Forces and equilibrium - Orthopaedic Biomaterials in Research and Practice - page 8

resultant force

When a number of forces act on an object, the effect is the same as the
action of a single force called the resultant. The resultant force is equal
to the sum of the forces, acting at a point where they intersect. Any
multiple of non-parallel forces may have a single and unique point of
intersection.
Since the effect of the forces may be replaced by the effect of the
resultant, a first condition for equilibrium is described with the follow-
ing rule:

Translational equilibrium exists if the resultant of forces on an object is
equal to zero.

Equilibrium may be investigated in two ways. The first is through
inspection of the direct forces without decomposition into their compo-
nent forces. When this is not possible because of non-orthogonal forces,
it is often convenient to resolve the forces into orthogonal components
before determining their sum in any direction.

PROBLEM 1.3
If a limb is placed in split Russell's traction (Figure 1.5), what are the
magnitude and direction of the force on the distal femur?
A. 8 kgf horizontally to the left
B. 45 N horizontally to the left
C. 45 N inclined 35° from the horizontal, proximal to distal
D. 29.4 N vertically up
E. None of the above
Is the limb in Figure 1.5 in equilibrium? It does not appear to be
by this calculation, since the resultant force is not equal to zero. More
careful consideration leading to a complete solution must include the

29 N

49 N

30°

Graphic

| R | = 44 N
∆ = 36°

Exact
R H = 49 N - 29.4 sin 30°
R V = 29.4 cos 30°
R = R 2 H + R V = 42.7 N
θ = tan -1 ( R V / R H ) = 36.6°

3 kg

5 kg

1 cm = 50 N

FIGUre 1.5 split russell's traction (Problem 1.3).