Question
What is the approximate speed at which the force of air drag on a car is equal to the weight of the car? Hint: Start by estimating the mass and the frontal area of the car.
Step 1
The weight of the car, denoted as $W$, is given by the product of its mass $m$ and the acceleration due to gravity $g$. This can be written as: \[W = mg\] Show more…
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The drag force exerted on a car by air depends on a dimensionless drag coefficient, the density of air, the car velocity, and the frontal area of the car. That is, $F_{D}=F_{D}\left(C_{\text {drag. }}\right.$ $A_{\text {front }} \rho, V$ ). Based on unit considerations alone, obtain a relation for the drag force.
The aerodynamic drag on a car depends on the "shape" of the car. For example, the car shown in Fig. $\mathrm{P} 9.42$ has a drag coefficient of 0.35 with the windows and roof closed. With the windows and roof open, the drag coefficient increases to $0.45 .$ With the windows and roof open, at what speed is the amount of power needed to overcome acrodynamic drag the same as it is at 65 mph with the windows and roof closed? Assume the frontal area remains the same. Recall that power is force times velocity.
The drag force exerted on a car by air depends on a dimensionless drag coefficient, the density of air, the car velocity, and the frontal area of the car. That is, $F_{D}=$ function $\left(C_{\text {Drag }} A_{\text {front },} \rho, V\right) .$ Based on unit considerations alone, obtain a relation for the drag force.
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