Loading...

PPT – Unit Conversions PowerPoint presentation | free to download - id: 823e88-NDJjO

The Adobe Flash plugin is needed to view this content

MEASUREMENT

- Unit Conversions

Today's Objectives

1) Importance of unit conversions 2) Parts of a

measurement 3) Units in equations

4) Documenting unit conversions

2

Are Units important?

3

Are Units important?

"The 'root cause' of the loss of the spacecraft

was the failed translation of English units into

metric units in a segment of ground-based,

navigation-related mission software, as NASA has

previously announced," said Arthur Stephenson,

chairman of the Mars Climate Orbiter Mission

Failure Investigation Board. "The failure review

board has identified other significant factors

that allowed this error to be born, and then let

it linger and propagate to the point where it

resulted in a major error in our understanding of

the spacecraft's path as it approached Mars."

http//mars.jpl.nasa.gov/msp98/orbiter/

4

International System of Units (SI)

Fundamental

Derived Dimensions

Dimensions

Force N (newton) kgm/s2

Length m

Energy J (joule) Nm

Mass kg

Power W (watt) J/s

Time s

SI prefixes listed in table need to have prefixes

with a memorized for exams!!!

8

U. S. Customary System (USCS)

Fundamental

Derived Dimensions

Dimensions

Mass slug lb

fs2/ft

Length ft

32.174 lb

Force lb

m

f

Energy ftlb

Time s

f

Power ftlb

f/s

9

A. SI Prefix Conversions

- 1. Find the difference between the exponents of

the two prefixes. - 2. Move the decimal that many places.

A. SI Prefix Conversions

Prefix

Symbol

Factor

move left

move right

A. SI Prefix Conversions

0.2

- 1) 20 cm ______________ m
- 2) 0.032 L ______________ mL
- 3) 45 ?m ______________ nm
- 4) 805 dm ______________ km

32

45,000

0.0805

A. SI Prefix Conversions

0.532

532 m _______ km

NUMBER

UNIT

B. Dimensional Analysis

- The Factor-Label Method
- Units, or labels are canceled, or factored out

Converting units

- Factor label method
- Regardless of conversion, keeping track of units

makes things come out right - Must use conversion factors
- - The relationship between two units
- Canceling out units is a way of checking that

your calculation is set up right!

B. Dimensional Analysis

- Steps
- 1. Identify starting ending units.
- 2. Line up conversion factors so units cancel.
- 3. Multiply all top numbers divide by each

bottom number. - 4. Check units answer.

Common conversion factors

- English Factor
- 1 gallon 4 quarts 4 qt/gal or 1gal/4 qt
- 1 mile 5280 feet 5280 ft/mile or 1 mile/5280

ft - 1 ton 2000 pounds 2000 lb/ton or 1 ton/2000

lb - Common English to Metric
- 1 liter 1.057 quarts 1.057 qt/L or 1

L/1.057 qt or

0.946 L/qt - 1 kilogram 2.2 pounds 2.2 lb/kg or 1

kg/2.2 lb - or 0.454 kg/lb
- 1 meter 1.094 yards 1.094 yd/m or

1m/1.094 yd - or 0.917m/yd
- 1 inch 2.54 cm 2.54 cm/inch or 1

in/2.54 cm

B. Dimensional Analysis

- Lining up conversion factors

1

1 in 2.54 cm

2.54 cm 2.54 cm

1

1 in 2.54 cm

1 in 1 in

Line Mole Method

Process to convert from one unit to another

Example Convert 3.00 m to inch

? 3.00 m

100 cm

1 in

1 m

2.54 cm

ANSWER 118 in

5

Line Mole Method

Process to convert from one unit to

another

Example Convert 3.00 m/s to m/hr

? 3.00 m

60 s

60 min

s

min

hr

ANSWER 10,800 m/hr

6

Example Metric conversion

How many milligrams are in a kilogram?

B. Dimensional Analysis

- How many milliliters are in 1.00 quart of milk?

1.00 qt

1 L 1.057 qt

1000 mL 1 L

946 mL

B. Dimensional Analysis

- You have 1.5 pounds of gold. Find its volume in

cm3 if the density of gold is 19.3 g/cm3.

1 cm3 19.3 g

1.5 lb

1 kg 2.2 lb

1000 g 1 kg

35 cm3

B. Dimensional Analysis

- How many liters of water would fill a container

that measures 75.0 in3?

75.0 in3

(2.54 cm)3 (1 in)3

1 L 1000 cm3

1.23 L

B. Dimensional Analysis

- 5) Your European hairdresser wants to cut your

hair 8.0 cm shorter. How many inches will he be

cutting off?

8.0 cm

1 in 2.54 cm

3.1 in

B. Dimensional Analysis

- 6) Taft football needs 550 cm for a 1st down.

How many yards is this?

550 cm

1 in 2.54 cm

1 ft 12 in

1 yd 3 ft

6.0 yd

B. Dimensional Analysis

- 7) A piece of wire is 1.3 m long. How many 1.5

cm pieces can be cut from this wire?

1.3 m

100 cm 1 m

1 piece 1.5 cm

86 pieces

As an Individual

(on a piece of paper)...

Use the Factor Label Method to convert the

following

34.6 m/s to mph

1)

15 ft3 to Liters

2)

3) Can you use FLM when converting from Celsius

to Kelvin? Why or why not?

