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175 Cards in this Set
- Front
- Back
Newton's 1st law (1st version)
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An object that is free of external influences moves in a straight line and covers equal distances
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Newton's 1st law (2nd version)
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An object that is free of external influences moves at a constant velocity
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Newton's 2nd law
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the force exerted on an object is equal to the product of that object's mass times its acceleration
-the acceleration is the same direction as the force F=ma |
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Position
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An object's location
(A dropped ball falling downward)-Position= initial position+initial velocity x time+1/2 acceleration x time^2 |
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Vectors
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Are arrows drawn to show directions while their lengths represent their sizes, or magnitude it's used
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net vector
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shows the objects actual direction of motion. The length measurement of the net vector tells the actual speed of the object
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Force
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A push or pull
Force=ma |
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net Force
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the sum of all forces on an object. It determines the objects acceleration
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Inertia
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-A body at rest tends to remain at rest
-A body in motion tends to remain in motion |
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Velocity
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An object's change in position with time
(a dropped ball falling downward)- velocity= initial velocity + acceleration x time |
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Acceleration
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the rate of change in velocity with time
Accereration=final velocity- initial velocity/ time required |
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Mass
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the measure of an objects inertia
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weight
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Weight=mass x g
An object's weight is proportional to its mass. G is called the acceleration due to gravity on earth's surface, the constant g is=9.8 meters/ second^2 |
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Kilogram
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measure of mass of an object
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Galileo
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was the first to analyze motion in terms of measurements and mathematics
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Newton's 3rd law
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for every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object
to every action there is an equal and opposite reaction |
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Support Force
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prevents something from penetrating a surface. The support force points directly away from that surface
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Van der Waals forces
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molecules and atoms usually attract when they are far apart
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Pauli Exclusion Principle
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no two identical fermoins may occupy the same quantum state simultaneously
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Work
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the means of transferring energy
work = the force parallel to the displacement time the displacement Work=F,,d (force and distance are the same direction) |
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Gravitational potential energy
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the work done is
W=m g h =force x distance =change is gravitational potential energy |
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Energy
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the capacity to do work
-a conserved quantity -energy is always conserved -there are all kinds of energy: elastic, chemical, gravitational potential, thermal, kinetic... |
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Kinetic energy
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energy of motion
KE= ½ mv^2 |
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Potential energy
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Stored energy
Gravitational PE= mgh |
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Center of mass
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-the point about which an object’s mass balances
-a free object rotates about its center of mass, while its center of mass follows the path of a falling object |
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Angular Position
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an object’s orientation
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Angular Velocity
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its change in angular position with time
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Torque
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-a twist or spin
-a force can produce a torque -Torque= lever arm x force (where the lever arm is perpendicular to the force) --all that matters is the force perpendicular to the lever arm |
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Newton’s 1st law of rotational motion
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a rigid object that’s not wobbling and that is free of outside torques rotates at a constant angular velocity
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Rotational Inertia
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-a body at rest tends to remain at rest
-a body that’s rotating tends to continue rotating |
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Angular Acceleration
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an objects change in angular velocity with time
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Rotational mass
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- measure of an objects rotational inertia
-is big when mass is far from axis of rotation |
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Newton’s 2nd law of rotational motion
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- the torque exerted on an object is equal to the product of that object’s rotational mass times its angular acceleration. The direction of angular acceleration and the torque are the same
-Torque= Rotational mass x Angular acceleration |
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Net Torque
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- the sum of all torques on an object
-determines that object’s angular acceleration |
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Wheels
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-use friction to control motion
-eliminate the “bad” effects of friction -use static friction to control motion and eliminate the production of thermal energy |
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Frictional forces
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- Increase when you:
– push the surfaces more tightly together – roughen the surfaces • Peak static force is greater than sliding force: – Surface features can interpenetrate better Friction force drops when sliding begins |
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Static Friction
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-the force that prevents two surfaces from starting to slip
