Calculate the power required of a 1190 kg car as it climbs a 11° hill at a steady 103 km h-1. The total friction and air resistance is 700 N. Answer in kW, to the nearest whole number.
To calculate the power required for a car to climb a hill, we need to consider the gravitational force, the force of friction and air resistance, and the velocity of the car.
First, let's calculate the gravitational force acting on the car as it climbs the hill. The gravitational force can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity
where mass is the mass of the car (1190 kg) and acceleration_due_to_gravity is approximately 9.8 m/s^2.
Force_gravity = 1190 kg * 9.8 m/s^2
Force_gravity ≈ 11662 N
Next, let's calculate the component of the gravitational force that acts parallel to the slope of the hill. This force can be calculated as:
Force_parallel = Force_gravity * sin(angle)
where the angle is the inclination of the hill (11°) and sin(angle) is the sine of the angle in radians.
Force_parallel = 11662 N * sin(11°)
Force_parallel ≈ 2106 N
Now, let's calculate the total force acting against the car, including friction and air resistance.
Force_total = Force_parallel + force_of_friction_and_air_resistance
Force_total = 2106 N + 700 N
Force_total = 2806 N
Finally, let's calculate the power required by the car using the formula:
Power = Force_total * velocity
where velocity is the steady velocity of the car (103 km/h or 28.6 m/s).
Power = 2806 N * 28.6 m/s
Power ≈ 80,211.6 W
To convert watts to kilowatts, divide the power by 1000:
Power ≈ 80,211.6 W / 1000
Power ≈ 80.2 kW
Rounded to the nearest whole number, the power required by the car as it climbs the hill at a steady 103 km/h is approximately 80 kW.