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0593_C08_fm Page 251 Monday, May 6, 2002 2:45 PM

Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 251

F*
T*

G

W

FIGURE 8.7.1 FIGURE 8.7.2
A body B moving as a projectile. A free-body diagram of projectile B.

8.7 Projectile Motion
To illustrate the use of Eqs. (8.6.5) and (8.6.6), consider a body thrown into the air as a
projectile as in Figure 8.7.1. Then, the only applied forces on B are due to gravity, which
can be represented by the single weight force W passing through G as:

W =−MgN (8.7.1)
3
where N is the vertical unit vector shown in Figure 8.7.1. Figure 8.7.2 shows a free-body
3
diagram of B. Using d’Alembert’s principle, the governing equations of motion of B are,
then,

W + F * = 0 (8.7.2)

and

*
T = 0 (8.7.3)
or

a =− gN (8.7.4)
RG
3
and

T = T = T = 0 (8.7.5)
1 2 3

Suppose the acceleration of G is expressed in the form:

RG
xN + ˙˙
a = ˙˙ yN + ˙˙ (8.7.6)
zN
1 2 3