A car of the projected area of 2.8 m^2 is running into a airstream of temperature 30^∘ C he dra

step 1 Given the area being 2 .8 square meters, C sub D is .3. The temperature is 30 degrees Celsius. T

A car of the projected area of 2.8 m^2 is running into a...

A car of the projected area of $2.8 \mathrm{~m}^{2}$ is running into a airstream of temperature $30^{\circ} \mathrm{C}$ he drag coefficient for the car is $C_{D}=0.3$. Determine the power the engine must supply to maintain a constant speed of $140 \mathrm{~km} / \mathrm{h}$.

Key Concepts

Power Calculation for Constant Speed

To maintain a constant speed, the engine must supply power to counteract the work done against the aerodynamic drag force. The power required is calculated by multiplying the drag force by the velocity. This concept underscores the relationship between drag, force, and the rate at which energy must be expended to sustain motion.

Drag Equation

The drag equation relates the drag force to the properties of the moving body and the fluid through which it moves. The equation is typically expressed as F = 0.5 * ? * v² * C_D * A, where ? is the air density, v is the velocity, C_D is the drag coefficient, and A is the projected area. This equation is fundamental in estimating the aerodynamic resistance encountered by the vehicle.

Projected Area

The projected area is the effective frontal area exposed to the oncoming airflow. It determines the extent to which the air interacts with the object and directly influences the magnitude of the drag force acting on the vehicle.

Drag Coefficient

The drag coefficient is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment, relative to its projected area. It encapsulates the effects of the object's shape and surface roughness on the aerodynamic drag, making it a crucial parameter in calculating drag forces.

Aerodynamic Drag

Aerodynamic drag is the force exerted by air resistance on a body moving through it. This force increases with the square of the velocity and depends on factors like the vehicle's shape, speed, and the properties of the air. It represents the main resistive force that the engine must overcome to maintain a constant speed.

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