Page 10 - Fisika Terapan for Engineers and Scientists

210 CHAPTER 7 Work and Energy

(a) SOLUTION: (a) Figure 7.8a shows the inclined track.The roller-coaster car moves
Displacement is s. down the full length of this track. By inspection of the right triangle formed by the
incline and the ground, we see that the displacement of the car has a magnitude
s h
h s (7.10)
sin f
[Here we use the label (Greek phi) for the angle of the incline to distinguish it
from the angle appearing in Eq. (7.5).] Figure 7.8b shows a “free-body” diagram
for the car; the forces acting on it are the normal force N and the weight w. The
From triangle, we see weight makes an angle 90 with the displacement. According to Eq. (7.5),
that sin = h /s.
we then find that the work W done by the weight w is
h
W ws cos u mg cos(90 f)
(b) sin f
N Since cos(90 ) sin , the work is
h
W mg sin f mgh (7.11)

sin f
s
90° – w Alternatively, we can use components to calculate the work. For example, if we
choose the x axis horizontal and the y axis vertical, the motion is two-dimensional,
and we need to consider x and y components. The components of the weight are
Angle between weight w 0 and w mg. According to Eq. (7.9), the work done by the weight is
and displacement is x y
= 90 – . then
W w x w y 0 x ( mg) y 0 ( mg) ( h) mgh
FIGURE 7.8 (a) A roller-coaster car x y
undergoing a displacement along an
Of course, this alternative calculation agrees with Eq. (7.11).
inclined plane. (b) “Free-body” diagram
showing the weight, the normal force, and (b) The work done by the normal force is zero, since this force makes an angle
the displacement of the car. of 90 with the displacement.
COMMENTS: (a) Note that the result (7.11) for the work done by the weight is inde-
pendent of the angle of the incline—it depends only on the change of height, not
on the angle or the length of the inclined plane. (b) Note that the result of zero
work for the normal force is quite general.The normal force N acting on any body
rolling or sliding on any kind of fixed surface never does work on the body, since
this force is always perpendicular to the displacement.

✔ Checkup 7.1

QUESTION 1: Consider a frictionless roller-coaster car traveling up to, over, and down
Concepts
in from a peak.The forces on the car are its weight and the normal force of the tracks. Does
Context the normal force of the tracks perform work on the car? Does the weight?
QUESTION 2: While cutting a log with a saw, you push the saw forward, then pull
backward, etc. Do you do positive or negative work on the saw while pushing it
forward? While pulling it backward?
QUESTION 3: While walking her large dog on a leash, a woman holds the dog back to
a steady pace. Does the dog’s pull do positive or negative work on the woman? Does
the woman’s pull do positive or negative work on the dog?