-is what makes it possible to stir a car -propels a wheel -forces can vary from zero to an upper limit -no wear occurs, no work is done (no distance) |
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Bearings
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-eliminate sliding friction in wheel hub
-behave like wheels (roll without slipping) |
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Sliding Friction
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-is a force that opposes relative motion
-tends to convert kinetic energy into “thermal” energy -forces have fixed magnitudes -work is done (distance in the direction of force) -wear occurs -work is turned into thermal energy |
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Power
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Power=work/time
-the rate at which energy is transferred -with more power, more work can be done (and more energy transferred) in the same amount of time 1 horsepower= 746 watts= 746 joules/ sec |
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Momentum
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-anything moving has momentum
-a conserved quantity (can’t create or destroy) in the absence of external forces -a vector -momentum= mass x velocity |
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Angular Momentum
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-a conserved quantity
-a directed quantity (vector) -Angular momentum= Rotational mass x Angular velocity -is conserved in the absence of external torques -Angular momentum= Rotational mass x Angular velocity |
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Impulse
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-the only way to transfer momentum
-impulse is a vector -impulse=force x time -Final momentum – initial momentum -Impulse= Force applied times the time the force is applied F x t -due to Newton’s 3rd law: An impulse of one object on a second is accompanied by an equal but oppositely directed impulse of the second on the first |
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Conservation of linear momentum-
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states that, in the absence of net external forces, the total vector momentum before a collision the same as the total vector momentum after the collision
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Elastic collision/ Inelastic collision
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no loss of kinetic energy in elastic collision/ kinetic energy is lost
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Newton’s 3rd law of Rotational Motion-
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for every torque that one object exerts on a second object, there is an equal but oppositely directed torque that the second object on the first object
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Angular Impulse
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- the only way to transfer angular momentum
-Angular impulse is a vector -Because of Newton’s 3rd law or rotation: An angular impulse of one object on a second is accompanied by an equal but oppositely directed angular impulse of the second on the first |
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Changing Rotational Mass-
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-Mass can’t change, so the only way an object’s velocity can change is if its momentum changes
-Rotational mass can change its angular velocity without changing its angular momentum |
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Springs
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always produce a force that opposes the distorting force
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A free Spring Free Spring
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• A free spring adopts a certain length
• Its ends experience zero net force • Its ends are in equilibrium • The spring is at its equilibrium length |
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A Distorted Spring
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• If you distort a spring, forces act on its ends
• These forces – act to restore the spring to equilibrium length – are called “restoring forces” – are proportional to the distortion |
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Hooke’s Law
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The restoring force on the end of a spring is equal to a spring constant times the distance the spring is distorted. That force is directed opposite the distortion.
F = -k x Restoring Force = – Spring constant x Distortion |
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Spring Scales
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Measure-support force by measuring how far a spring is stretched
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Equilibrium
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• An object in equilibrium
– experiences zero net force – is not accelerating • At equilibrium, – individual forces balance one another perfectly – an object at rest remains at rest – an object in motion coasts |
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Weighing Via Equilibrium
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• Use upward support force to counter gravity
• Attain equilibrium • Support force balances weight • Measure the support force |
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Spring Scales and Acceleration
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• Weight measurement requires equilibrium
• Without equilibrium, – spring force doesn’t balance weight – “measurement” is meaningless and inaccurate • You must not bounce on a scale! (Wait for the scale to settle before reading) |
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Balance scale
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measures MASS
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Weight as a Measure
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-Is dependent on measuring location
-Depends on Acceleration Due to Gravity |
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Mass as a Measure
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Does not depend on measuring location
– Is “intrinsic”, like length |
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Approaching energy =
Rebounding energy = |
“Collision” energy
“Rebound” energy Measure of a ball’s liveliness. •Ratio of outgoing to incoming speeds. |
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Coefficient of Restitution
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Outgoing Speed/Incoming Speed
Incoming speed- approaching speed Outgoing speed- separating speed Concrete surface: • golf ball: 0.86 • billiard ball: 0.80 • glass marble: 0.66 • baseball: 0.6 |
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Center of Percussion
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At the center of percussion, the forward translational velocity and the backward rotational velocity are equal and opposite
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Circular motion
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force is toward the center of circle
Acceleration always points toward the middle of the circle Uniform circular motion- constant speed |
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Thermal Energy
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• is “disordered” energy
• gives rise to temperature • is actually the kinetic and potential energies of constituent particles • does not include “ordered” energies: – The kinetic energy of the bulk object moving or rotating. – The potential energy of outside interactions. conduction, convection and radiation all transfer heat from hot to cold |
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Heat
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• Is the energy that flows between objects because of their difference in temperatures
• Heat is thermal energy on the move • Technically: Object’s don’t contain heat Heat Transfer Mechanisms |
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Conduction:
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Heat flow through mate-In an insulator.
