Given that force 𝐹 one is parallel
to force 𝐹 two, where 𝐹 one equals two 𝐹 two and their resultant is acting at a
point that is 16 centimeters away from 𝐹 one, determine the distance between the
resultant’s line of action and 𝐹 two.
So what I’ve done first actually is
draw a little sketch to actually represent what we’ve got here. So we got force 𝐹 one and I’ve
said it’s at point 𝐴. I’ve got a resultant at point 𝐶,
which is 16 centimeters away from the force 𝐹 one. Then, we’ve also got 𝐹 two, which
is our other force. I’ve called this a point 𝐵.
And what I’m gonna actually call
our forces are two 𝑥 for 𝐹 one and 𝑥 for 𝐹 two. And that’s because we know that 𝐹
one is equal to two of 𝐹 two. So if we’ve got 𝐹 one is two 𝑥,
well that’s two times 𝑥 which is our 𝐹 two.
And if we take a look at the
question, we can see that actually what we’re trying to find is the distance 𝐶𝐵
because we want to find the distance between the resultant’s line of action and our
force 𝐹 two. Well, in order to actually solve
this problem, what we’re actually gonna do is to take anticlockwise and clockwise
moments about the point 𝐶. So it’s about the point that the
resultant’s force is actually acting at.
Well, if we take the clockwise
moment first, we’re gonna be able to see the clockwise moment is gonna be equal to
𝐹 one multiplied by 𝐴𝐶. And that’s because 𝐴𝐶 is actually
the perpendicular distance from our point 𝐶. And this is gonna be equal to two
𝑥 multiplied by 16. So again, we decided that we should
call our force two 𝑥, which gives us a moment of 32𝑥.
And then, we’re actually gonna take
the anticlockwise moment. And this is gonna be equal to 𝐹
two multiplied by 𝐶𝐵, which is gonna give us the distance 𝐶𝐵 multiplied by 𝑥
cause we said that the force 𝐹 two is 𝑥.
Now, it’s worth mentioning here
that actually in this case our units would be newton centimeters. We usually like to work in newton
meters. But because we’re actually just
trying to find the distance of line of action, it won’t actually affect this
problem. So we can actually just keep them
as values we have here, which are 32𝑥 and 𝐶𝐵𝑥. So therefore, we can actually make
these equal to each other. So we have 32𝑥 is equal to
So therefore, if we actually divide
each side of our equation by 𝑥, what we’re gonna be left with is 32 is equal to
So therefore, we can say that given
that force one is parallel to force two, where force one is equal to two times force
two, and the resultant is acting at point that is 16 centimeters away from force
one, the distance between the resultant’s line of action and force two is gonna be
equal to 32 centimeters.