Calculating how to overcome drag

[rosie_burk]

Homework Statement

Studetns examine the aerodynamics of a model car which has a drag force in air of 10 N at 10 m/s.

They wish to estimate what the drag will be for a full scale model, and the energy lost on a given trip. The drag coefficient C remains constant C= 0.6. The cross-sectional area A of the car is increased to 2 times its original area, and the speed is now increased to 20 m/s.
How much work does this car do in overcoming air resistance in a journey of 1000 m. Answer in joule.

Homework Equations

new drag force = (C/0.5) * (area/original area)* original drag force
then Energy to overcome drag = Work = force x distance.

The Attempt at a Solution

(.6*.5)(20/10)(10)=24

24*1000=2400

but answer is 40000

 

[Fightfish]

Drag force is proportional to the cross-sectional area and velocity of the object. Since the drag coefficient remains the same, we can effectively ignore it.
Thus it is clear that when I double cross-sectional area or velocity, the magnitude of the drag force would be doubled as well. When both are doubled simultaneously, the drag force is quadrupled to 40N. The relation between old and new drag force would be:
$$\frac{F_{1}}{F_{2}} = \frac{A_{1} v_{1}}{A_{2} v_{2}}$$
The drag coefficient cancels out, so there is no need to include it.
And, 24*1000=2400?? Do take more effort in putting forth your attempt here...

 

[tomcue]

joules

I would first commend the students for their efforts in examining the aerodynamics of a model car and exploring the concept of drag. I would then offer the following response to their calculations:

Your calculations for the new drag force and energy to overcome drag are correct. However, the work done in overcoming air resistance is not simply equal to the energy required. Work is defined as the product of force and displacement in the direction of the force. In this case, the force is the new drag force and the displacement is the distance traveled (1000 m).

Therefore, the work done in overcoming air resistance is:

Work = new drag force * distance = 24 N * 1000 m = 24,000 joules

This is the amount of work done by the car in overcoming air resistance in a journey of 1000 m. To calculate the energy lost, we need to consider the efficiency of the car's engine. If we assume an efficiency of 50%, then the energy lost due to drag would be twice the work done, which is equal to 48,000 joules.

I would also suggest that the students consider other factors that may affect the drag on a full-scale car, such as the shape and design of the car, the surface roughness, and the air density. These factors can significantly impact the drag force and the energy lost during a trip. Overall, it is important to continue exploring and experimenting with different variables to gain a better understanding of the complex concept of drag.