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When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the mechanical energy loss due to frictional forces exerted on the car by the air and the road. If the power developed by the engine is 179 hp, estimate the total friction force acting on the car when it is moving at a speed of 27 m/s. One horsepower equals 746 W.

Respuesta :

AMB000

Answer:

[tex]F=4945.7N[/tex]

Explanation:

Most of the power developed by the engine is used to compensate for the mechanical energy loss due to frictional forces because these are the only forces on the horizontal direction the automobile is subjected to, besides of that generated by the engine itself. If the automobile is moving at constant speed, then these the force the engine provides is equal to the total friction force acting on the car.

We calculate then the force the engine provides. We know that power relates to work by the equation [tex]P=\frac{W}{t}[/tex], and that work relates to force by the equation [tex]W=Fd[/tex], so combining them we have:

[tex]P=\frac{Fd}{t}=Fv[/tex]

Which can be written as:

[tex]F=\frac{P}{v}[/tex]

And since [tex]179hp[/tex] are [tex]179hp(\frac{746W}{1hp})=133534W[/tex], for our values the force the engine provides is:

[tex]F=\frac{133534W}{27m/s}=4945.7N[/tex]

Which is also then the total friction force acting on the car.

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