Page 9 - Fisika Terapan for Engineers and Scientists

7.1 Work 209

(a)
F
s
q
(a) Zero work is done (b) Positive work is
when q = 90°. done for q 90°.
(b)
F
F
q
F s
s 90°
q
F cos q s

Work done by F is positive
when q 90°, so F has
a component parallel to
displacement s.

FIGURE 7.6 (a) A constant force F acts during FIGURE 7.7 (a) The force exerted by the woman is perpendicular to the
a displacement s. The force makes an angle with displacement. (b) The force exerted by the woman is now not perpendicular
the displacement. (b) The component of the force to the displacement.
along the direction of the displacement is F cos .

tors (see Section 3.4). The standard notation for the dot product consists of the two
vector symbols separated by a dot:

dot product (scalar product)
A B AB cos (7.6)

Accordingly, the expression (7.5) for the work can be written as the dot product of the
force vector F and displacement vector s,

W F # s (7.7)
In Section 3.4, we found that the dot product is also equal to the sum of the products
of the corresponding components of the two vectors, or

A B A B A B A B (7.8)
x x y y z z
If the components of F are F ,F , and F and those of s are x, y, and z, then the
x y z
second version of the dot product means that the work can be written
W F x F y F z (7.9)
x y z
Note that although this equation expresses the work as a sum of contributions from the
x, y, and z components of the force and the displacement, the work does not have sep-
arate components.The three terms on the right are merely three terms in a sum. Work
is a single-component, scalar quantity, not a vector quantity.

A roller-coaster car of mass m glides down to the bottom of a
EXAMPLE 3 Concepts
straight section of inclined track from a height h. (a) What is in
Context
the work done by gravity on the car? (b) What is the work done by the normal
force? Treat the motion as particle motion.