Clocks 1 Clocks. Clocks 2 Introductory Question You’re bouncing gently up and down at the end of a...
-
Upload
baldwin-mcdaniel -
Category
Documents
-
view
213 -
download
0
Transcript of Clocks 1 Clocks. Clocks 2 Introductory Question You’re bouncing gently up and down at the end of a...
Clocks 1
ClocksClocks
Clocks 2
Introductory QuestionIntroductory Question
You’re bouncing gently up and down You’re bouncing gently up and down at the end of a springboard, without at the end of a springboard, without leaving the board’s surface. If you leaving the board’s surface. If you bounce harder, the time it takes for bounce harder, the time it takes for each bounce willeach bounce will
A.A. become shorterbecome shorter
B.B. become longerbecome longer
C.C. remain the sameremain the same
Clocks 3
Observations About Observations About ClocksClocks
They divide time into uniform intervalsThey divide time into uniform intervals They count the passage of those They count the passage of those
intervalsintervals Some involve obvious mechanical Some involve obvious mechanical
motionsmotions Some seem to involve no motion at allSome seem to involve no motion at all They require an energy sourceThey require an energy source They have limited accuracyThey have limited accuracy
Clocks 4
4 Questions about Clocks4 Questions about Clocks
Why don’t we use hourglasses any Why don’t we use hourglasses any more?more?
Are all repetitive motions equally Are all repetitive motions equally accurate?accurate?
Why are some watches more Why are some watches more accurate?accurate?
How do clocks use harmonic How do clocks use harmonic oscillators?oscillators?
Clocks 5
Question 1Question 1
Why don’t we use hourglasses any Why don’t we use hourglasses any more?more?
Clocks 6
Non-Repetitive ClocksNon-Repetitive Clocks
Devices that measure a single interval of Devices that measure a single interval of timetime SandglassesSandglasses Water clocksWater clocks CandlesCandles
Though common in antiquity,Though common in antiquity, they are poorly suited to subdividing the they are poorly suited to subdividing the
dayday They require frequent operator interventionThey require frequent operator intervention and that operator requirement limits accuracyand that operator requirement limits accuracy
Clocks 7
Repetitive MotionsRepetitive Motions
Repetitive motions measure many Repetitive motions measure many intervalsintervals
A device with a stable equilibriumA device with a stable equilibrium tends to oscillate about that equilibriumtends to oscillate about that equilibrium and its oscillation entails at least two types of and its oscillation entails at least two types of
energyenergy kinetic energykinetic energy a potential energy (e.g., gravitational, elastic, a potential energy (e.g., gravitational, elastic,
magnetic)magnetic) Once started, this motion repeats Once started, this motion repeats
spontaneouslyspontaneously
Clocks 8
Repetitive-Motion ClocksRepetitive-Motion Clocks
Developed about 500 years agoDeveloped about 500 years ago Require no operator interventionRequire no operator intervention Accuracy limited only by the repetitive Accuracy limited only by the repetitive
motionmotion Motion shouldn’t depend on externals Motion shouldn’t depend on externals
such assuch as the temperature, air pressure, or time of day,the temperature, air pressure, or time of day, the clock’s store of energy,the clock’s store of energy, or the mechanism that observes the motionor the mechanism that observes the motion
Clocks 9
Question 2Question 2
Are all repetitive motions equally Are all repetitive motions equally accurate?accurate?
Clocks 10
Some SpecificsSome Specifics
A little terminologyA little terminology Period: time of full repetitive motion cycle Period: time of full repetitive motion cycle Frequency: cycles completed per unit of timeFrequency: cycles completed per unit of time Amplitude: peak extent of repetitive motionAmplitude: peak extent of repetitive motion
An important application of that An important application of that terminologyterminology In an ideal clock, the repetitive motion’s In an ideal clock, the repetitive motion’s
period shouldn’t depend on its amplitudeperiod shouldn’t depend on its amplitude
Clocks 11
Harmonic Oscillators Harmonic Oscillators (Part (Part 1)1)
A harmonic oscillatorA harmonic oscillator has a stable equilibrium and a restoring has a stable equilibrium and a restoring
force that’s proportional to displacement force that’s proportional to displacement from that equilibriumfrom that equilibrium
has a period that’s independent of has a period that’s independent of amplitudeamplitude
At its heart, a harmonic oscillator At its heart, a harmonic oscillator consists ofconsists of an inertial object – a massan inertial object – a mass and a springlike restoring force – a springand a springlike restoring force – a spring
Clocks 12
Harmonic Oscillators Harmonic Oscillators (Part (Part 2)2)
The period of a harmonic oscillator The period of a harmonic oscillator decreases asdecreases as the mass becomes smaller – less inertiathe mass becomes smaller – less inertia the spring becomes stiffer – a stiffer restoring the spring becomes stiffer – a stiffer restoring
forceforce Common harmonic oscillators includeCommon harmonic oscillators include
a mass on a spring (the prototypical form)a mass on a spring (the prototypical form) a penduluma pendulum a flagpolea flagpole a tuning forka tuning fork
Clocks 13
Introductory Question Introductory Question (revisited)(revisited)
You’re bouncing gently up and down You’re bouncing gently up and down at the end of a springboard, without at the end of a springboard, without leaving the board’s surface. If you leaving the board’s surface. If you bounce harder, the time it takes for bounce harder, the time it takes for each bounce willeach bounce will
A.A. become shorterbecome shorter
B.B. become longerbecome longer
C.C. remain the sameremain the same
Clocks 14
Question 3Question 3
Why are some watches more Why are some watches more accurate?accurate?
