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

Two parallel forces have magnitudes of 10 N and 20 N. The distance between their lines of action is 30 cm. 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΄.

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### 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 Iβve done to just start with, Iβve 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 weβre 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 thatβs 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 πΆ. And that point πΆ is what Iβve labelled where the resultant is going to act. And itβs 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 πΉπ΅, cause thatβs our force at π΅, multiplied by 30 minus π₯. And the reason itβs actually 30 minus π₯ is because 30 is the distance between π΄π΅, and we know that the distance between π΄πΆ is actually π₯. So therefore, we know that the anticlockwise moment is gonna be 20 multiplied by 30 minus π₯.

Okay, great! So now letβs look at the clockwise moment about the point πΆ. Well, the clockwise moment is gonna be equal to πΉπ΄, so the force at π΄, multiplied by π₯. So therefore, our clockwise moment about the point πΆ is gonna be equal to 10π₯.

So great! Weβve 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.