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Forces on wheels and fuel consumption in cars

Motivated by real classroom discussions, we analyse the forces acting on moving vehicles, specifically friction forces on the wheels. In usual cars, with front-wheel drive, when the car accelerates these forces are in the forward direction in the front wheels, but they are in the opposite direction in the rear wheels. The situation may be intriguing for students, but it may also be helpful and stimulating to clarify the role of friction forces on rolling objects. In this article we also study thermodynamical aspects of an accelerating car, relating the distance traveled with the amount of fuel consumed. The fuel consumption is explicitly shown to be Galilean invariant and we identify the Gibbs free energy as the relevant quantity that enters in the thermodynamical description of the accelerating car. The more realistic case of the car's motion taking into account the dragging forces is also discussed.