Adjacent atoms jiggle one another Atoms do work, yielding microscopic exchanges of energy (typically slow) -In a conductor Mobile electrons carry heat Heat flows quickly, over long distances via mobile electrons rials |
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Convection:
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Heat flow through moving fluids
Fluid transports heat (thermal energy stored in atoms) -fluid warms up near a hot object -fluid cools down near a cold object Natural buoyancy drives convection -warned fluid rises away from hot object -cooled fluid descends away from cold object |
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Radiation:
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Heat flow through light
-heat transferred by electromagnetic waves (radio, infrared, microwaves, light, …) -higher temperature yields more radiated heat |
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Woodstoves
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Conduction
-moves heat through the stove’s metal walls Convection -circulates hot air around the room Radiation -transfers heat directly as light |
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Water exists in a few phases
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•Liquid
•Solid (ice) •Gas (steam) Bonds form different structures (phases) Generally: •Liquids denser than gas •Solids denser than liquids |
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Gas
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•Mostly independent molecules
•In motion because of thermal energy •Compressible •Fluid (changes shape easily) •Fills volume |
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Liquid
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•Molecules loosely bound into loops and
chains •In motion because of thermal energy •Incompressible •Fluid (changes shape easily) |
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Solid
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•Molecules bound into orderly structure
•In motion because of thermal energy •Incompressible •Cannot change shape |
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Phase equilibrium
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•Multiple phases exist at one temperature
•Molecules leave and enter phases at equal rates • Ice / liquid water: 0 °C • Liquid water / steam: 100 °C |
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Phase transitions
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•Transformation from one phase to another
• In water, absorbs/releases latent heat (energy in bonds) •Represents a change in order Example: Phase transition – melting -Phase transitions can be affected by pressure -There are more than three phases of most substances. |
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Sublimation:
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from solid to gas
Ice, melting- liquid water, evaporation- steam |
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Deposition:
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from gas to solid
Steam, condensation- liquid water, freezing- ice Deposition – frost on your windows. Frost in the freezer |
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Sublimation
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freezer burn (from solid to gas)
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Evaporation
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liquid- latent heat to – steam
A cooling process. Your body regulates its temperature this way |
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Condensation
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- steam- latent heat to - liquid
Lower temperature favors condensation and increased relative humidity -Relative= Humidity landing rate/ Leaving rate |
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Relative Humidity
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• At 100% relative humidity,
– ice is in phase equilibrium with steam (< 0 °C) – water is in phase equilibrium with steam (> 0 °C) • Below 100% relative humidity, – ice sublimes (< 0 °C) (goodbye ice cubes!) – water evaporates (> 0 °C) • Above 100% relative humidity, – frost forms (< 0 °C) – steam condenses (> 0 °C) |
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Boiling water
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•Pressure of steam below 100 C < atmospheric pressure (14 lb / in2)
•Steam bubble below 100 C is crushed! •Pressure of steam at 100 C = atmospheric pressure (14 lb / in2) •Steam bubble above 100 C can grow through evaporation |
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Dissolving salt in water
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•Lowers the vapor pressure (increases the boiling temperature)
•Lowers the melting temperature |
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Thermal Radiation
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•All materials contain electric charges
•Thermal energy makes charges accelerate •Accelerating charges emit electromagnetic waves (antennas!) •All materials emit electromagnetic waves Cu+ Objects at different Objects temperatures emit electromagnetic radiation. |
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Black Body:
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Object that emits radiation but does not reflect radiation. It absorbs all incoming radiation!
