Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

Symbolic Solution

For this problem, we could start with the equation that relatesF 2 toF 1 , and then simplify the

similar quantities such as pandgin the following manner:

Often, this approach is preferred over the direct substitution of values into the equation right

away because it allows us to change a value of a variable such asm 1 or the areas and see what

happens to the result. For example, using the symbolic approach, we can see clearly that ifm 1

is increased to a value of 200 kg, thenm 2 changes to 1800 kg.

6 6..6 6 SSiiggnniifificcaanntt DDiiggiittss ((FFiigguurreess))

Engineers make measurements and carry out calculations. Engineers then record the results of meas-

urements and calculations using numbers. Significant digits (figures) represent and convey the extent

to which recorded or computed data is dependable. For example, consider the instruments shown

in Figure 6.4. We are interested in measuring the temperature of room air using a thermometer, the

dimensions of a credit card using an engineering ruler, and the pressure of a fluid in a line using the

pressure gage shown. As you can see from these examples, the measurement readings fall between

the smallest scale division of each instrument. In order to take the guess work out of the reading and

for consistency, we record the measurement to one half of the smallest scale division of the measur-

ing instrument. One half of the smallest scale division commonly is called theleast countof the meas-

uring instrument. For example, referring to Figure 6.4, it should be clear that the least count for the

thermometer is 1F (the smallest division is 2F), for the ruler is 0.05 in., and for the pressure gage

is 0.5 inches of water. Therefore, using the given thermometer, it would be incorrect to record the

air temperature as 71.25F and later use this value to carry out other calculations. Instead, it should

be recorded as 71   1 F. This way, you are telling the reader or the user of your measurement that

the temperature reading falls between 70F and 72F. Note the correct way of recording the depend-

ability of a measurement using the sign and the least count value.

As stated earlier, significant digits (figures) represent and convey the extent to which

recorded or computed data is dependable. Significant digits are numbers zero through nine.

However, when zeros are used to show the position of a decimal point, they are not considered

significant digits. For example, each of the following numbers 175, 25.5, 1.85, and 0.00125 has

three significant digits. Note the zeros in number 0.00125 are not considered as significant

m 2 

1 R 22

2

1 R 12

2 m^1 S^ m^2 

1 15 cm 2

2

1 5 cm 2

2 1 100 kg^2 900 kg

F 2 

A 2

A 1

F 1 m 2 g

p 1 R 22

2

p 1 R 12

2 1 m^1 g^2

F 2 8829 N 1 m 2 kg 2 1 9.81 m/s

2

2 1 m 2 900 kg

F 2 

A 2

A 1

F 1 

p 1 0.15 m 2

2

p 1 0.05 m 2

2 1 981 N^2 8829 N

144 Chapter 6 Fundamental Dimensions and Units

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