Final answer:
To determine the maximum grade a car with a 140 hp engine at 25% efficiency can climb at 50 km/h, one must convert horsepower to watts, account for engine efficiency, and then calculate the power needed to overcome gravity and friction at the given speed. The maximum incline can then be determined by setting the available power equal to the required power to move upwards.
Step-by-step explanation:
To calculate the maximum grade that the automobile can climb at 50 km/h with a 140 hp engine at 25% efficiency, we should first convert the horsepower to watts. Since 1 hp is equal to 746 W, we have:
140 hp × 746 W/hp = 104,440 W (total power output)
However, the engine only has a 25% efficiency, so the actual power available for climbing the grade is 25% of the total power output:
104,440 W × 25% = 26,110 W (usable power for climbing)
The power required for climbing can be expressed as the product of the force needed to overcome gravity and the car's vertical velocity. The force due to gravity on a slope can be derived from the car's mass, the gravitational constant (9.8 m/s²), and the grade of the slope, while the vertical velocity is the product of the car's speed in the direction of the slope and the sine of the slope angle. To find the maximum grade, we would set the usable power for climbing equal to the power required to overcome both gravity and the frictional force (300 N) at the climbing speed of 50 km/h (which would need to be converted to m/s).
Without specifying the grade, we cannot carry out numerical calculations here, but the above process outlines the approach one would take. Remember that additional factors such as air resistance and mechanical losses in the car itself can also affect the calculation.