A bus of mass 6 metric tons is pulled at a speed of 18 KMPH on a smooth incline of inclination 1 in 20. Power of the engine is, (g=10m^–2)

To determine the power required for a bus of mass 6 metric tons (6000 kg) moving at a constant speed of 18 km/h (5 m/s) up a smooth incline with a gradient of 1 in 20, we can follow these steps:

Convert Speed to Meters per Second:

18 km/h = 18,000 meters / 3,600 seconds = 5 m/s.

Calculate the Incline Angle:

An inclination of 1 in 20 means for every 20 meters horizontally, there's a 1-meter vertical rise.

The sine of the incline angle (θ) is:

sin(θ) = rise / hypotenuse = 1 / √(1² + 20²) = 1 / √401.

Determine the Gravitational Force Component Along the Incline:

The force due to gravity acting down the incline is:

F = m * g * sin(θ).

Given:

m = 6000 kg.

g = 10 m/s².

sin(θ) ≈ 1 / 20 (since for small angles, sin(θ) ≈ tan(θ) = rise/run).

Therefore:

F ≈ 6000 kg * 10 m/s² * (1/20) = 6000 * 10 / 20 = 3000 N.

Calculate the Power Required:

Power (P) is the product of the force along the incline and the velocity:

P = F * v.

Substituting the known values:

P = 3000 N * 5 m/s = 15,000 W.

Converting to kilowatts:

P = 15,000 W / 1000 = 15 kW.