Welcome

Course: AP Physics

Room: 207

Teacher: Mrs. LaBarbera

Email:dlabarbera@vcmail.ouboces.org

Tel: 845-457-2400 ext 17207

Post session: Tuesday – Thursday in Room 207

Objectives• Introduction of AP physics

• Lab safety

• Sign in lab safety attendance sheet

• Classical Mechanics

• Coordinate Systems

• Units of Measurement

• Changing Units

• Dimensional Analysis

Registering Mastering Physics(See instructions at mastering physics sign up info)• Go to http://www.masteringphysics.com• Register with the access code in the front of theaccess kit in your new text, or pay with a creditcard if you bought a used book.• WRITE DOWN YOUR NAME AND PASSWORD• Log on to masteringphysics.com with your newname and password.• The VC zip code is • The Course ID: APPHYSICSLABARBERA2010

Introduction to AP course

• Hand out

Lab safety General guidelines

1. Conduct yourself in a responsible manner.

2. Perform only those experiments and activities for which you have received instruction and permission.

3. Be alert, notify the instructor immediately of any unsafe conditions you observe.

4. Work area must be kept clean.

5. Dress properly during a laboratory activity. Long hair should be tied back, jackets, ties, and other loose garments and jewelry should be removed.

6. When removing an electrical plug from its socket, grasp the plug, not the electrical cord. Hand must be completely dry before touching an electrical switch, plug, or outlet.

7. Report damaged electrical equipment immediately. Look for things such as frayed cords, exposed wires, and loose connections. Do not use damaged electrical equipment.

7. Report damaged electrical equipment immediately. Look for things such as frayed cords, exposed wires, and loose connections. Do not use damaged electrical equipment.

Homework – due Friday, 9/91. Read and sign the Lab Requirement Letter – be sure

to include both your signature and your parent or guardian’s signature.

2. Read and sign the Student Safety Agreement – both your signature and your guardian’s signature.

3. Reading assignment: 1.1 – 1.6, answer reading questions

4. Questions: 1.2, 3, 9, 10, 19 – the solutions are on the school website.

Homework – due Tuesday, 9/13 – 11:00 pmMastering physics wk 1

Please sign in lab safety attendance sheet

Classical Mechanics• Mechanics is a study of motion and its causes.• We shall concern ourselves with the motion of a

particle. This motion is described by giving its position as a function of time.

Specific position & time → eventPosition (time) → velocity (time) → acceleration

• Ideal particle– Classical physics concept– Point like object / no size– Has mass

• Measurements of position, time and mass completely describe this ideal classical particle.

• We can ignore the charge, spin of elementary particles.

Position• If a particle moves along a

straight line → 1-coordinate curve/surface → 2-coordinate Volume → 3-coordinate

• General description requires a coordinate system with an origin.– Fixed reference point, origin– A set of axes or directions– Instruction on labeling a point relative to origin, the

directions of axes and the unit of axes.– The unit vector

Rectangular coordinates - Cartesian

Simplest system, easiest to visualize.

To describe point P, we use three coordinates: (x, y, z)

Spherical coordinate• Nice system for motion

on a spherical surface

• need 3 numbers to completely specify location: (r, Φ, θ)

− r: distance between point to origin

− Φ: angle between line OP and z: latitude = π/2 - Φ.

− θ: angle in xy plane with x – longitude.

Time • Time is absolute. The rate at which time elapse is

independent of position and velocity.• Absolute time + Euclidean geometry (some of angles in a

plane = 180o) is the foundation for classical/Newtonian physics. Under these conditions, the Laws of motion and the law of universal gravitation can not be challenged.

• We now know that time is not absolute when v → c, or when gravity is very strong. Known as time dilation. We also know that Euclidean geometry is not always true (hyperbolic geometry and elliptical geometry). A new theory of special relativity and general relative by A. Einstein works under these conditions. Space/time curve.

• However, when v << c, and when gravity is not very strong, time dilation and non Euclidean geometry will not affect the Newtonian physics that we will study.

Unit of measurement Quantity/dimension

being measuredSI unit (symbol) British (derived)

unit

Length/[L] meter (m) Foot (ft)

Time/[T] second (s) Second (s)

Mass/[M] kilogram (kg) Slug

Ele. Current/[I] ampere (A)

Temperature[Θ] Kelvin (K)

Amount of substance[N] Mole (mol)

Luminous intensity[J] Candela (cd)

International system of units (SI) consists of 7 base units. All other units can be expressed by combinations of these base units. The combined base units is called derived units

Physical Dimensions

• The dimension of a physical quantity specifies what sort of quantity it is—space, time, energy, etc.

• We find that the dimensions of all physical quantities can be expressed as combinations of a few fundamental dimensions: length [L], mass [M], time [T].

• For example, – Energy: E = ML2/T2

– Speed: V = L/T

• The meter is defined as the distance that light travels in a vacuum in (1/299,792,458) of a second. • d = c∙t (c = 299,792,458 m/s, exactly defined)

Length [L]

length depend on unit of timedistance

Speed of light, a constant

time

The furthest quasar: 2 x1026 m

Wavelength of visible light: 10-7 m

Radius of a proton: 10-15 m

Time [T]• One second is defined:• Originally as 1/(60x60x24) of a mean solar day. It is not

very precise since the earth’s rotation is by wind, tide, glacier, etc.

• Atomic standard: the time occupied by 9,192,631,770 vibrations of the light (of a specified wavelength) emitted by a Cesium-133 atom. Its accuracy is 10-13 s, 1 s in 300,000 years!

