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Copyright © Cengage Learning. All rights reserved.
1.4 Formulas
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A formula is a statement of a rule using letters to represent the relationship of certain quantities. In physics, one of the basic rules states that work equals force times distance.
If a person (Figure 1.16) lifts a 200-lb weight a distance of 3 ft, we say the work done is 200 lb 3 ft = 600 foot-pounds (ft-lb).
The work, W, equals the force, f,times the distance, d, or W = f d.
Formulas
Figure 1.16
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A person pushes against a car weighing 2700 lb but does
not move it. The work done is 2700 lb 0 ft = 0 ft-lb.
An automotive technician
(Figure 1.17) moves a diesel
engine weighing 1100 lb from the
floor to a workbench 4 ft high.
The work done in moving the
engine is 1100 lb 4 ft = 4400 ft-lb.
Formulas
Figure 1.17
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To summarize, if you know the amount of force and the
distance the force is applied, the work can be found by
simply multiplying the force and distance.
The formula W = f d is often written W = f d, or simply
W = fd.
Whenever there is no symbol between a number and a
letter or between two letters, it is assumed that the
operation to be performed is multiplication.
Formulas
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If W = fd, f = 10, and d = 16, find W.
W = fd
W = (10)(16)
W = 160
Example 1
Multiply.
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There are many other formulas used in science and technology. Some examples are given here:
a. d = vt
b. W = IEt
c. f = ma
d. P = IE
e.
f.
Formulas
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Formulas from Geometry
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The area of a triangle is given by the formula where b is the length of the base and h, the height, is the length of the altitude to the base (Figure 1.18).
(An altitude of a triangle is a line from a vertex perpendicular to the opposite side.)
Formulas from Geometry
Triangle
Figure 1.18
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Find the area of a triangle whose base is 18 in. and whose height is 10 in.
Example 4
Note: (in.)(in.) = in2
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The area of a parallelogram (a four-sided figure whose
opposite sides are parallel) is given by the formula A = bh,
where b is the length of the base and h is the perpendicular
distance between the base and its opposite side
(This formula can be used for all flat figures both slanted
and straight with the exception of a triangle and a
trapezoid)
Formulas from Geometry
Parallelogram
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1111
Find the area of a parallelogram with base 24 cm and
height 10 cm.
A = bh
A = (24 cm)(10 cm)
= 240 cm2
Example 5
Note: (cm)(cm) = cm2
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The area of a trapezoid (a four-sided figure with one pair of parallel sides) is given by the formula
where a and b are the lengths of the parallel sides (called bases), and h is the perpendicular distance between the bases (Figure 1.20).
Formulas from Geometry
TrapezoidFigure 1.20
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Find the area of the trapezoid in Figure 1.21.
Example 6
Figure 1.21
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Example 6
Add within parentheses.
Divide.
Multiply.
cont’d
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Practice Problems for Discussion 1.4
Pg. 22
7-12 use formulas from slide 6 and plug in given values to solve.
Ex. 7 use formula f=ma m=1600 a=24 so f = 1600(24)