A snowmobile with a mass of 100 kg moving along a horizontal section of the track at a speed of 30 km / h

A snowmobile with a mass of 100 kg moving along a horizontal section of the track at a speed of 30 km / h, developing a power of 22 kW. How much power they need to develop when going uphill with a 10-degree incline at the same speed.

m = 100 kg. V = 30 km / h = 8.3 m / s. N1 = 22 kW = 22 * ​​10 ^ 3 W. ∠α = 10 “. N2 -? With uniform motion, the power N is determined by the formula: N = Fт * V, Fт is the traction force, V is the speed of movement. N1 = Fт1 * V. N2 = Fт2 * V The thrust of the engine when moving along horizontal road Fт1 is equal to the friction force: Fт1 = μ * m * g. N1 = μ * m * g * V. μ * m * g = N1 / V. The thrust force of the engine when lifting Fт2 is equal to the sum of the friction force μ * m * g * cosα and the projection of gravity onto an inclined plane m * g * sin α: Ft2 = μ * m * g * cosα + m * g * sin α. Ft2 = N1 * cosα / V + m * g * sin α. N2 = (N1 * cosα / V + m * g * sin α) * V = N1 * cosα + m * g * sin α * V. N2 = 22 * ​​10 ^ 3 W * cos10 + 100 kg * 9.8 m / s ^ 2 * sin 10 “* 8.3 m / s = 23085 W.
Answer: the snowmobile must have a power of N2 = 23085 W.