Question Video: The Resultant of Two Parallel Forces Acting in the Same Direction Mathematics

𝐹 and 12 N are two parallel forces, where 𝑅 is their resultant. Given that 𝐴𝐡 = 72 cm and 𝐴𝐢 = 48 cm, determine the magnitudes of 𝐹 and 𝑅.

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Video Transcript

𝐹 and 12 N are two parallel forces, where 𝑅 is their resultant. Given that 𝐴𝐡 equals 72 centimeters and 𝐴𝐢 equals 48 centimeters, determine the magnitudes of 𝐹 and 𝑅.

Well first of all, what we’re actually gonna do is mark all the information that we’ve been given. So we know that 𝐴𝐡 equals 72 centimeters and 𝐴𝐢 equals 48 centimeters. So as we have 𝐴𝐢 and 𝐴𝐡, what we can also do is actually work out 𝐢𝐡 because distance 𝐢𝐡 is gonna be equal to 72 minus 48 which is gonna be 24 centimeters.

Okay, great, so we’ve now actually marked on all the distances that we need. So what weβ€˜re gonna try and find out first is magnitude of force 𝐹. What I’m actually gonna call it is force 𝐹 𝐡. So we’ve got 𝐹 𝐴 at 𝐴 and 𝐹 𝐡 at 𝐡. So to enable me to calculate 𝐹 𝐡, what I’m gonna do is actually take anticlockwise and clockwise moments by the point 𝐢. So our anticlockwise moment is gonna be equal to 𝐹 𝐡 multiplied by 𝐢𝐡. So, therefore, it’s gonna be equal to 24𝐹 𝐡.

Okay, great, so that’s our anticlockwise moment. And our clockwise moment is actually gonna be 𝐹 𝐴 multiplied by 𝐴𝐢 because it’s 𝐹 𝐴, which is our force, and 𝐴𝐢, which is our perpendicular distance from the point 𝐢 which we’re actually taking the moments about. So, therefore, what it’s gonna give us is 48𝐹 𝐴. Okay, great, so we now know the anticlockwise and the clockwise moments about the point 𝐢. So what we can do is actually make them equal to each other.

So, therefore, what we can say is that 24𝐹 𝐡 is gonna be equal to 48 multiplied by 12. That’s cause 12 is our 𝐹 𝐴 cause we actually got given that in the question that’s on the diagram. So, therefore, what we can say is that 24𝐹 𝐡 is equal to 576. So therefore now, to actually find 𝐹 𝐡, so to find our force, what we need to do is divide each side by 24. So, therefore, we get a value of 𝐹 𝐡 of 24 newtons. Okay, great, so now what we need to do is to actually move on to the magnitude of 𝑅.

Now to enable us to actually find the magnitude of 𝑅, what we can actually do is say that because the forces are actually like and parallel, then therefore the magnitude of 𝑅 is gonna be equal to force 𝐴 add force 𝐡. So, therefore, it’s gonna be equal to 12 because that was our force 𝐴 plus 24 because that was our force 𝐡 that we actually found out. So, therefore, the magnitude of 𝑅 is gonna be equal to 36 N, so 36 newtons. So, therefore, we can say that if 𝐹 and 12 N are two parallel forces, where 𝑅 is their resultant and given that 𝐴𝐡 equals 72 centimeters and 𝐴𝐢 equals 48 centimeters, then the magnitudes of forces 𝐹 and 𝑅 are 24 newtons and 36 newtons, respectively.

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