1 units conversions chapter 14 it is absolutely essential to report units with the number answers
TRANSCRIPT
2
Unit Historyinch width of your thumb
foot originally the length of your foot, now
greater
yard three feet, from nose to middle finger
5
Mass Mass the quantity of matter in an object
the measurement of the inertia
measured in kilograms (kg)
6
WeightWeightthe force upon an object due to gravity
Weight = Mass Acceleration of gravity
Fg = mg
measured in Newtons (N) in the metric system or pounds (lb) in the British system
7
Engineering Mass and Engineering Mass and WeightWeight
Pound-Mass lbm
One pound-mass weighs 1 pound. 1 slug = 32.2 lbm
Pound-Force lbf
It is the same as a pound (lb). 1 lbf = 1 lb
11
Dimensions
Dimension Symbol
Length
Mass
time
force
electric current
absolute temperature
luminous intensity
[L]
[M]
[T]
[F]
[A]
[
/]
12
Base Units
Fundamental Dimension Base Unit
time
electric current
absolute temperature
luminous intensity
amount of substance
second (s)
ampere (A)
kelvin (K)
candela (cd)
mole (mol)
13
The International System of Units (SI)
Fundamental Dimension Base Unit
length [L]
mass [M]
time [T]
electric current [A]
absolute temperature []
luminous intensity [l]
amount of substance [n]
meter (m)
kilogram (kg)
second (s)
ampere (A)
kelvin (K)
candela (cd)
mole (mol)
15
SI Prefixes
nano
micro
milli
centi
deci
deka
hecto
kilo
mega
giga
PrefixDecimal
Multiplier Symbol
10-9
10-6
10-3
10-2
10-1
10+1
10+2
10+3
10+6
10+9
n
m
c
d
da
h
k
M
G
16
Supplementary SI Dimensions
Supplementary Dimension Base Unit
plane angle
solid angle
radian (rad)
steradian (sr)
18
U.S. Customary System of Units (USCS)
Fundamental Dimension Base Unit
length [L]
force [F]
time [T]
foot (ft)
pound (lb)
second (sec)
Derived Dimension Unit Definition
mass [FT2/L] slug lbf sec2/ft
20
American Engineering System of Units (AES)
Fundamental Dimension Base Unit
length
mass
force
time
electric charge [Q]
absolute temperature
luminous intensity
amount of substance
foot (ft)
pound (lbm)
pound (lbf)
second (sec)
coulomb (C)
degree Rankine (oR)
candela (cd)
mole (mol)
21
Converting Between Foot and Meter
To convert from foot to meter, multiply by
3.048* E-01
To convert from meter to foot, multiply by
(3.048* E-01)-1
22
Thought Item
Concerning the previous slide, which of the following is true?a. There are exactly 0.3048 m/ft.b. There are exactly 0.3048 ft/m.c. Neither a not b.
Hint: Think about this physically..
23
American Engineering System
Note, there is a problem when we use the same unit (“pound”, meaning lbf and lbm) to describe two different dimensions.Newton's Second Law: F = ma
1 lbf = 1 lbm ft/s2 ??? NO!!!
Must have conservation of units.
24
Conservation of Units
Principle of conservation of units: units on the left side of an equation
must be the same as those on the right side of an equation
dimensional homogeneity
25
AES and Newton’s Law
Must maintain dimensional homogeneity:
Now we have lbf = lbf
See gcderived.ppt for the derivation of gc
cg
maF
2f
mc
sec lb
ft lb32.174g
26
Pairs Exercise (5 min.)Use a different pairing...The force of wind acting on a body can be computed by the formula:
F = 0.00256 Cd V2 A
where: F = wind force in lbf , Cd= drag coefficient (no units), V = wind velocity in miles per hour and A = projected area in ft2
Is this dimensionally homogeneous?What are the dimensions of 0.00256?
27
Reality Check...
Are units really important?Is checking your work and your team’s work really important?
Mars Lander (ABC news)Mars Lander (NASA)
29
Temperature Exercise
You take water from the faucet (80 oF) and bring it to a boil on the stove.What is the temperature change in oC?What is the initial temperature in oC?
30
A Solution
For the temperature change, the best solution process is to use degree equivalents
C deg 3.73
F deg )80212(
C deg
F deg 8.1
C deg 1
x
x