Question

A car requires a constant power of `50` `hp` to maintain a constant velocity of `10` `ms^-1` (about `36` `kmh^-1`). What is the magnitude of the net force impeding motion (friction plus air resistance)?

Answer 1

Converting the power from hp to kW and dividing by the velocity (see the explanation below for why we do that) we find that the net force resisting motion is `3750` `N`.

Explanation:

Our first step is to convert horsepower `(hp)` to kilowatt `(kW)`, since the other units we are using are SI units. This is quite easy: `1` `hp` = `0.75` `kW`, so `50` `hp` = `37.5` `kW`. This is a power of `37500` `W` (One kW = 1000 W).

There are a few logical steps to get to our answer:

Power is defined as the rate at which work is done: the amount of work done per second:

`P=W/t`

The work done is the applied force times the distance traveled:

`W=Fd`

Substituting this into the first equation above, we get:

`P=Fd/t`

But distance over time is just velocity, `v=d/t`,

`P=Fv`

Rearranging to make `F` the subject:

`F=P/v`

Substituting in the information we have:

`F=37500/10 = 3750` `N`.

In this case, the mass of the car is unneeded information in the question: the net force resisting motion is `3750` `N`.