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The Blackbody Spectrum
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The wave length and intensity of electromagnetic waves from a black body depend only on its temperature
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The Stefan Stefan-Boltzmann Law
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P = e σT4A
Power = emissivity ×Stefan‐Boltzmann constant ×temperature4×surface area This amount of power that a surface, which has an emissivity of e, a temperature of T and a surface area of A, radiates σis the Stephan Boltzmann constant with value 5.67 x 10–18 J / (s m2K4) |
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Emissivity, e
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-The efficiency with which an object
emits or absorbs energy Ranges from e=0 to e=1 e is low (near 0) -For white, shiny, or clear surfaces (poor emitter / absorber) E is high (near1) -For black surfaces (good emitter / absorber) |
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Reducing Conductive Losses
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•Heat flow by conduction is given by thermal conductivity, k:
Heat flow= k x temperature difference x area/ Distance of separation •Thermal conductivity is a material property: Argon 0.016 W/m∙K Air 0.025 W/m∙K Glass 0.8 W/m∙K Copper 380.0 W/m∙Kseparation |
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Higher temperature
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-Increasing thermal motion
-Increasing separation between atoms -Expansion of volume and outer dimension of object Heat expansion depends on material |
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Earth as a Greenhouse
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Radiation from the sun enters the atmosphere the emissivity for visible light is small the energy from the Solar radiation heats atmosphere + surface. The emissivity for infrared is larger than for visible light. Some infrared reflected back some escapes to space
Changing the emissivity Increasing the emissivity (eg. byadding CO2or methane to theatmosphere) would change thesurface (greenhouse) temperature |
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Heat Machines
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Air conditioners (this lecture)
– use work to transfer heat from cold to hot – “heat pumps” Automobiles (next lecture) – use flow of heat from hot to cold to do work – “heat engines” |
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Thermodynamics
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• Rules governing movement of thermal energy
• Relationships between – thermal energy and mechanical work – disordered energy and ordered energy • Codified in the laws of thermodynamics |
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0th Law
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Law about Thermal Equilibrium “If two objects are in thermal equilibrium with a third object, then they are in thermal equilibrium with each other.”
If TA=TB and TB=TC then TA=TC… …and no heat flows. |
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1st Law
Law about Conservation of Energy |
-“Change in internal energy equals
heat in minus work out”- Internal energy = Thermal + stored energies Heat in = Heat transferred into the object Work out = Outside work done by the object |
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2nd Law
Law about Disorder (Entropy) |
“Entropy of a thermally isolated system never decreases”
Order versus Disorder • It is easy to convert ordered energy into thermal (disordered) energy • It is hard to convert thermal energy into ordered energy • Statistically, order disorder is one-way |
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Natural heat flow
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Heat naturally flows from hot to cold
–Remove heat from hot object: entropy decreases – Add heat to cold object: entropy increases Entropy of combined system increases A joule of thermal energy is more disordering to a cold object than to a hot object |
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Unnatural heat flow
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• Heat does NOT naturally flow cold to hot
– Removing heat from cold object decreases entropy – Adding heat to hot object increases entropy • More entropy is removed than added – The same amount of heat causes a greater change on cooler object’s entropy. • Therefore, some ordered energy |
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Air conditioner uses a working fluid
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Evaporator: located in room air
– transfers heat from room air to fluid Condenser: located in outside air – transfers heat from fluid to outside air Compressor: located in outside air – does work on fluid and creates entropy |
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Heat Engines
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As heat flows naturally from hot to cold, a heat engine diverts some heat and converts it into useful work.
• Natural heat flow increases entropy • Converting heat to work decreases entropy • If more entropy is created than destroyed, the overall entropy doesn’t decrease and some heat can become work! |
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Efficiency
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As the temperature difference between
hot and cold increases: –A heat pump becomes less efficient –A heat engine becomes more efficient It’s all about entropy • More entropy is created (by heat moving) when the cold region is made colder • That means more heat can be diverted into work without violating the 2nd law! |
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Internal Combustion Engine
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• Burns fuel and air in enclosed space
• Produces hot burned gases • Allows heat to flow from hot engine to cold outside air • Converts some of this heat into useful work |
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Efficiency Limits
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• An ideal engine is never perfect (never has 100% efficiency)
–Not all the thermal energy can become work –Some heat must be ejected into the atmosphere • However, ideal efficiency improves as –the burned gases become hotter –the outside air becomes colder • Real engines never reach ideal efficiency Efficiency is all about compression ratio |
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Repetitive Motions
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• An object with a stable equilibrium tends to oscillate about that equilibrium
• This oscillation involves at least two types of energy: kinetic and a potential energy • Once the motion has been started, it will repeat When energy traded back and forth between kinetic and potential energy: “resonance” |
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Resonance
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Many objects in nature have natural resonances!
