Forces - Biomechanics of the Human Body - page 3

Exercise 1.1 Research and describe the laws of force of the interaction between
electric charges (Coulomb's law) and gravitational attraction between bodies
(Newton's universal law of gravitation). Specify the properties which give origin
to such forces. Discuss the relationship between both forces and the distance
between bodies. Discuss why, in the first case, forces can be either attractive or
repulsive and, in the second case, there is only the force of attraction.

1.3 Representation of Forces: Diagram of Forces

Vectors are characterized by both magnitude and direction and can be represented
graphically or mathematically. Force is an example of a vector quantity, and it is
indicated by F or by boldface letter F . In a diagram, a vector is represented by an
arrow whose direction determines the line of action; its length obeys a scale
and is proportional to the magnitude or intensity of the force. The head of the
arrow determines the direction of the vector and its origin, the location where
the force is applied. In Fig. 1.3 , three force vectors with different magnitudes
(length

¼ intensity) and directions are depicted. The magnitude of vector F is

written F .
A system of coordinates can be used to represent a force vector. In the case
of rectangular coordinates, shown in Fig. 1.4 , a force can be described through
its projection on each axis. The sign of a rectangular component is positive (+)
or negative (

) when the arrow is directed upward and to the right or
downward and to the left, respectively. The following trigonometric relations can
be used:

tan θ ¼ F y = F x ; sin θ ¼ F y = F and cos θ ¼ F x = F :

q

F x þ

The magnitude F can be obtained by the Pythagorean theorem: F ¼ F y .

F 1

F 3

Fig. 1.3 Three force
vectors with different
magnitude and direction

F 2