A train is hauled by 2-8-2 locomotive with 22.5 tonnes and on each driving axle. Assuming the coefficient of rail-wheel friction to be 0.25, what would be the hauling capacity of the locomotive? A. 15.0 tonnes B. 22.5 tonnes C. 45.0 tonnes D. 90.0 tonnes

15.0 tonnes
22.5 tonnes
45.0 tonnes
90.0 tonnes

The correct answer is $\boxed{\text{C}}$, 45.0 tonnes.

The hauling capacity of a locomotive is the maximum weight of the train that it can pull. It is determined by the locomotive’s power, the coefficient of rail-wheel friction, and the weight of the locomotive itself.

The power of a locomotive is the amount of force that it can exert on the train. It is measured in horsepower (hp). The coefficient of rail-wheel friction is a measure of how much friction there is between the wheels of the locomotive and the rails. It is a dimensionless number between 0 and 1. The weight of the locomotive is the force that the locomotive exerts on the rails.

The hauling capacity of a locomotive can be calculated using the following formula:

$H = \frac{P}{f} + W$

where:

  • $H$ is the hauling capacity of the locomotive in tonnes
  • $P$ is the power of the locomotive in hp
  • $f$ is the coefficient of rail-wheel friction
  • $W$ is the weight of the locomotive in tonnes

In this case, the power of the locomotive is 22.5 hp, the coefficient of rail-wheel friction is 0.25, and the weight of the locomotive is 22.5 tonnes. Substituting these values into the formula gives:

$H = \frac{22.5 \text{ hp}}{0.25} + 22.5 \text{ tonnes} = 45.0 \text{ tonnes}$

Therefore, the hauling capacity of the locomotive is 45.0 tonnes.

Option A is incorrect because it is the weight of the locomotive itself, not the hauling capacity. Option B is incorrect because it is the coefficient of rail-wheel friction, not the hauling capacity. Option D is incorrect because it is the power of the locomotive, not the hauling capacity.