Repetitive motion characterized by a: period (or frequency) and amplitude Resonance: energy can be stored in motion at a specific frequency |
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Properties of oscillation
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Period:
time of one full cycle Frequency (1/Period): cycles completed per second Amplitude: extent of repetitive motion In an ideal clock, the period (and frequency) should not depend on amplitude Frequency depends on two properties Mass, Stiffness |
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The Harmonic Oscillator
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A special example of something with a
natural resonance Anything with a stable equilibrium and a restoring force (F) that’s proportional to the distortion away from equilibrium (x) (F = - k x, where k is a constant) • Period is independent of amplitude • Examples: 1. Simple pendulum (small amplitude) 2. Mass on a spring |
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Pendulum
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• Period= 2π√length/g
• Period only independent of amplitude for small amplitude Near earth’s surface, 1 m pendulum has a 2 second period |
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Quartz Oscillators
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• Crystalline quartz is a harmonic oscillator
• Oscillation decay is extremely slow (very pure tone) • Quartz is piezoelectric –Mechanically-electrically coupled motion induced and measured electrically Most modern clocks use a quartz oscillator -Can think of bonds between atoms in a crystal as springs. So, the restoring force is proportional to the distance from equilibrium. Simple harmonic motion! (F = -k x) |
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Atomic Clocks
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• Particles in an atom (neutrons, protons, electrons) can have only a very specific amount of total energy.
• Changing from one quantum state to another requires or releases a fixed amount of energy • That energy can be converted into a frequency so can be the basis of a very accurate clock. 1 sec = 9,192,631,770 periods of the radiation corresponding to the ground state hyperfine transition in 133Cs |
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Sound as a wave!
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• Sound is a longitudinal pressure wave in a medium (gas, liquid or solid)
• Anything that vibrates a medium produces sound • Air is the most common medium for carrying sound |
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Waves
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• Waves have a wavelength: distance to next crest or trough
• Waves have an amplitude: peak change in pressure for sound in air • Any mechanical wave “represents the natural motion of an extended object around stable equilibrium shape or situation” |
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Frequency
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The frequency, or pitch, of sound is the number of times per second that the wave repeats itself (or 1/period) wave speed = frequency × wavelength
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Resonator
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Producing Musical Sound
Usually involves a resonator -An object’s natural vibration or resonant frequency is determined by its: -Mass -Size and shape -Elastic nature (stiffness) -Composition -Musical resonators -Stretched strings (violin string) -Hollow tubes (flute) -Stretched membrane (drum) |
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Modes of Oscillation 1
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Fundamental Vibration (First Harmonic)
-Center of string vibrates up and down -Frequency of vibration (pitch) is -proportional to tension -inversely proportional to length -inversely proportional to density (mass/length) |
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Modes of Oscillation 2
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-Higher-Order Vibrations (Overtones or Harmonics)
-Second harmonic is like two half-strings -Third harmonic is like three third-strings, … -Each higher mode has one more node in its oscillation -Harmonics come in integer multiples (1,2,3,4…) |
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The Sound Box
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-Strings don’t project sound well
-Air flows around objects -Surfaces project sound much better -Air can’t flow around surfaces easily -Movement of air is substantial |
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Beautiful Music
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-Transfer of vibration to a “sound box” is important in instrument design
-helps to project the sound effectively -helps to “color” the sound, making the instrument sound unique -The method of exciting the string also affects the sound. -Plucking a string transfers energy quickly and excites many vibrational modes -Bowing a string transfers energy slowly -excites the string at its fundamental frequency -each stroke adds to the string’s vibrational energy |
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Air Column as Resonant System
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-A column of air is a harmonic oscillator
-Its mass gives it inertia -Pressure gives it a restoring force -It has a stable equilibrium -Restoring forces are proportional to displacement -Stiffness of restoring forces determined by -pressure -pressure gradient |
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Air Column Properties
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-An air column vibrates as a single object
-Pressure antinode occurs at center of open column -Velocity antinode occurs at ends of open column -Pitch (frequency) is -inversely proportional to column length -inversely proportional to air density -Just like a string, an air column can vibrate at many different frequencies. -A closed pipe vibrates as half an open pipe -pressure antinode occurs at sealed end -frequency is half that of an open pipe |
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Net Charge
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• Net charge is the sum of an object’s charges
• Most objects have zero net charge (neutral) • Neutral objects contain equal + & – charges There is a different way to think about forces on charges… •Potential •Electric fields |