Conversion Factors Handout

14

Units in Equations

Addition/Subtraction All terms must have the

same units

Multiplication/Division Units may cancel, like

variables

Homogeneity Units on both sides of the "" sign

must be the same

Transcendental Functions (sin x , ln x , ex )

the argument (x) does not have a dimension

7

Valid Units?

30 m 2

10 m

20 m

s

s

12 mile

28 mile

40 mile

hour

hour

hour

8

H\classes\eng1101\fall05\lectures\spring05\en1.13

b.sketch.amy.sxi

Converting Area and Volume

Caution Make sure the units cancel

Area 150 ft2 to yd2

1 yd

1 yd

150 ft2

(10)2 yd2

150 ft2

OR

3 ft

3 ft

(3)2 ft2

Volume 12 ft3 to Liters

(12)3 in3

(2.54)3 cm3

12 ft3

(1)3 m3

1000 L

(1)3 ft3

(1)3 in3

(100)3 cm3

1 m3

16

Chemical Herbicide Spill

Line Mole Method - Example

Problem

The permeability of sand is 1.0x10-4cm/s. If a

chemical herbicide is dumped on a sandy soil, how

long (in hours) will it take for the contaminant

to reach the well 150 feet away.

Diagram

150 feet

Herbicide

Well

Permeability of Sand 1.0x10-4 cm/s t Time

(hours) 1.0x10-4 cm/s __?__ ft/hr

10

Chemical Herbicide Spill

Factor Label Method - Example

Theory

Permeability Distance/Time Assumptions

Sand has constant permeability in area Herbicide

moves per permeability of sand

Solution 10-4 cm s

11

Chemical Herbicide Spill

Line Mole Method - Example

Theory

Permeability Distance/Time Assumptions

Sand has constant permeability in area Herbicide

moves per permeability of sand

Solution

1 in

1 ft

60 s

60 min

1.0x10-4 cm

s

2.54 cm

12 in 1 min

1 hr

0.011811 ft/hr

12

Chemical Herbicide Spill

Line Mole Method - Example

Solution

Permeability 0.011811 ft/hr Time Distance /

Permeability

t 150 ft

OR t 150 ft

hr

0.011811 ft/hr

0.011811 ft

t 12700 hours 13000 hours

How many years is that?

t 12700 hr

1 day

1 yr

1.4 yr

24 hr

365 day

13

As an individual, solve... Water Tower Problem

Problem Statement

- Your home town is growing so rapidly that another

water tower is necessary to meet the needs of the

community. Civil and environmental engineers

predict that the water tower will need to hold

1.00 x 10.06 kilograms of water. The engineers

also estimate the density of the water to be 999

kilograms per cubic meter.

- If this tower is 50.0 meters high and spherical,

what volume (gal) of water will the tower hold

and what will the diameter (ft) of the tower have

to be?

14

Diagram

mass of water 1.00 x 106 kg

density of water 999 kg/m3

tower height 50.0 m

? volume of water (L)

? diameter (ft)

Theory

4

r3

Volume of a sphere

3

23 3 V

diameter

2 r

www.algonquin.org/pw.htm

4

Assumptions

tower is spherical

15

Solution

1.00 x106 kg

1000 L

1 m3

volume of water

1.00 x 106 L

1 m3

999 kg

4

23 3 V

r3

diameter

2 r

Volume of a sphere

3

4

1.00 x 106 L

0.035315 ft3

volume of water

3.53 x 104 ft3

1 L

3.53 x 104 ft3

23 3

diameter

2 r

40.7 ft

4

16

http//en.wikipedia.org/wiki/Golf

Golf Ball Design

Minimum allowed diameter of a golf ball is

42.67mm Maximum Mass 45.93g

The surface usually has a pattern of 300-400

dimples designed to improve the ball's

aerodynamics.

The method of construction and materials greatly

affect the ball's playing characteristics such as

distance, trajectory, spin and feel.

Have a two-, three-, or four-layer design

constructed from various synthetic materials

Harder materials, such as Surlyn, usually result

in the ball's traveling longer distances,

Softer covers, such as Balata, tend to generate

higher spin, more "feel" and greater stopping

potential.

Golf balls are separated into three groups

depending on their construction two-, three-, or

four-piece covers.

17

http//en.wikipedia.org/wiki/Golf

Golf Ball Design

Minimum allowed diameter of a golf ball is

42.67mm

Assuming a golf ball has a spherical shape

What is the golf ball diameter in inches? What

is the volume of a golf ball in cubic centimeters

and cubic inches?

Maximum Mass 45.93g

What is the mass of a golf ball in pounds? What

is the density of a golf ball in g/cm3 and

lb/in3?

18

Golf Shafts

Golf shafts are what connects the grip to the

golf head

The profile of the golf shaft is circular in

shape and is usually thicker at the grip end than

at the club head end.

Any strong and light material may be used to make

the golf shaft.

Almost all shafts today are made of either

graphite or tempered steel

The shaft is a tapered tube made of metal

(usually steel), or graphite fiber. The shaft is

roughly 1/2 inch in diameter (12 mm) near the

grip and between 35 to 45 inches (89-115 cm) in

length.

19

Golf Shafts

Almost all shafts today are made of either

graphite or tempered steel

Graphite 2.09-2.23 g/cm3

Steel 7,861.093 kg/m³ (0.284 lb/in³)

How much would the shaft of a golf club weigh in

pounds if it were constructed from graphite or

steel?

Assume

Shaft Diameter 1/2 inch and solid Shaft

Length 40 inches

Why would you choose a graphite club over a steel

club or vice versa?

What is tempered steel?

20