Page 9 - mechanics

Chapter – 2 Concurrent forces in 2D

resultant problems where the resultant is already known to be
zero. The vector equation of equilibrium can be written as

R = Rx i + Ry j = 0, (2.41)

From the equality condition of vectors in Cartesian form in
equation (2.37), we have

R x =0 (2.42)
R y =0

or in another form

 Fx = 0 (2.43)
 Fy = 0

Thus, resolving all forces acting on the particle to their x
and y components, the problem is reduced to adding all x
component together and y components and equating to zero.

These vector equations are sometimes written in a scalar
informal way using the concept of balance. This means
equating the magnitudes of the forces acting to the right to the
magnitude of forces acting to the left and forces acting upward
to those acting downward. As this technique uses magnitudes,
no signs are included for forces in either direction.

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