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Electric Fields
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Two views of charge forces:
• Charge/Charge: – Charge 1 pushes directly on Charge 2 • Charge/Field/Charge: – Charge 1 creates an Electric Field – Electric Field pushes on Charge 2 Electric Fields are Real! |
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Electric Fields 2
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• The magnitude of the electric field is proportional to the magnitude of the force on a positive test charge
• The direction of the field is the direction of the force on a positive test charge |
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Voltage
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• Charge has electrostatic potential energy (EPS)
• Voltage measures the EPS per unit of charge – Raising the voltage of a positive charge takes work – Lowering the voltage of a negative charge takes work • Voltage is measured in joules/coulomb or volts |
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Voltage Gradients & Electric Fields
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• Objects accelerate to reduce potential energy
• A charge – has electric potential energy proportional to voltage – so it accelerates toward lower voltage – but it also accelerates because of an electric field • Voltage gradients are electric fields! |
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Charges In and
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• Charges can move inside metals
– They move to minimize potential energies – They give the metal a uniform voltage – There is thus no electric field inside a metal • However, outside metals – Charges can’t move so easily – so voltages can vary with location – and there can thus be electric fields Rapidly changing potential means very large electric fields / forces! |
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Corona Discharges
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• Outside a sharp or narrow charged metal
• the electric field is very strong • charges are pushed onto passing air particles: corona discharge • Corona discharges can dissipate static electricity |
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Photoconductors
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•In the dark, a semiconductor is insulating
•In the light, a semiconductor may conduct |
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A Battery
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• Battery “pumps” electrons from – end to + end
(outside of the battery) – Chemical potential energy is consumed – Electrostatic potential energy is produced • In the battery: The current undergoes a rise in voltage – Alkaline cell: 1.5 volt rise – Lead-acid cell: 2.0 volt rise – Lithium cell: 3.0 volt rise • Chain of cells produces larger voltage rise |
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A Light Bulb
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• Filament barely lets charge flow through it
– Electrostatic potential energy is consumed – Thermal energy is produced – It’s a resistor! • Current undergoes a drop in voltage – Two-cell alkaline flashlight: 3.0 volt drop |
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A Simple Circuit
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• A battery – the energy source
• A wire – the outgoing current path • A light bulb – the energy destination (the load) • A wire – the return current path |
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The most confusing thing about circuits
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• Current is + charges moving
• Really, negative charges move in the opposite direction • We say that current flows in the direction of movement of positive charge |
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Current
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• Current measures the electric charge passing through a region per unit of time
• Current is measured in coulombs/second or amperes (amps) • Electric fields cause currents to flow |
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Circuits 1
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• Steady current requires a circuit path (loop)
– Charge mustn’t accumulate anywhere – Closed conducting loop avoids accumulation • Steady current flow requires energy – Currents lose energy (and voltage) in conductors –Missing energy becomes thermal energy – Lost energy must be replaced |
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Circuits 2
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• A circuit can transport energy
– Current obtains energy from a battery – Current delivers energy to a light bulb – Current starts the trip over again |
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Short Circuits
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• If a conducting path bridges the load
– Current bypasses the load – Circuit is abbreviated or “short” • No appropriate energy destination (load) • Energy loss and heating occurs in the wires • A recipe for fires! |
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Ohm’s Law (V=I x R)
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• The currents passing through most wires and
other devices experience voltage drops • In an “ohmic device,” the voltage drop is proportional the current: voltage drop = resistance • current V = I × R where resistance is a constant for the device |
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Power is
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• Energy per unit of time
• Measured in joules/second or watts • Current times voltage in a circuit: P = I × V • Batteries are power sources • Loads are power consumers Note that since P = I x V and V = I x R, P = I2 × R: higher resistance means more power loss! (for fixed current) |
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Battery Power (P)
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• Current (I): units of charge pumped /sec
• Voltage (V) rise: energy /unit of charge • power produced = current x voltage rise (P = I × V ) |
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Load Power (P)
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• Current (I): units of charge passed /sec
• Voltage (V) drop: energy taken /unit charge • power received = current x voltage drop (P = I × V) |
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Sound is a wave!
