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Units Conversions

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Units Conversions

Chapter 14

It is absolutely essential to report units with the number answers.

- inch
- width of your thumb

- foot
- originally the length of your foot, now greater

- yard
- three feet, from nose to middle finger

- fathom
- 6 feet, arm span

- mile
- 1000 paces, 5280 feet

- furlong
- 220 yards

Example:

T = 77 K

- the quantity of matter in an object
- the measurement of the inertia
- measured in kilograms (kg)

- the 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

- 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

Dimension

Symbol

Length

Mass

time

force

electric current

absolute temperature

luminous intensity

[L]

[M]

[T]

[F]

[A]

[q]

[/]

Base Unit

Fundamental Dimension

time

electric current

absolute temperature

luminous intensity

amount of substance

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

Fundamental Dimension

Base Unit

length [L]

mass [M]

time [T]

electric current [A]

absolute temperature [q]

luminous intensity [l]

amount of substance [n]

meter (m)

kilogram (kg)

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

- See fundamentalSI.ppt for information about these 'things'

Decimal Multiplier

Prefix

Symbol

nano

micro

milli

centi

deci

deka

hecto

kilo

mega

giga

10-9

10-6

10-3

10-2

10-1

10+1

10+2

10+3

10+6

10+9

n

m

m

c

d

da

h

k

M

G

Supplementary Dimension

Base Unit

plane angle

solid angle

radian (rad)

steradian (sr)

Fundamental Dimension

Base Unit

length [L]

force [F]

time [T]

foot (ft)

pound (lb)

second (sec)

Derived Dimension

Unit

Definition

lbf sec2/ft

mass [FT2/L]

slug

F = ma

W = mg

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)

- 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

- 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..

- 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.

- 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

- Must maintain dimensional homogeneity:
- Now we have lbf = lbf
- See gcderived.ppt for the derivation of gc

- 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?

Are units really important?

Is checking your work and your team’s work really important?

Mars Lander (ABC news)

Mars Lander (NASA)

- 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?

- For the temperature change, the best solution process is to use degree equivalents

- For the temperature value we use temperature conversion:
oC = (5/9)*(80 - 32) = 26.7 oC