21-Sep-10 Physics 1 (Garcia) SJSU

Periodic MotionAtomic Structure

(Chapter 11)

Lecture 12

Periodic Motion CharacteristicsPeriodic Motion CharacteristicsPeriod T: time required for one cycle of periodic motion (unit: s)Frequency f: number of cycles per unit time

The frequency unit is called a Hertz (Hz):Amplitude A: maximum distance object moves from equilibrium (unit: m)

Frequency and Period1/ and 1/f T T f= =

is the frequency (units: Hz oscillations per second)f

≡

is the period (units: s)T

Example: Frequency and Period

What is the frequency of a pendulum swing that takes 2 seconds to complete a cycle?

Note that 1 Hz = 1/s

f = 1/T = 1/(2s) = 0.5 s-1 = 0.5 Hz

Examples of Periodic MotionExamples of Periodic Motion

• Mass on a spring

• Pendulum

• Object in uniform circular motion

• Frequency is same as angular speed

• Vibrating guitar string

• Vibrating vocal cords

Example: Mass on Spring

An air-track glider is attached to spring, pulled 20 cm to the right, and released at t=0. It makes 15 complete oscillations in 10 s.

What is the frequency of oscillation?

f = 15 oscillations / 10s = 1.5 Hz

The Simple PendulumThe Simple PendulumA simple pendulum consists of a mass m (of

negligible size) suspended by a string of length L(and negligible mass).

The pendulum does periodic motion.

Period of Simple PendulumPeriod of Simple PendulumThe period of a simple pendulum depends only on g and the length L of the string (and is independent of mass):

T

Atoms

“All things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.”

—Richard Feynman

Characteristics of AtomsCharacteristics of atoms:• Incredibly tiny (<10-9 m)• Numerous • Perpetually in motion

(according to temperature)• Ageless

Nucleus

Orbiting electrons

Which one of the following is an incorrect statement about the atom?

A. Atoms are smaller than a billionth of a meter.B. Atoms are mostly empty space, just as the solar

system is mostly empty space.C. Atoms are perpetually moving.D. Atoms are manufactured in plants, and in humans

during pregnancy.

Characteristics of AtomsCHECK YOURSELF

Atomic StructureAn atom is composed of• nucleus

– concentration of nearly all the atom mass– made up of protons (positive electric charge) and

neutrons (no electric charge)– Very, very small (<10-14 m)

• electrons– even smaller than nucleus– 2000 times less massive than nucleus– negative electric charge (same amount as proton)– may be thought of as “orbiting” nucleus

• Number of electrons in atom equal to number of protons in nucleus

The ElementsAtom’s name is set by number of protons• 1 proton -- Hydrogen• 2 protons -- Helium• 3 protons - LithiumElemental substance (or just “element”)• Composed of only one kind of atom

– Lightest and most abundant is hydrogen.• To date, about 115 elements are known.

– 90 occur in nature.– Others produced in laboratory are unstable.

The ElementsComposition of living things includes these 5 elements:• Oxygen • Carbon • Hydrogen • Nitrogen • Calcium

Periodic Table of the Elements

Periodic table:• A chart (chemist’s road map) of elements

arranged by atomic number (# protons)– Classified by the number of protons in the nucleus

• Arranged from left to right– Each successive one having one more proton and

electron than the preceding element– Atoms on the far right, have “filled outer shells” and

are known as “noble” gases

Periodic Table of the Elements

Relative Sizes of Atoms

IsotopesIsotopes:• Atoms of the same element with different

numbers of neutrons• Identical behavior• Identified by their mass number (total

number of protons and neutrons in the nucleus )

Example: Iron isotope with 26 protons contains 30 neutrons. Mass number is 56; referred to as “iron-56”.

The atomic number of an element matches the number of

A. protons in the nucleus of an atom.B. electrons in a neutral atom.C. Both of the above.D. None of the above.

IsotopesCHECK YOURSELF

A nucleus with an atomic number of 44 and a mass number of 100 must have

A. 44 neutrons.B. 56 neutrons.C. 100 neutrons.D. All of the above.

IsotopesCHECK YOURSELF

Compounds and Mixtures• When atoms of different elements bond to one

another, they make a compound.– A compound is different from the elements from

which it is made.– It can only be separated into its constituent

elements by chemical means.– Example: Table Salt (a compound of sodium and

chlorine atoms)

• A substance that is mixed together without chemically bonding is called a mixture.– Example: Air (a mixture of several gases)

MoleculesMolecules• Two or more atoms bonded together

Example: • NH3 (ammonia)• 3 atoms of hydrogen and 1 atom of nitrogen

Chemical ReactionsChemical reaction:• A process in which atoms rearrange to form different

moleculesExample: • Pulling molecules apart requires energy.

– During photosynthesis, sunlight’s energy breaks bonds of CO2 to produce O2 and C.

• Combining atoms releases energy.– Oxygen atoms combine with iron atoms to form

rust.

AntimatterMatter:• Composed of atoms with electrically positive nuclei and

negative electrons Antimatter:• Composed of atoms with negative nuclei (anti-protons)

and positive electrons (positrons)Each anti-particle is identical to the regular particle except that the electric charge has the opposite sign.

Dark Matter

Dark matter• is unseen and unidentified matter very different

from the observable elements and particles that comprises about 23% of matter in the universe.

Dark energy• is an antigravity energy that causes the universe

to continue to expand.

The Three Basic Phases of Matter

Sequence of increasing molecule motion (and kinetic energy)

Solid Liquid Gas

DensityThe (mass) density of a material is its mass M per unit volume V:

The densities of most liquids and solids vary The densities of most liquids and solids vary slightly with changes in temperature and slightly with changes in temperature and pressurepressure

Densities of gases vary greatly with changes Densities of gases vary greatly with changes in temperature and pressurein temperature and pressure

Density ValuesMaterial Density (kg/m3)Water (at 4°C) 1,000 (1 g/cm3)Lead 11,300Gold 19,300Air 1.29Helium 0.18The specific gravity of a substance is the

ratio of its density to that of water.

21-Sep-10 Physics 101

Demo: Gold Brick

Compute density of gold brick.Dimensions: (20.5 cm)x(10 cm)x(5 cm)Volume: 1025 cubic centimeters (1.025 x 10-3 m3)Mass: 19.8 kgDensity = (19.8 kg) / (1.025 x 10-3) = 19.3 kg/m3

Check with table that this is density of gold

21-Sep-10 Physics 101

Demo: Fool’s GoldUse displacement to find irregular volumes.Pyrite (called Fool’s Gold) is an iron ore (FeS2).Pyrite sample has:Mass: 0.061 kgVolume: 12 x 10-6 m3

Density=(.061)/(12x10-6) )= 5.1x 103 kg/m3

About a quarter the density of real gold.

21-Sep-10 Physics 101

Check YourselfWater expands when it freezes into ice.

Which has more volume, kilogram of ice or kg of water?

Which has more mass, a kg of ice or a kg of water?

Which has a higher density, water or ice (or the same)?

Which has more mass, a liter of ice or a liter of water?

Key Points of Lecture 12Key Points of Lecture 12

Before next lecture, skim Hewitt Chap. 11.

Homework Assignment #8 is due before 11:00 PM on Thursday, Sept. 23.

Homework Assignment #9 is due before 11:00 PM on Sunday, Sept. 26.

• Periodic Motion & the Pendulum• Atomic Structure• Elements • Isotopes• Compounds, Mixtures• Density