### Video Transcript

Two parallel forces have magnitudes
of 10 newtons and 20 newtons. The distance between their lines of
action is 30 centimeters. If the two forces are acting in the
same direction, find their resultant π
and the distance π₯ between its line of
action and point π΄.

So what Iβve done to just start
with, Iβve actually labelled our forces. We have force π΄ and force π΅. Force π΄ is 10 newtons and Force π΅
is equal to 20 newtons. And as weβre given forces are like
and parallel, what we can say is that the resultant force is gonna be equal to force
π΄ plus force π΅, which is gonna be equal to 10 plus 20. So therefore, what we can say is
that the magnitude of force are is gonna be equal to 30 N, so 30 newtons.

Okay, great! So thatβs the resultant magnitude
found. What we need to do now is find the
distance π₯ between its line of action and point π΄. So in order to actually find out
what π₯ is, what we need to do is actually take anticlockwise and clockwise moments
about the point πΆ. And that point πΆ is what Iβve
labelled where the resultant is going to act. And itβs actually the distance π₯
away from π΄.

Well, if we take a look at the
anticlockwise moment first, well the anticlockwise moment is going to be equal to
πΉπ΅, cause thatβs our force at π΅, multiplied by 30 minus π₯. And the reason itβs actually 30
minus π₯ is because 30 is the distance between π΄π΅, and we know that the distance
between π΄πΆ is actually π₯. So therefore, we know that the
anticlockwise moment is gonna be 20 multiplied by 30 minus π₯.

Okay, great! So now letβs look at the clockwise
moment about the point πΆ. Well, the clockwise moment is gonna
be equal to πΉπ΄, so the force at π΄, multiplied by π₯. So therefore, our clockwise moment
about the point πΆ is gonna be equal to 10π₯.

So great! Weβve actually worked out the
anticlockwise and the clockwise moments. But what we can do is actually
equate these because these are actually gonna be equal to each other. So therefore, what we actually get
is that 20 multiplied by 30 minus π₯ is equal to 10π₯. So therefore, if we actually expand
the parentheses, we get 20 multiplied by 30, which gives us 600, and 20 multiplied
by negative π₯, which gives us negative 20π₯. And this is all equal to 10π₯.

And then the next stage is to
actually add 20π₯ to each side. So we actually get that 600 is
equal to 30π₯. So therefore, what we do is then
divide each side by 30. So we get 600 over 30 is equal to
π₯. So we get π₯ is equal to 20. So therefore, what we can say is
that if we have two parallel forces that have magnitudes of 10 newtons and 20
newtons and they have a distance between their lines of action of 30 centimeters and
they act in the same direction, the resultant is gonna be equal to 30 newtons and
the distance π₯ between the line of action and actually the point π΄ where we have
the force of 10 newtons acting is going to be equal to 20 centimeters.