(II) A typical compact car experiences a total drag force at 55 mi / h of about 350 N . If this

step 1 The efficiency of a car output can be written as efficiency is equal to work over Q input. Q inp

(II) A typical compact car experiences a total drag force at...

(II) A typical compact car experiences a total drag force at 55 $\mathrm{mi} / \mathrm{h}$ of about 350 $\mathrm{N}$ . If this car gets 35 miles per gallon of gasoline at this speed, and a liter of gasoline $(1 \mathrm{gal}=3.8 \mathrm{L})$ releases about $3.2 \times 10^{7} \mathrm{J}$ when burned, what is the car's efficiency?

(II) A typical compact car experiences a total drag force at
55 $\mathrm{mi} / \mathrm{h}$ of about 350 $\mathrm{N}$ . If this car gets 35 miles per gallon of
gasoline at this speed, and a liter of gasoline $(1 \mathrm{gal}=3.8 \mathrm{L})$
releases about $3.2 \times 10^{7} \mathrm{J}$ when burned, what is the car's
efficiency?

Key Concepts

Aerodynamic Drag

Aerodynamic drag refers to the resistive force exerted by air on a moving object. In vehicle dynamics, drag is a critical factor that determines the energy costs associated with overcoming air resistance at a given speed. It is modeled as a force that opposes the vehicle's motion and directly affects the work required to maintain a constant speed.

Work Done Against Drag

The concept of work in physics is defined as the force applied over a distance. When a vehicle overcomes drag, the work done is calculated by multiplying the drag force by the distance traveled. This work represents the useful mechanical energy output that is needed to counteract the resistive forces acting on the car during motion.

Energy Content of Fuel

The energy content of fuel describes the amount of chemical energy released when the fuel is burned. In energy conversion systems like an internal combustion engine, the fuel’s energy content is a key parameter because it determines how much energy is available for conversion into mechanical work. Accurately quantifying this energy is essential for assessing the overall efficiency of the energy conversion process.

Energy Conversion Efficiency

Energy conversion efficiency is the ratio of useful work output to the total energy input from the fuel. In the context of the problem, it measures how effectively the chemical energy stored in gasoline is converted into mechanical energy to overcome aerodynamic drag. This concept is crucial in understanding losses in real-world energy systems and evaluating the performance of engines and vehicles.

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