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• Sound is a longitudinal pressure wave in a medium (gas, liquid or solid)
• Anything that vibrates a medium produces sound • Air is the most common medium for carrying sound Waves • Waves have a wavelength: distance to next crest or trough • Waves have an amplitude: peak change in pressure for sound in air • Any mechanical wave “represents the natural motion of an extended object around stable equilibrium shape or situation” |
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Frequency and Pitch
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The frequency, or pitch, of sound is the number of times per second that the wave repeats itself (or 1/period)
wave speed = frequency × wavelength |
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Intervals
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Playing two frequencies together sounds nice when they are in small integer ratios
• Octave 2:1 • Fifth 3:2 • Fourth 4:3 • Third 5:4 |
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Producing Musical Sound
Usually involves a resonator |
- An object’s natural vibration or resonant frequency is determined by its:
Mass Size and shape Elastic nature (stiffness) Composition Musical resonators Stretched strings (violin string) Hollow tubes (flute) Stretched membrane (drum) |
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String as Harmonic Oscillator
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Its mass gives it inertia
Its tension and curvature give it a restoring force -It has a stable equilibrium -Its restoring force is proportional to displacement |
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Modes of Oscillation
Fundamental Vibration (First Harmonic) |
Center of string vibrates up and down
Frequency of vibration (pitch) is proportional to tension inversely proportional to length inversely proportional to density (mass/length) |
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Modes of Oscillation
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Higher-Order Vibrations (Overtones or Harmonics)
Second harmonic is like two half-strings Third harmonic is like three third-strings, … Each higher mode has one more node in its oscillation Harmonics come in integer multiples (1,2,3,4…) |
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The Sound Box
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- Strings don’t project sound well
- Air flows around objects - Surfaces project sound much better Air can’t flow around surfaces easily - Movement of air is substantial! |
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Beautiful Music occurs
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• Transfer of vibration to a “sound box” is important in instrument design
o helps to project the sound effectively o helps to “color” the sound, making the instrument sound unique • The method of exciting the string also affects the sound. o Plucking a string transfers energy quickly and excites many vibrational modes o Bowing a string transfers energy slowly - excites the string at its fundamental frequency - each stroke adds to the string’s vibrational energy |
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Air Column as Resonant System
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• A column of air is a harmonic oscillator
o Its mass gives it inertia o Pressure gives it a restoring force o It has a stable equilibrium o Restoring forces are proportional to displacement • Stiffness of restoring forces determined by o pressure o pressure gradient |
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Air Column Properties
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• An air column vibrates as a single object
o Pressure antinode occurs at center of open column o Velocity antinode occurs at ends of open column • Pitch (frequency) is o inversely proportional to column length o inversely proportional to air density • Just like a string, an air column can vibrate at many different frequencies. • A closed pipe vibrates as half an open pipe o pressure antinode occurs at sealed end o frequency is half that of an open pipe |
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Observations About Flashlights
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• They turn on and off with a switch
• More batteries usually means brighter • Orientation of multiple batteries matters • Flashlights dim as batteries age |
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A Battery
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• Battery “pumps” electrons from – end to + end
(outside of the battery) – Chemical potential energy is consumed – Electrostatic potential energy is produced • In the battery: The current undergoes a rise in voltage – Alkaline cell: 1.5 volt rise – Lead-acid cell: 2.0 volt rise – Lithium cell: 3.0 volt rise • Chain of cells produces larger voltage rise |
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Net Charge
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• Net charge is the sum of an object’s charges
• Most objects have zero net charge (neutral) • Neutral objects contain equal + & – charges |
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Electric Fields
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Two views of charge forces:
• Charge/Charge: – Charge 1 pushes directly on Charge 2 • Charge/Field/Charge: – Charge 1 creates an Electric Field – Electric Field pushes on Charge 2 Electric Fields are Real! |
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Electric Fields
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• The magnitude of the electric field
is proportional to the magnitude of the force on a positive test charge • The direction of the field is the direction of the force on a positive test charge • Rapidly changing potential means very large electric fields / forces! |
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Voltage
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• Charge has electrostatic potential energy (EPS)
