The First Condition of Equilibrium is that the vector sum of all the forces acting on a body vanishes. This can be written as
F = F1+ F2+ F3+ F4+.
. . = 0
where ,
the Greek letter sigma, again means the summation of whatever follows -- the
summation of the forces, in this case.That's all there is!
However, remember the following
=>> Ensure that you have included all the forces. This means carefully draw a free body diagram. Include gravity (the weight) and all contact forces. =>> Remember that forces are vectors.
That means that the first condition of equilibrium,
F = 0 really means
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Example: Consider the 98 newton weight (or 10 kg mass) supported by a rope.
But this rope is now tied together with two other ropes as shown here.
To answer this, look at the forces exerted on the knot where the three ropes are joined. The knot at rest so the sum of the forces acting on it must be zero.
Draw a free-body diagram showing just those forces.
which really meansF = 0
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- 0.707 TL + 0.866 TR = 0 0.866 T R = 0.707 TL |
0.707 TL + 0.5 TR - 98 N = 0 0.707 TL + 0.5 TR = 98 N |
( 0.866 + 0.5 ) TR = 98 N 1.366 TR = 98 N TR = 98 N / 1.366 TR = 71.7 N |
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TL = 1.22 TR TL = 1.22 ( 71.7 N ) TL = 87.8 N |