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• #1
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Calculate the resultant of the four forces shown and their total moment about A. Hence determine the perpendicular distance from A to the line of the single force which would have the same effect as the forces F1, F2, F3 and F4 combined.
Assume the following values:
F1 = 55N, F2 = 33N, F3 = 74N and F4 = 68N
Note that, in this diagram, angles shown are not drawn accurately

Could you please give me some clue of how to answer this question? my main problem is that I don't know how to find the distance between A and each forces, I'm so confused.

## The Attempt at a Solution

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• #2
PhanthomJay
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If you break up each of the forces into their x and y components, the perpendicular distances from the line of action of the forces components to point A will become obvious. Then the moment about A of all forces can be obtained by summing all moments of each component force. Watch plus and minus signs.

• #3
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PhanthomJay,Thank you very much,Considering what you said I used this formula to find each force and then The total force:

F * (sin or cos) * perpendicular distance = Moment

F1 * sin90 * 2 = 110
F2 * sin78 * 5 = 161.39
F3 * sin42 * 3 = 148.54
-(F4) * cos77 * 2 = -30.59

the total force = 389.34

If this is right then how can I find the prependicular distance for the total force? or how can I draw the total force on the picture?

• #4
PhanthomJay
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Gold Member
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507
PhanthomJay,Thank you very much,Considering what you said I used this formula to find each force and then The total force:

F * (sin or cos) * perpendicular distance = Moment

F1 * sin90 * 2 = 110
F2 * sin78 * 5 = 161.39
F3 * sin42 * 3 = 148.54
-(F4) * cos77 * 2 = -30.59
These values are the correct moments of the y components of the forces about A. You need to calculate the moments of the x components also.
the total force = 389.34
This is the total moment about A from the y component of forces. You need to determne the total moments from the x component of the forces also.
If this is right then how can I find the prependicular distance for the total force? or how can I draw the total force on the picture?
The sum total of the y components of forces is the y component of the resultant single force, Ry. The sum of the total x components of forces is the x component of the resultant single force, Rx. If you divide the total moment of the y component forces by the total y component forces, you get the perp distance from the line of action of Ry to A. If you divide the total moment of the x component forces by the total x component forces, you get the perp distance from the line of action of Rx to A. The magnitude and direction of R is determined from pythagoras' theorem and trig, and it passes through the coordinate where Rx and Ry meet.

• #5
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PhanthomJay , You are brilliant, Thank you so much, couldn't be explained better than that.
wonderful.

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