Question

As a sports car travels along 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

12.0 N

Step-by-step explanation:

First of all, let's convert the power from horsepower to Watts:

`P=0.371 hp \cdot 746 = 276.8 W`

Then, we know that the power exerted by the engine is given by

`P=Fv`

where

F is the force exerted by the engine

v is the velocity of the car

We know that

v = 23 m/s

So, we can re-arrange the equation to find the force exerted by the engine of the car:

`F=(P)/(v)=(276.8)/(23)=12.0 N`

Now, the equation of the forces acting on the car is:

`F-F_f = ma`

where

`F_f` is the force of friction acting on the car

a is the acceleration

However, the car is moving at constant velocity, so a = 0 and the equation becomes

`F-F_f = 0`

Which means that the force of friction is equal to the force produced by the engine:

`F_f = F = 12.0 N`