Video Transcript
A train of mass 170 metric tons is
moving along a horizontal section of track at a constant speed of 60 kilometers per
hour. Given that the engine’s power
output is 410 horsepower, find the magnitude of the resistance 𝑅 to the train’s
motion per metric ton of the train’s mass.
So what we have is our train, and
it’s moving along a track at constant speed. And we know that that speed is 60
kilometers per hour. And we know that the current power
output to maintain that speed is 410 horsepower. And we also know there’s gonna be a
locomotive force. And what you would think is, hold
on, if there’s a force, would that mean that the train would be accelerating? However, what we also know is that
there are opposing forces. And it’s these opposing forces,
well, the magnitude of resistance, that we’re looking to find in this question.
But what we do know is that the
magnitude of resistance is going to be equal to our force, so our electromotive
force. And that’s because the train is
traveling at a constant speed, so there is no acceleration. So therefore, what we can do is use
our formula for power. And that is that power is equal to
the force multiplied by the speed. However, if we want to find the
force, and ultimately the resistant force, then we can rearrange our formula to
force is equal to power divided by speed.
So you might think at this point,
okay, great, we just plug in our values. Well, this isn’t the case. And that’s because our units are
not in the correct units. So what we want to do is convert
our units to the standard SI units. So I’m gonna start with power. And what we know is that one
horsepower is equal to 735 watts. So therefore, our power is gonna be
equal to 410 multiplied by 735, and that’s gonna be watts, which is gonna give us a
power of 301,350 watts. Okay, great. So that’s our power dealt with.
So then next, we can concentrate on
the speed. And we know that one kilometer per
hour is equal to one over 3.6 meters per second. So therefore, we know that the
speed is going to be equal to 60 multiplied by one over 3.6 meters per second, which
is the same as 60 divided by 3.6 meters per second, which is gonna be equal to 16
and two-thirds meters per second. I’ve written it here as a fraction
just to maintain accuracy as we’re gonna be using these values later in the
calculation.
So therefore, we can now use our
formula to calculate the force. And this is gonna be equal to
301,350, so that’s our power, divided by 16 and two-thirds, which is our speed,
which is gonna give us a force of 18,081 newtons. Okay, great. But what we already said is that
this would be the same as the resistant force. However, in this question, what we
want to find out is not just the resistive force, but in fact, the magnitude of the
resistance to the train’s motion per metric ton of the train’s mass.
Well, what we know from the
question is the mass is equal to 170 metric tons. So therefore, we can say that the
magnitude of the resistance 𝑅 to the train’s motion per metric ton of the train’s
mass is going to be equal to, then we’re gonna have the force that we calculated
divided by the train’s mass, which is gonna be equal to 18,081 newtons over 170
metric tons. I’ve kept the units in on this
calculation just so we can see what the units of our answer are going to be. We can see that it’s gonna be
newtons per metric ton. So therefore, this is gonna be
equal to 106.36 newtons per metric ton. And we’ve rounded it here to two
decimal places.
