The drag force acting on the car increases as the speed of the car
increases.
The correct values are;
- PART A; The power of engine against gravity is <u>40 kW</u>
- PART B; Engine power exerted against the air is <u>b) 200 kW</u>
- PART C; The air resistance force is <u>b) 4 kN</u>
- PART D The power the car exerts is <u>c) 25 kW</u>
Reasons:
The given parameters are;
Mass of the car = 2,000 kg
Engine power, P = 320 Hp = 240 kW
Inclination of the direction of motion, sin(θ) = 0.04
Speed of the car, v = 180 km/hr (50 m/s)
Losses = Air drag ∝ v²
PART A Power engine exerts against gravity;
The gravitational force acting along the plane = m·g·sin(θ)
The power of engine against gravity, = × v
Therefore;
= 2000 kg × 10 m/s² × 0.04 × 50 m/s = 40,000 W = 40 kW
The power of engine against gravity, = <u>40 kW</u>
PART B Engine power exerted against the air;
Let represent the engine power exerted against the air, and we have;
P = +
Therefore;
= P -
Which gives;
= 240 kW - 40 kW = 200 kW
Engine power exerted against the air, is <u>b) 200 kW</u>
PART C Air resistance force at the given speed
Let represent the air resistance force, we have;
Therefore;
Which gives;
The air resistance force, is <u>b) 4 kN</u>
PART D Power exerted by car moving on flat ground
∝ v²
= k·v²
4 kN = k × (50 m/s)²
The drag force when the car is moving at<em> v =</em> 25 m/s, is therefore;
= 1.6 kg/m × (25 m/s)² = 1,000 N
Power, P = Force × Speed
Therefore, P = × v
P = 1,000 N × 25 m/s = 25 kW
The power the car exerts, P is <u>c) 25 kW</u>
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