Life time of a proton: ~1039 s

Age of the universe: 5 x1017 s

Life time of most unstable particle ~10-23 s

Mass [M]• Standard: One kilogram is the mass of a Platinum-

Iridium cylinder kept at the International Bureau of Weights and Measures in Paris. Not very accessible.

• To measure mass of atoms, we use atomic mass unit. – 1 u = 1/12 (carbon 12)– 1 u = 1.66054 x 10-27 kg

Known universe: ~1053 kg

elephant: 5 x103 kg

Electron 9x10-31 kg

Derived units

• Like derived dimensions, when we combine basic unit to describe a quantity, we call the combined unit a derived unit.

• Example:– Volume = L3 (m3)– Velocity = length / time = LT-1 (m/s)– Density = mass / volume = ML3 (kg/m3)

Unit conversions• The amount of a physical quantity remains the same, no

matter what system of units is used to obtain a numerical measure of that quantity.

• For instance, we might measure the length of an (American) football field with a meter stick and a yard stick. We’d get two different numerical values, but obviously there is one field with one length.

• We’d say that. 100 yards = 91.44 meters. In other words,

0.144.91

100

meters

yards

Note: the units are a part of the measurement as important as the number. They must always be kept together.

• Suppose we wish to convert 2 miles into meters. (2 miles = 3520 yards.)

• The units cancel or multiply just like common numerical factors. Since we wanted to cancel the yards in the numerator, the conversion factor was written with the yards in its denominator.

• Since each conversion factor equals 1, we can do as many conversions as we please—the physical measurement is unchanged, though the numerical value is changed.

meters 688.3218yards 100

meters 44.91yards 3520

Chain – link – conversion

example• Convert 80 km/hr to m/s.

• Given: 1 km = 1000 m; 1 hr = 3600 s

ms80

km

hrx

km1000 m x

3600 shr = 22

Units obey same rules as algebraic variables and numbers!!

Dimensional analysis• We can check for error in an equation or expression by

checking the dimensions. Quantities on the opposite sides of an equal sign must have the same dimensions. Quantities of different dimensions can be multiplied but not added together.

• For example, a proposed equation of motion, relating distance traveled (x) to the acceleration (a) and elapsed time (t).

2

2

1atx

Dimensionally, this looks like

At least, the equation is dimensionally correct; it may still be wrong on other grounds, of course.

T2L =L

T2= L

Another example

d = v / t

•use dimensional analysis to check if the equation is correct.

L = (L ∕ T ) ∕ T

[L] = L ∕ T2

Significant Figures (Digits)

• Instruments cannot perform measurements to arbitrary precision. A meter stick commonly has markings 1 millimeter (mm) apart, so distances shorter than that cannot be measured accurately with a meter stick.

• We report only significant digits—those whose values we feel sure are accurately measured. There are two basic rules: – (i) the last significant digit is the first uncertain digit– (ii) when multiply/divide numbers, the result has no more

significant digits than the least precise of the original numbers.

The exercises in the textbook assume there are 3 significant digits.

Addition and subtraction with measured values

• Measured values must have the same units before they are added or subtracted.

• The sum or difference is rounded to the same decimal place value as the least sensitive measurement.

• Example: what is the perimeter of a rectangle are 4.3 cm and 0.08 m?

0.25 m or 25 cm

4.3 cm8 cm 4.3 cm8 cm

24.6 cm

Scientific Notation and Significant Digits

• Scientific notation is simply a way of writing very large or very small numbers in a compact way.

• The uncertainty can be shown in scientific notation simply by the number of digits displayed in the mantissa

9

8

10088.18780000000010.0

10998.2299792485

3105.1 2 digits, the 5 is uncertain.

3 digits, the 0 is uncertain.31050.1

Examples

2100.880053.7965.283.02.37.756

2 digits

1101.1.114016.112.3563.3 2 digits

1108.11859291886.176.5

2 digits

SI prefixes• SI prefixes are prefixes (such as k, m, c,

G) combined with SI base units to form new units that are larger or smaller than the base units by a multiple or sub-multiple of 10.

• Example: km – where k is prefix, m is base unit for length.

• 1 km = 103 m = 1000 m, where 103 is in scientific notation using powers of 10

Some prefixes

n 10-9

μ 10-6

m 10-3

c 10-2

k 103

Convert the following

5 Tg ___________ kg

2 μm ___________ m

6 cg ___________ kg

7 nm ___________ m

4 Gg ___________ kg

5 x 109

2 x 10-6

6 x 10-5

7 x 10-9

4 x 106

Percent error• Measurements made during laboratory work

yield an experimental value • Accepted value are the measurements

determined by scientists and published in the reference table.

• The difference between and experimental value and the published accepted value is called the absolute error.

• The percent error of a measurement can be calculated by

Percent error = accepted value

X 100%experimental value – accepted value

(absolute error)

example

• In an experiment, a student determines that the acceleration due to gravity is 9.98 m/s2. determine the percent error. (the accepted value is 9.81 m/s2)

Percent error = 1.7%

Percent error = accepted value

X 100%experimental value – accepted value

Class work in note page, do not delete

Class work

Unit conversion practice

• Do not delete. The practice is on the note page

Homework – due Friday, 9/16Reading assignment: • 1.7 – 1.9• Notes posted on VC website: Chapter 2: Mathematics -

The Language of Science

Questions: 1.32, 31, 38, 41, 55, 59, 68 – the solutions are on the school website.

Homework – due Tuesday, 9/20 – 11:00 pmMastering physics wk 2