Forces - Biomechanics of the Human Body - page 8

(a) By the method of parallelogram
(b) By calculation, applying the laws of trigonometry, considering that the angle
between the forces is 50

(a) We begin to solve the problem by adopting a scale as shown in the figure. The
resultant was obtained by the method of parallelogram. Applying the factor of
scale in R , the intensity of R is calculated as being 80 N. The direction of R is
shown in the figure.
(b) If the angle between the forces is 50 :

1 = 2

45 2 45 2 cos 50 Þ

R ¼ð þ þ 2 45 45 ¼ 82 N :

R ¼ 82 N :

Note: The precision of the graphic method is not very good. It can be improved by
drawing the figure in a larger scale.

Exercise 1.2 The leg of Example 1.1 is now moved away such that the angle
between the forces will be 30 , maintaining the same value of force F 1 ¼ W :

(a) In this case, will the value of the magnitude of R be greater or smaller than the
answer of Example 1.1?
(b) Determine the magnitude of R .

1.6 Newton's Laws

1.6.1 Newton's First Law of Motion (Law of Inertia)

A body will maintain its state of motion, remaining at rest or in uniform motion
unless it experiences a net external force, that is, a resultant force. This law implies
two equilibrium situations, one of static equilibrium and another of dynamic
equilibrium. In simpler terms, we can say that when a body is in static equilibrium,
the net force applied to it is zero.

Exercise 1.3 A vertical upward traction force of 60 N, shown in the figure of
Exercise 1.3, is applied on a head of a person standing straight. Suppose that the
weight of the head is 45 N. Determine the resultant force on the head.