### Video Transcript

πΉ and 12 N are two parallel forces, where π
is their resultant. Given that π΄π΅ equals 72 centimeters and π΄πΆ equals 48 centimeters, determine the magnitudes of πΉ and π
.

Well first of all, what weβre actually gonna do is mark all the information that weβve been given. So we know that π΄π΅ equals 72 centimeters and π΄πΆ equals 48 centimeters. So as we have π΄πΆ and π΄π΅, what we can also do is actually work out πΆπ΅ because distance πΆπ΅ is gonna be equal to 72 minus 48 which is gonna be 24 centimeters.

Okay, great, so weβve now actually marked on all the distances that we need. So what weβre gonna try and find out first is magnitude of force πΉ. What Iβm actually gonna call it is force πΉ π΅. So weβve got πΉ π΄ at π΄ and πΉ π΅ at π΅. So to enable me to calculate πΉ π΅, what Iβm gonna do is actually take anticlockwise and clockwise moments by the point πΆ. So our anticlockwise moment is gonna be equal to πΉ π΅ multiplied by πΆπ΅. So, therefore, itβs gonna be equal to 24πΉ π΅.

Okay, great, so thatβs our anticlockwise moment. And our clockwise moment is actually gonna be πΉ π΄ multiplied by π΄πΆ because itβs πΉ π΄, which is our force, and π΄πΆ, which is our perpendicular distance from the point πΆ which weβre actually taking the moments about. So, therefore, what itβs gonna give us is 48πΉ π΄. Okay, great, so we now know the anticlockwise and the clockwise moments about the point πΆ. So what we can do is actually make them equal to each other.

So, therefore, what we can say is that 24πΉ π΅ is gonna be equal to 48 multiplied by 12. Thatβs cause 12 is our πΉ π΄ cause we actually got given that in the question thatβs on the diagram. So, therefore, what we can say is that 24πΉ π΅ is equal to 576. So therefore now, to actually find πΉ π΅, so to find our force, what we need to do is divide each side by 24. So, therefore, we get a value of πΉ π΅ of 24 newtons. Okay, great, so now what we need to do is to actually move on to the magnitude of π
.

Now to enable us to actually find the magnitude of π
, what we can actually do is say that because the forces are actually like and parallel, then therefore the magnitude of π
is gonna be equal to force π΄ add force π΅. So, therefore, itβs gonna be equal to 12 because that was our force π΄ plus 24 because that was our force π΅ that we actually found out. So, therefore, the magnitude of π
is gonna be equal to 36 N, so 36 newtons. So, therefore, we can say that if πΉ and 12 N are two parallel forces, where π
is their resultant and given that π΄π΅ equals 72 centimeters and π΄πΆ equals 48 centimeters, then the magnitudes of forces πΉ and π
are 24 newtons and 36 newtons, respectively.