Final answer:
The maximum grade an automobile can climb is determined by balancing the available engine power at 25% efficiency against the work done while overcoming both gravity and a 300 N frictional force.
Step-by-step explanation:
The question pertains to the calculation of the maximum grade an automobile can climb given certain engine specifications and operating conditions. To determine this, we need to evaluate the available power at maximum efficiency and the forces acting on the car.
The power output of the engine is stated to be 140 horsepower (hp) and it operates at 25% efficiency. Since 1 hp equals to 746 watts, we can calculate the maximum power output in watts. However, since the question does not ask for the calculation itself, but rather for the understanding of concepts, we will focus on explaining the process.
The maximum rate at which the car can do work (which is power) against gravity and friction must equal the power output of the engine at maximum grade. The frictional force is given as 300 N. In moving at a constant speed of 50 km/h up the grade, the work done against gravity is based on the car's weight (mass times the acceleration due to gravity) and the steepness of the grade (slope).
The work done against friction is the frictional force times the distance covered. The balance between the engine's power output and the sum of the work done against gravity and friction will dictate the steepest grade the car can handle at the specified speed.