Given that a car’s maximum speed is
270 kilometers per hour and its engine generates a force of 96 kilograms-weight,
determine the power of its engine.
All right, so let’s say that this
is our car moving along at its maximum speed of 270 kilometers per hour. The car does this, we’re told, when
its engine generates a force of 96 kilograms-weight. That force, we’ll call it 𝐹,
pushes the car forward, which we might think would make the car accelerate. But actually, the car maintains
this constant speed because there are opposing forces to the car’s motion. We don’t need to consider them in
detail, but in general these will be frictional forces.
Our goal is to determine the power
of this car’s engine. And we can start doing this by
recalling that power is equal to force multiplied by speed. This suggests that we can calculate
the power of our car’s engine by multiplying the given force by the given speed. The challenge to this, though, is
that the units involved are not on a consistent basis. Ultimately, we would like to
express our engine’s power in horsepower. But if we multiply these values as
is, we’ll get a result in kilograms-weight kilometers per hour. To clarify the meaning of the units
involved, we can convert them to more familiar SI base units.
One kilogram-weight is equal to 9.8
newtons of force. Likewise, one kilometer per hour is
equal to one over 3.6 meters per second. This means that if we take the
value 96 and we multiply it by 9.8, then we’ll have a total force in units of
newtons. And then if we work with 270,
dividing this by 3.6, we’ll have a speed in units of meters per second. All this is helpful because it
means if we were to calculate this power now, we would get an answer in the SI base
unit of power, watts.
As we mentioned, though, we would
like to give our final answer in units of metric horsepower. One metric horsepower is equal to
735 watts, which means if we divide the right-hand side of our equation by 735 watts
per horsepower, where, just like with our other conversions, we’re effectively
multiplying by one, which is why we can apply this operation to just one side of our
equation, then the units of newton meters per second cancel with watts in the
denominator and our units of horsepower come up top so that finally we have an
expression for power in the units of interest.
When we enter this expression on
our calculator, we get a result of exactly 96 horsepower. This is the power of our car’s