PHY 2048Summer 2010

LECTURE 1

Measurements

POWERS OF TEN

1

10

100

1,000

10,000

100,000

1,000,000

= 101

= 102

= 103

= 104

= 105

= 106

1

0.1

0.01

0.001

0.0001

0.00001

0.000001

= 10-1

= 10-2

= 10-3

= 10-4

= 10-5

= 10-6

Wright the following numbers in scientific notation:

45100 = 4.5 x 104

310,000,000,000 = 3.1 x 1011

0.001000 = 1.0 x 10-3

0.0000000000012 = 1.2 x 10 -12

What number is 510-

5107

A. 5B. 0.5C. 50D. 500E. None of the above

500 x 6000 = (5x102) x (6x103) = 30 x 105 = 3x106

6000 ÷ 500 = (6 x 103) ÷ (5x102) = 60 ÷ 5 =12

0.005 x 0.000006 = (5x10-3) x (6x10-6) = 30x10-9=3x10-8

0.003 ÷ 0.000006 = (3x10-3) ÷ (6x10-6) =

0.5x103 = 5x102 =500

There are questions like "how fast", "how far", or "how much" which, when answered, we must supply a unit of measurement:

How fast: 50 How fast: 50

How far: 30How far: 30

How much: 8How much: 8

Because of this, numbers in science will always have "units". These units are just as important as the numbers when communicating observations.

Never write a number without its units.

miles per hour

miles

pounds

TheThe British System of Measurement is commonly is commonly used as the day to day system in the United used as the day to day system in the United States. We are familiar with this system: we know States. We are familiar with this system: we know about pounds, feet, and gallons. However, the about pounds, feet, and gallons. However, the British system is an impossible system to do British system is an impossible system to do conversions between units since the relations conversions between units since the relations between units have no pattern (they are between units have no pattern (they are arbitrary). arbitrary).

1 mile = 1760 yards

1 yard = 3 feet

1 foot = 12 inches

TheThe International System of measurementof measurement (abbreviated(abbreviated SI SI) is commonly called the ) is commonly called the metric metric systemsystem in the United States. The relation in the United States. The relation between units are multiples of ten.between units are multiples of ten.

All science measurements are made using this system.

1 kilometer = 1000 meters1 kilometer = 1000 meters

1 meter = 100 1 meter = 100 centimeterscentimeters

1 centimeter = 10 1 centimeter = 10 millimetersmillimeters

Relation betweenRelation between SISI andand BritishBritish systems

m yd 1 yd = 0.9 m

m mile 1 mile = 1600 m

mm in 1 in = 25 mm

metric British approximate relationmetric British approximate relation

liter quart 1 quart = 1 liter liter gallon 1 gallon = 3.8 litersg lb 1 lb = 450 g

1 meter = 3.3 ft = 39 inches1 cm = 0.39 inches1km = 0.62 miles

1 ft = 30 cm1 inch = 2.5 cm1 mile = 1.6 km

1 kg weights 2.2 lb on earth1 lb on earth has a mass of 0.45 kg

Celsius temperature =5 x (Fahrenheit temperature – 32) / 9

Fahrenheit temperature = 32 + (9 x Celsius temperature) / 5

Using wrong units caused trouble as recently as September 1999, when a

probe launched by NASA was lost in the atmosphere of Mars because the

engineers who built the engines were working in British units and the scientists who were controlling the engines were

working in SI units. This lets us emphasize that units are part of every

result.

In physics, there are three basic quantities that are the basis for

everything:

Length, Time, Mass

We understand all these quantities from experience but

we find very hard to define!

International System of UnitsInternational System of Units((abbreviatedabbreviated SISI from Systfrom Systèmeème Internationale)Internationale)

Length meter m

Time second s

Mass kilogram Kg

Quantity unit symbol

The meter, second, and kilogram are The meter, second, and kilogram are called called base unitsbase units in SI in SI

Other units are expressed in terms of them

Common prefixes in SICommon prefixes in SI

μ micro 10-6

m milli 10-3

c centi 10-2

the prefix is read and multiplies the unit by

K kilo 103

M mega 106

G giga 109

Prefixes are standard letters that are attached in front Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10.of a unit and make it a multiple of some power of 10.

Common Prefixes

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

101 deka da

10–1 deci d

10–2 centi c

10–3 milli m

10–6 micro m

10–9 nano n

10–12 pico p

10–15 femto f

PowerPower PrefixPrefix AbbreviationAbbreviation

Mass is the quantity of matter in an object. It is also the measure of the

inertia that an object exhibits in response to any effort made to start

it, stop it, or change its state of motion in any way.

To compare the inertia, or mass, of two objects, accelerate them side-by-side. The one that requires the most force is

the one with the larger mass.

