- #1
gnits
- 137
- 46
- Homework Statement
- To prove forces around a quadrilateral form a couple
- Relevant Equations
- Balance of linear forces and torques
Can I please ask for help with the following:
Forces proportional to the sides of a quadrilateral taken in order act respectively along those sides. Prove that the resultant of the system is a couple whose magnitude is represented by twice the area of the quadrilateral.
Not sure where to start here. To be a couple I need to show that the resultant is pure torque. So I might start by showing that the horizontal and vertical resultant is zero. Here's a diagram, but it isn't helping me much (does this question hold true if the quadrilateral is concave?):
(could define x-axis to run A to B and y-axis to be vertical).
Let:
|AB| = a
|BC| = b
|CD| = c
|DA| = d
Then, is the question saying:
F1 = k * a
F2 = k * b
F3 = k * c
F4 = k * d
(For a scalar k).
If so I don't see how to go about showing that the horizontal and vertical resultant will be zero.
Thanks for any help,
Mitch.
Forces proportional to the sides of a quadrilateral taken in order act respectively along those sides. Prove that the resultant of the system is a couple whose magnitude is represented by twice the area of the quadrilateral.
Not sure where to start here. To be a couple I need to show that the resultant is pure torque. So I might start by showing that the horizontal and vertical resultant is zero. Here's a diagram, but it isn't helping me much (does this question hold true if the quadrilateral is concave?):
(could define x-axis to run A to B and y-axis to be vertical).
Let:
|AB| = a
|BC| = b
|CD| = c
|DA| = d
Then, is the question saying:
F1 = k * a
F2 = k * b
F3 = k * c
F4 = k * d
(For a scalar k).
If so I don't see how to go about showing that the horizontal and vertical resultant will be zero.
Thanks for any help,
Mitch.