Question

A level stretch of road with constant speed, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the sports car by the air and the road. If the power developed by the engine is 0.371 hp, calculate the total friction force acting on the sports car (in N) when it is moving at a speed of 23 m/s. One horsepower equals 746 W.

Answer 1

The magnitude of the force friction force is 12.0 N.

Explanation:

The car in this problem is moving at constant speed: this means that its acceleration is zero, so according to Newton's second law, the net force acting on it is also zero:

$F=ma$

where  F is the net force, m is the mass, a is the acceleration.

Here, there are two forces acting on the car in the horizontal direction:

- The thrust of the engine, $F_t$, forward

- The frictional force, $F_f$, backward

Since the net force on the car is zero, the two forces must be equal and opposite: so, the magnitude of the frictional force is equal to the magnitude of the thrust.

The power produced by the engine is:

$P=0.371 hp \cdot 746 W/hp =276.8 W$

And for an object moving at constant speed, the power is given by

$P=F_t v$

where

$F_t$ is the magnitude of the thurst

v is the velocity of the object

In this case, the car is moving at

v = 23 m/s

So, we can find the magnitude of the thrust:

$F=\frac{P}{v}=\frac{276.8}{23}=12.0 N$

And so, the force of friction is also 12.0 N.

Learn more about power and Newton's second law here:

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