International System of UnitsInternational System of Units

Quantity unit symbol

International System of UnitsInternational System of Units

Length meter m

Quantity unit symbol

International System of UnitsInternational System of Units

Length meter m

Time second s

Quantity unit symbol

International System of UnitsInternational System of Units

Length meter m

Time second s

Mass kilogram Kg

Quantity unit symbol

International System of UnitsInternational System of Units((abbreviatedabbreviated SISI from Systfrom Systèmeème Internationale)Internationale)

Length meter m

Time second s

Mass kilogram Kg

Quantity unit symbol

The meter, second, and kilogram are called base units in SI

Other units are expressed in terms of them

Dimensions of Some Common Physical QuantitiesDimensions of Some Common Physical Quantities

Distance [L]

Area [L2]

Volume [L3]

Velocity [L]/[T]

Acceleration [L]/[T2]

Energy [M][L2]/[T2]

QuantityQuantity DimensionDimension

If a distanceIf a distance d d has units ofhas units of metersmeters, and , and a timea time T T has units ofhas units of secondsseconds, does the , does the quantityquantity T + dT + d make sense physically? make sense physically? What about the quantityWhat about the quantity d/T d/T ??

The quantity The quantity T + dT + d does not make sense does not make sense physically, because it adds together physically, because it adds together variables that have different physical variables that have different physical dimensions. The quantity dimensions. The quantity d / Td / T does make does make sense, however; it could represent the sense, however; it could represent the distance distance dd traveled by an object in the traveled by an object in the time time TT..

Which of the following equations is Which of the following equations is dimensionally consistent?dimensionally consistent?(a) v = at, (b) v = ½ at2 (c) t = a/v,

(d) v2 = 2ax

To find a speed requiresTo find a speed requires measurementsmeasurements

ofof lengthlength andand timetime..

Average speed is Average speed is distance traveleddistance traveled divided by the divided by the time time used.used.

average speed = distance/timeaverage speed = distance/time

v = d/tv = d/t

What is the unit of speed in SI?What is the unit of speed in SI?

Speed=length/time

Quantity unit symbol

International System of UnitsInternational System of Units

Length meter m

Time second s

Mass kilogram Kg

Speed meter/sec m/s

Quantity unit symbol

Photographs can be used to measure motion.

While the camera’s shutter was open, both the runners and the camera moved to blur

this photo.

The real speed at any moment is called instantaneous speed.

Galileo was the first to analyze motion in terms of measurements

and mathematics.

He described He described accelerationacceleration, , which is the which is the rate of change of rate of change of

speedspeed..

(final speed – initial speed)(final speed – initial speed)acceleration = ______________________ acceleration = ______________________

time requiredtime required

Galileo did experiments to Galileo did experiments to convince others that the convince others that the

acceleration caused by gravity acceleration caused by gravity would be the same for all freely would be the same for all freely falling objects if there was no falling objects if there was no

air to retard their motion.air to retard their motion.

He dropped two heavy metal He dropped two heavy metal balls together from the leaning balls together from the leaning

tower in Pisa, Italy. Although one tower in Pisa, Italy. Although one weighed far more than the weighed far more than the

other, they reached the ground other, they reached the ground almost at the same time.almost at the same time.

A tennis ball and a golf ball A tennis ball and a golf ball dropped side-by-side in air. The dropped side-by-side in air. The

tennis ball is affected more by the tennis ball is affected more by the air’s resistance than the golf ball.air’s resistance than the golf ball.

The larger the object is, and the The larger the object is, and the faster it is falling, the greater the faster it is falling, the greater the air’s resistance to its motion, as air’s resistance to its motion, as

skydivers all know…skydivers all know…

Skydivers depend on air to retard their Skydivers depend on air to retard their downward acceleration.downward acceleration.

When most of the air When most of the air is removed from a is removed from a container, feathers container, feathers

and apples fall almost and apples fall almost side-by-side, their side-by-side, their

speeds changing at speeds changing at almost the same rate.almost the same rate.

If If allall the air were the air were removed, they would removed, they would

accelerate downward at accelerate downward at exactlyexactly the same rate. the same rate.

International System of UnitsInternational System of Units

Length meter m

Time second s

Mass kilogram Kg

Speed meter/sec m/s

Quantity unit symbol

Acceleration meter/sec2 m/s2

Here two heavy balls begin Here two heavy balls begin

“free fall” at the same “free fall” at the same

time.time.

The red one is dropped, so The red one is dropped, so

it moves straight it moves straight

downward.downward.

The yellow ball is given The yellow ball is given

some speed in the some speed in the

horizontal direction as it is horizontal direction as it is

released.released.

A Vector and Its Scalar Components

The vector ŕ is defined by its length (1.50m) and its direction angle(25o) measured counterclockwise

from the positive X axis.

A Vector and Its Scalar Components

Alternatively, the vector ŕ can be defined by its X component, rx=1.36m, and its Y component,

ry=0.634m.

A Vector Whose x and y Components Are Positive

Vector Angle

Vector Angle

Adding Several Vectors

Identical Vectors A at Different Locations

A + B = B + A

A + B = B + A

Graphical Addition of Vectors

Component Addition of Vectors

Component Addition of Vectors

Vector Subtraction

Vector Subtraction

D= A – B

Dx= Ax – Bx

Dy= Ay - By

Unit Vectors

The unit vectors x and ŷ points in the positive x and y directions, respectively.

Vector Components

Multiplying a Vector by a Scalar