• Voltage measures the EPS per unit of charge – Raising the voltage of a positive charge takes work – Lowering the voltage of a negative charge takes work • Voltage is measured in joules/coulomb or volts |
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Charges In and Around Metals
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• Charges can move inside metals
– They move to minimize potential energies – They give the metal a uniform voltage – There is thus no electric field inside a metal • However, outside metals – Charges can’t move so easily – so voltages can vary with location – and there can thus be electric fields |
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Corona Discharges
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• Outside a sharp or narrow charged metal
• the electric field is very strong • charges are pushed onto passing air particles: corona discharge • Corona discharges can dissipate static electricity |
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Photoconductors
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• In the dark, a semiconductor is insulating
• In the light, a semiconductor may conduct |
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Observations about
Household Magnets |
• Two magnets can attract or repel
• Magnets can stick to certain metals • Magnets affect compasses • The earth seems to be magnetic • Some magnets use electricity to operate |
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Magnetic Poles
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• Two types:
north & south • Like poles repel, opposites attract • Forces increase with decreasing separation • Analogous to electric charges EXCEPT: o No isolated magnetic poles ever found! o Net pole on an object is always zero! |
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Magnetic Fields
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• A magnetic field pushes on magnetic pole
• The magnitude of the field is proportional to the magnitude of the force on a test pole • The direction of the field is the direction of the force on a north test pole • But isolated magnetic poles don’t seem to exist! |
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Torque on a dipole
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• Magnitude of torque proportional to magnetic field
• Torque always acts on dipole to line it up with field |
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Ferromagnetism
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• Most atoms are magnetic
• Most materials are not o Atomic magnetism is perfectly cancelled • Some materials do not have full cancellation o Magnetism is usually hidden by randomness o However, ferromagnets can be permanently magnetized by applied magnetic fields |
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Refrigerators and Magnets
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• A refrigerator’s steel has magnetic domains
• Domains cancel so steel appears nonmagnetic • When a magnetic pole is near steel o it causes some domains to grow, others to shrink o and the steel develops magnetic polarization o so that it attracts the magnetic pole • Magnets thus stick to steel refrigerators |
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Electromagnetism I
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• Magnetic fields
o Push on magnetic poles o Bend moving electric charges • Electric fields o Push on electric charges |
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Current
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• Current is moving positive charge
• Current is measured in coulombs/second or amperes (amps) • Electric fields cause currents to flow • Currents produce magnetic fields: |
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Current
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• Current is moving positive charge
• Current is measured in coulombs/second or amperes (amps) • Electric fields cause currents to flow • Currents produce magnetic fields: |
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Current
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• Current is moving positive charge
• Current is measured in coulombs/second or amperes (amps) • Electric fields cause currents to flow • Currents produce magnetic fields: |
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Magnetic Fields
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• A magnetic field pushes on magnetic pole
• The magnitude of the field is proportional to the magnitude of the force on a test pole • The direction of the field is the direction of the force on a north test pole • But isolated magnetic poles don’t seem to exist! |
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Torque on a dipole
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• Magnitude of torque proportional to magnetic field
• Torque always acts on dipole to line it up with field |
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Ferromagnetism
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• Most atoms are magnetic
• Most materials are not o Atomic magnetism is perfectly cancelled • Some materials do not have full cancellation o Magnetism is usually hidden by randomness o However, ferromagnets can be permanently magnetized by applied magnetic fields |
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Refrigerators and Magnets
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• A refrigerator’s steel has magnetic domains
• Domains cancel so steel appears nonmagnetic • When a magnetic pole is near steel o it causes some domains to grow, others to shrink o and the steel develops magnetic polarization o so that it attracts the magnetic pole • Magnets thus stick to steel refrigerators |
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Electromagnetism I
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• Magnetic fields
o Push on magnetic poles o Bend moving electric charges • Electric fields o Push on electric charges |