Video Transcript
A car with an engine of 164
horsepower is moving at its maximum speed of 216 kilometers per hour. Calculate the magnitude of the
force generated by its engine.
So what we’ve got here is a sketch
of our car. And we’re gonna show here that our
car is moving with a speed of 216 kilometers per hour. And we know that its engine is
generating a power of 164 horsepower. Well, what we want to find or
calculate is the force. And this is the force that’s moving
the car forwards. But at this point, let’s think
about this force because we might think that this would cause the car to
accelerate. However, there are opposing forces
to the car’s motion. These don’t need to be considered
in detail in this question. But in general, what they are would
be frictional forces.
So now what we want to do is
consider a formula we know, and that’s the formula for power. And we know that power is equal to
force times speed. Well, therefore, as we’re trying to
find force in this question, we can rearrange this formula. And we can rearrange it so that
force is equal to power over speed.
Okay, great, so at first glance,
this looks like it’s gonna be very straightforward. Because what we could do is just
say that, well, the force is gonna be 164 over 216, so 164 horsepower over 216
kilometers per hour. However, this would give us the
force in horsepowers per kilometers per hour, which is not what we’re looking to
do.
So what we’re going to do first is
change our units into SI base units. Well, first of all, if we take a
look at our power, our power, as we said, is in horsepower. And what we can recall is that one
horsepower is equal to 735 watts. And then if we look at our speed,
it’s in kilometers per hour. Well, we know that one kilometer
per hour is equal to one over 3.6 meters per second. So that’s another really useful
conversion we’re gonna use.
So what can do first of all is work
out our power in watts. And what this is gonna be is 164
multiplied by 735, which is gonna be 120,540 watts. And our speed is gonna be equal to
216 multiplied by one over 3.6, which is the same as 216 divided by 3.6, which is
gonna give us the speed of 60 meters per second.
Okay, great, so we now have our SI
base units for our power and our speed. So let’s work out our force. So therefore, our force is gonna be
120,540 over 60, which is gonna give us a force of 2,009 newtons. So great, we’ve found the
force. But what we want to do here at this
stage is also show what the force could be in another unit. And that unit is gonna be
kilogram-weight. And to do that, what we’re going to
do is use another conversion factor. And that is that one
kilogram-weight is equal to 9.8 newtons.
So therefore, our force in
kilogram-weight is gonna be 2,009 divided by 9.8. So therefore, we can say that the
magnitude of the force generated by the engine of the car is 2,009 newtons or 205
kilogram-weight.
