Forces and equilibrium - Orthopaedic Biomaterials in Research and Practice - page 4

A ´ A

FIGUre 1.1 applied force and reaction force.

as A , denotes a vector quantity). We see that in this case, the force is
not large enough to make the cube move; thus, the cube is s aid to be
in equilibrium, and there must be an equal force opposing A . T ha t is,
there must be a force ′ = A () t h at has the same magnitude as A ( A
or A indicates the magnitude of A ) and the opposite direction, so that
the sum of the forces (the net force) is zero. In this case, the opposing
force is a reaction force, which is produced by friction between the
cube and the surface on which it rests (see Chapter 11 for a discussion
of frictional forces). There are limits to the frictional reaction force; if
A is increased until it is greater than A (without changing the direc-
tion of either force), the cube will no longer be in static equilibrium and
will begin to move.

Working with vectors

Although vectors have both magnitude and direction, it is possible to add
and subtract them in much the same way as simple numbers. There are
two principal techniques for this: direct and after resolution.
In Figure 1.2, we see that vectors are added directly by placing the
tail of the second vector to the head of the first vector and so on and then
connecting the free head and tail with a new vector. Thus, CAB =+ ,

DABC =++ . Subtraction is performed by reversing the direction of

the second vector, so that EAB =+−( . When multiple

vectors are present, the order of addition and subtraction has no effect on
the result, as is the case for regular numbers. (“Regular” numbers pos-
sess only magnitude and are called scalars .)

=− or EA B

PROBLEM 1.1
In Figure 1.2, if A = 15 N, what is C ? Assume 1 cm = 5N.

ANSWER:

A scale rule shows that A is 3 cm long; thus, 1 cm = 5 N.* Since D is
5 cm long, D =×= 55 25 N .