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1.4 Formulas

22

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

33

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

44

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

55

If W = fd, f = 10, and d = 16, find W.

W = fd

W = (10)(16)

W = 160

Example 1

Multiply.

66

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

77

Formulas from Geometry

88

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

99

Find the area of a triangle whose base is 18 in. and whose height is 10 in.

Example 4

Note: (in.)(in.) = in2

1010

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

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

1212

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

1313

Find the area of the trapezoid in Figure 1.21.

Example 6

Figure 1.21

1414

Example 6

Add within parentheses.

Divide.

Multiply.

cont’d

1515

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)