What is the Resultant of Four Proportional Forces on a Quadrilateral?

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Homework Help Overview

The problem involves determining the resultant of four forces that are proportional to the sides of a quadrilateral ABCD. The forces act along the sides AB, BC, and CD, with a fourth force acting from A to D. The original poster attempts to find the magnitude and direction of the resultant and the point where it intersects CD.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss vector summation and the direction of resultant forces, with some questioning the correctness of the original poster's approach. There are hints about the geometry involved, particularly regarding the line BL and its relationship to the forces.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance without offering complete solutions. There is an exploration of the relationships between the forces and their resultant, with some participants expressing uncertainty about the next steps.

Contextual Notes

There is a mention of a different answer in the book that lacks a complete solution, which adds to the confusion. Participants are also reminded of forum rules regarding the provision of full solutions.

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Homework Statement



Four forces act along and are proportional to the sides of the quadrilateral ABCD, three act in the direction AB,BC and CD and the fourth acts from A to D; find the magnitude and direction of their resultant, and determine the point In which it meets CD.

The Attempt at a Solution


i summed up the vectors and its AD then it meets CD at D but its a wrong solution according to my book
 
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hi batballbat! :smile:

hint: the resultant of AB and BC must go through B, mustn't it? :wink:
 
there is a different answer in the book but not a complete solution. and i don't know how to come up with such a solution
 
(just got up :zzz: …)

what is the answer?

maybe you can work backwards from that? :smile:
 
solution:
through B draw BL, parallel to AC, to meet CD in L; bisect DL in X; the resultatnt is a force through X, parallel to AD, and equal to twice AD.
 
yes, that's what i have :smile:

ok, can you see that that the resultant of the forces AB and BC must lie along the line BL ?
 
yes
please give a full solution
 
batballbat said:
please give a full solution

what?? :frown:

read the forum rules again

now explain why the resultant of the forces AB and BC must lie along the line BL
 
because the two forces are acting on B and the resultant of AB and BC acts along BL by parallelogram law
 
  • #10
batballbat said:
because the two forces are acting on B and the resultant of AB and BC acts along BL by parallelogram law

that's correct :smile:

ok, now you need to combine that resultant (along BL) with the force CD …

which point must that go through?
 
  • #11
that i do not know and i guess that's what's troubling me.
should i translate the vector CD?
ALso the resultant acts along BL but is not equal to BL isn't it?
 
  • #12
resultant acts along AD
 

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