How Does Speed Affect Car Fuel Efficiency and Required Forces?

[courtney1121]

Estimate the ratio of the forces required to keep your car at a speed of 75 mph to that required to keep your car at a speed of 65 mph. What impact does this have on your gas mileage?

Where should I start?

 

[courtney1121]

OK so you will have a force of gravity, normal force, drag, and static friction. Gravity will be down, normal will be up, drag will be towards the left and static friction will be towards the right since they are trying to keep the car at a certain speed.

So where to go from here?

 

[kyle8921]

Well, the first thing to consider is that the force required to keep a car at a constant speed is directly related to the resistance forces acting on the car. These forces include air resistance, rolling resistance, and the force required to overcome the car's own weight.

To estimate the ratio of forces required to keep the car at 75 mph versus 65 mph, we can use the equation F = ma, where F is the force, m is the mass of the car, and a is the acceleration. Since we are looking at a constant speed, the acceleration is 0, so the equation simplifies to F = 0. This means that the force required to maintain the car's speed is equal to the sum of all the resistance forces acting on the car.

Assuming all other factors are constant, the main difference between the forces acting on the car at 75 mph and 65 mph is the air resistance. Air resistance increases with the square of the speed, so at 75 mph, the air resistance will be significantly higher than at 65 mph. This means that the force required to maintain the car's speed at 75 mph will be higher than at 65 mph.

To estimate the exact ratio, we would need to know the specific aerodynamic properties and weight of the car, as well as the road conditions. However, as a general estimate, the force required to maintain a car at 75 mph may be around 15-20% higher than at 65 mph.

Now, how does this impact gas mileage? Well, as we've established, the force required to maintain a car's speed is directly related to the resistance forces acting on the car. And the higher the resistance, the more energy (and therefore, fuel) is needed to overcome it. So, maintaining a speed of 75 mph will require more fuel than maintaining a speed of 65 mph. This means that your gas mileage will likely be lower at 75 mph compared to 65 mph.

In fact, studies have shown that driving at higher speeds (above 60 mph) can significantly decrease gas mileage. So, it's always a good idea to follow speed limits and drive at a steady, moderate speed to maximize your gas mileage and save on fuel costs.