Clocks 15
The Limits to the The Limits to the AccuracyAccuracy
Clocks exhibit fundamental limits:Clocks exhibit fundamental limits: Oscillation decay limits preciseness of Oscillation decay limits preciseness of
periodperiod Clocks also exhibit practical limits:Clocks also exhibit practical limits:
Sustaining motion can influence the periodSustaining motion can influence the period Observing the period can influence the Observing the period can influence the
periodperiod Sensitivity to temperature, pressure, wind, Sensitivity to temperature, pressure, wind,
……
Clocks 16
Question 4Question 4
How do clocks use harmonic How do clocks use harmonic oscillators?oscillators?
Clocks 17
Pendulums Pendulums
Pendulum (almost) a harmonic Pendulum (almost) a harmonic oscillatoroscillator
Period proportional to Period proportional to (length/gravity)(length/gravity)1/21/2
Period (almost) independent of Period (almost) independent of amplitudeamplitude
Clocks 18
Pendulum ClocksPendulum Clocks
Pendulum is clock’s timekeeperPendulum is clock’s timekeeper For accuracy, the pendulumFor accuracy, the pendulum
pivot–center-of-gravity distance ispivot–center-of-gravity distance is temperature stabilizedtemperature stabilized adjustable for local gravity effectsadjustable for local gravity effects
streamlined to minimize air dragstreamlined to minimize air drag motion sustained, measured gentlymotion sustained, measured gently
Limitation: clock mustn't moveLimitation: clock mustn't move
Clocks 19
Balance Ring ClocksBalance Ring Clocks
A torsional spring causes a balance-A torsional spring causes a balance-ring harmonic oscillator to twist ring harmonic oscillator to twist back and forthback and forth
Gravity exerts no torque about the Gravity exerts no torque about the ring’s pivot and has no influence on ring’s pivot and has no influence on the periodthe period
Twisting is sustained andTwisting is sustained andmeasured with minimalmeasured with minimaleffects on the ring’s motioneffects on the ring’s motion
Clocks 20
Quartz OscillatorsQuartz Oscillators
Crystalline quartz is a harmonic Crystalline quartz is a harmonic oscillatoroscillator Crystal provides the inertial massCrystal provides the inertial mass Stiffness provides restoring forceStiffness provides restoring force
Oscillation decay is extremely slowOscillation decay is extremely slow Fundamental accuracy is very highFundamental accuracy is very high Quartz is piezoelectricQuartz is piezoelectric
mechanical and electrical changes coupledmechanical and electrical changes coupled motion is induced and measured electricallymotion is induced and measured electrically
Clocks 21
Quartz ClocksQuartz Clocks
Electronic system starts crystal vibratingElectronic system starts crystal vibrating Vibrating crystal triggers electronic Vibrating crystal triggers electronic
countercounter Nearly insensitive to gravity, temperature,Nearly insensitive to gravity, temperature,
pressure, and accelerationpressure, and acceleration Slow vibration decaySlow vibration decay
leads to precise periodleads to precise period Tuning-fork shape yieldsTuning-fork shape yields
slow, efficient vibrationslow, efficient vibration
Clocks 22
Summary about ClocksSummary about Clocks
Most clocks involve harmonic Most clocks involve harmonic oscillatorsoscillators
Amplitude independence aids Amplitude independence aids accuracyaccuracy
Clock sustains and counts Clock sustains and counts oscillationsoscillations
Oscillators that lose little energy Oscillators that lose little energy work bestwork best