Understanding the Concepts
* Power: The rate at which work is done. In this case, the power is used to overcome gravity and move the car uphill.
* Work: The force applied over a distance. Work is done against gravity when the car climbs the incline.
* Force of Gravity: The force pulling the car downwards, calculated as mass * acceleration due to gravity (9.8 m/s²).
* Inclination: A 10% incline means for every 100 meters traveled horizontally, the road rises 10 meters vertically.
Calculations
1. Calculate the force of gravity:
* Force (Fg) = mass * acceleration due to gravity
* Fg = 1500 kg * 9.8 m/s² = 14700 N
2. Calculate the component of gravity acting parallel to the incline:
* This component is what the car needs to overcome to ascend.
* We'll use the angle of the incline, which can be found using trigonometry:
* tan(angle) = 10/100 = 0.1
* angle = arctan(0.1) ≈ 5.71°
* Force parallel to incline (Fp) = Fg * sin(angle)
* Fp = 14700 N * sin(5.71°) ≈ 1470 N
3. Calculate the velocity at which the car can climb:
* Power = Force * Velocity
* Velocity = Power / Force
* Velocity = 20,000 W / 1470 N ≈ 13.61 m/s
Result
The car can ascend the 10% incline at a maximum velocity of approximately 13.61 meters per second.
Important Notes
* This calculation assumes no losses due to friction, air resistance, or inefficiency in the car's drivetrain. In reality, the actual maximum velocity will be lower.
* This calculation provides the theoretical maximum speed. The car's actual speed may be limited by factors such as engine performance, gear ratios, and driver input.
