shayan ganji

2022-03-20

Estimate the terminal sped of a typical car having an engine with a constant power in a flat road, by using the concept of drag force.

user_27qwe

Skilled2023-04-24Added 375 answers

To estimate the terminal speed of a car with a constant power engine on a flat road, we can use the concept of drag force.

The drag force on a car is given by the equation:

${F}_{d}=\frac{1}{2}\cdot \rho \cdot {v}^{2}\cdot {C}_{d}\cdot A$

Where:

- ${F}_{d}$ is the drag force in N (Newton)

- $\rho $ is the air density in kg/m^3 (kilograms per cubic meter)

- v is the velocity of the car in m/s (meters per second)

- ${C}_{d}$ is the drag coefficient, which depends on the shape of the car and its orientation relative to the airflow

- A is the frontal area of the car in ${m}^{2}$ (square meters)

The drag force is opposed by the force of the car's engine, which is given by:

${F}_{\text{engine}}=\frac{{P}_{\text{engine}}}{v}$

Where:

- ${F}_{\text{engine}}$ is the force of the car's engine in N

- ${P}_{\text{engine}}$ is the power of the engine in W (Watts)

At the terminal speed of the car, the drag force and the force of the engine are equal and opposite. Therefore, we can set ${F}_{d}={F}_{\text{engine}}$ and solve for the velocity v:

$\frac{1}{2}\cdot \rho \cdot {v}^{2}\cdot {C}_{d}\cdot A=\frac{{P}_{\text{engine}\phantom{\rule{1ex}{0ex}}}}{v}$

Simplifying the equation, we get:

${v}^{3}=2\cdot \frac{{P}_{\text{engine}}}{\rho \cdot {C}_{d}\cdot A}$

Taking the cube root of both sides, we get:

$v={(2\cdot \frac{{P}_{\text{engine}}}{\rho \cdot {C}_{d}\cdot A})}^{\frac{1}{3}}$

So, the terminal speed of the car can be estimated using this equation, given the air density, the drag coefficient, the frontal area, and the power of the car's engine.

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