N = F * V, where F is the traction force of the tractor, V is the speed of the tractor.

V = N / F.

We will assume that the tractor moves uniformly, therefore, according to 1 Newton’s law, the action of forces on it is compensated.

Let’s write Newton’s 2 law in vector form: 0 = F + m * g + N, where F is the traction force, m * g is the gravity force, N is the surface reaction force.

OH: 0 = F – m * g * sinα.

OU: 0 = N – m * g * cosα.

F = m * g * sinα.

sinα = h / S.

F = m * g * h / S.

V = N * S / m * g * h.

V = 80,000 W * 4/2500 kg * 10 m / s2 = 12.8 m / s.

Answer: the tractor can drive uphill at a speed of V = 12.8 m / s.