If 7.00hp are required to drive a 1500-kg automobile at 66.0 km/h on a level road. What power is necessary to drive the car at 66.0 km/h down a 1.00 % grade? It requires 42.9 hp to drive the car at 66.0 km/h up a 10.0 % grade (a hill rising 10.0 m vertically in 100.0 m horizontally)? The total retarding force due to friction, air resistance, and so on is 285 N.
Is the following a statement of fact or a question?
<< It requires 42.9 hp to drive the car at 66.0 km/h up a 10.0 % grade (a hill rising 10.0 m vertically in 100.0 m horizontally)? >>
It is a fact.
Then why the question mark at the end?
Assume 35.9 extra hp is needed to provide the potential energy increase at that speed and 10% positive slope. At 1/10 the slope (1%) downwards, 3.6 hp is recovered from gravity, so the engine needs to provide only 3.4 hp.
To find the power necessary to drive a car at a certain speed down a 1.00% grade, we first need to determine the force acting on the car in the direction of motion. This force can be calculated using the formula:
Force = Mass x Acceleration
Since the car is moving at a constant speed, the acceleration is zero. Therefore, the force acting on the car is also zero in the absence of any other external forces. However, in this case, there is a total retarding force of 285 N acting on the car.
Hence, to keep the car moving at a constant speed down the 1.00% grade, we need to apply a force equal to the total retarding force, which is 285 N.
The power required to overcome this force can be calculated using the formula:
Power = Force x Velocity
Before proceeding to calculate the power, we need to convert the velocity from km/h to m/s.
Velocity = 66.0 km/h = (66.0 km/h) x (1000 m/km) x (1 h/3600 s) = 18.3 m/s
Now we can calculate the power:
Power = 285 N x 18.3 m/s = 5215.5 W
Therefore, the power necessary to drive the car at 66.0 km/h down a 1.00% grade is approximately 5215.5 Watts or 5.22 kW.
Regarding the power required to drive the car up a 10.0% grade, the given figure of 42.9 hp (horsepower) is already provided. To convert horsepower to watts, we can use the conversion factor:
1 horsepower (hp) = 745.7 Watts (W)
So, to convert 42.9 hp to watts:
Power = 42.9 hp x 745.7 W/hp = 32,034.93 W
Therefore, the power necessary to drive the car at 66.0 km/h up a 10.0% grade is approximately 32,034.93 watts or 32.03 kW.