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# SCI_206_Complete_Notes.doc - BluWiki

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SCI_206_Complete_Notes.doc - BluWiki

Topic 1

Thursday, October 05, 2006

1:56 PM

Topic 1: Motion

From Lecture

Newton's Laws

What are the 3 ways to describe motion?;

o Position, velocity, and acceleration

How can we describe position?;

o We use a vector, because it can tell us direction and distance (from some defined start

point)

What are the 2 parts of velocity?;

o How fast we are going (speed)

o What direction we are going in (direction)

What is acceleration?;

o It is how fast (and in what manner) our velocity is changing

What is Newton's first law?;

o An object that is not subject to any net outside forces moves at constant velocity

What is Newton's second law?;

o The force exerted on an object is equal to the product of the object's mass times its

acceleration

o The acceleration is in the same direction as the force

What is Newton's third law?;

o 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

Gravity and Componential Motion

What is gravity? What determines the effect we will experience due to gravity?;

o It is a downward force produced by the earth which acts on us, pulling us down

o The gravitational effect we experience is always an acceleration of ~10 m/s2 --

REGARDLESS of our mass

This means that (neglecting air resistance) a feather falls just as fast as a brick;

Why doesn't gravity cause us to fall through the floor?;

o Because of the "normal force": an upward force produced by the surface we are

standing on that counteracts the gravitational force so that we don't move

Describe the motion of a projectile launched at some angle with respect to the horizontal.;

o We can break up its initial velocity into horizontal and velocity components

Its horizontal velocity will never change, because there are no forces present to ;

change it (recall Newton's First Law)

Its vertical velocity will be subject to gravity, so its upward progress will slow, ;

eventually become zero, then start to head downwards

If you wanted to shoot a monkey in a tree, where should you aim? (Assume that the monkey will ;

drop and fall downwards as soon as the shot is fired).

o You should aim straight at the monkey (not above it or below it), because once the

bullet is in the air and the monkey has dropped, both objects are subject to the same

force (only gravity), and so they will meet at some point

Work and Energy

What is the difference between kinetic and potential energy?;

o Kinetic energy is the energy of movement: the amount of this one possesses is related

to one's velocity

o Potential energy is stored: the amount of this one possesses is related to its ability to

unleash energy

Discuss energy conversions.;

o Energy cannot be created or destroyed, but it can be converted from one form into

another

o The types of conversions which occur and their efficiencies affect the things we see in

the real world

For example, some materials bounce better than others because they do a ;

better job of converting kinetic energy to elastic potential (while others just

convert kinetic into heat)

Discuss work, in particular the way it is related to potential energy.;

o To do work on something is to exert a force on it and cause it to move some distance in

the direction of that force

o Work is related to potential energy because we can give an object potential energy by

doing work on it

For example, lifting a ball from the ground to a table;

Friction

Imagine a scenario where (with friction present) you are pushing a block horizontally across the ;

floor. Describe the different forces acting on the box.

o There is gravity acting downwards, and the normal force acting upwardso There is the human pushing force acting in the box's forward direction, and friction

acting opposite to that

The pushing force must exceed the frictional force in order for the box to start ;

moving from rest

Discuss the 2 kinds of friction. What kind of energy is produced by friction?;

o Static friction is friction that opposes the initiation of movement

o Kinetic friction is friction that slows down movement which has already startedo The energy lost from friction (remember that we would expect a given amount of

energy produced given the work we put into moving something…so when we have

reduced energy due to friction, where does that energy go?) becomes HEAT

Explain the "spiky" model of friction.;

o On a microscopic level, the two interacting surfaces are not smooth but rather have

many small bumps and crevices, almost like interlocking teeth

Thus moving the surfaces across each other requires energy to overcome this ;

interlocking mechanism

o When starting from rest, more of the "teeth" are "locked together" and thus the

frictional force experienced is greater

o When already moving, there are fewer teeth interlocked and thus the force is smallero If you press the two surfaces together (i.e. if the one on top is heavier), again the

"teeth" "interlock" more, and so friction increases (this is why friction is related to the

normal force)

Explain why a tablecloth can be pulled out from beneath a dinner set.;

o It is simply a function of the frictional force between the tablecloth and the dinner

plates: can we pull the tablecloth fast enough that it overcomes the frictional force

which is causing the plates to stick to the cloth? If so, the cloth will come right out from

beneath them...

Rotational Motion

Describe the motion of a tennis ball connected to a string being flung around in the head in a ;

CIRCULAR pattern.

o Its speed is always the same, but its velocity changes since its direction is always

changing

o It has an acceleration that is always the same in magnitude but always changing in

direction (though it is always pointed towards the middle)

The force creating this acceleration (since f = ma) is known as the "centripetal ;

force", and it is embodied in the tautness of the string

o If at any time in the motion the ball was separated from the string, it would fly off in a

line tangent to the circle (this is why we feel like we're falling out of the car when we go

around curves)

Recall the experiment where a water-filled bucket was rotated vertically in a circle. What ;

determines whether the water falls out?

o The relevant relationship here is that the centripetal force (discussed earlier) is related

to the velocity of the motion

And the centripetal force is made up of the tension which swinging the bucket ;

exerts on the arm PLUS the gravitational force - so if the necessary centripetal

force isn't even as much as the gravitational force, then the remainder of the

gravitational force will be used to allow the bucket to spill

Why do figure skaters spin faster when they bring their arms close into their body?;

o Because something called angular momentum is conserved, which is a function of

rotational inertia (analogous to mass) and rotational speed (analogous to velocity)

o As long as torque (a force which affects rotational velocity) is not added to or removed

from the system, angular momentum must stay constant - and so if we reduce our

rotational inertia by bringing our weight closer to the axis of rotation, the rotational

velocity must increase to counteract this

Why did Idziak's tricks with the strings and the hourglass work better when the hourglass was ;

spinning?

o Because the hourglass wants to conserve angular momentum, and it does this by

continuing to spin on the same axis

o If it were to wobble (i.e. become unstable), this would constitute spinning on another

axis and cause angular momentum to not be conserved - thus it tends to not do this

From Textbook

Chapter 1

Chapter 2

[do I need to have anything here?]

Topic 2

Sunday, October 08, 2006

12:28 AM

Topic 2: Resonance

From Lecture

Waves

What is a pulse on a string? Describe some characteristics of it.;

o It is a "bump" that travels along a string

o It has a defined direction and has the ability to be reflected off the ends of the stringo It does not cause the string itself to move - it only causes sections of the string to be

displaced vertically

What is a transverse wave? Identify the following features of a tranverse wave: amplitude, node, ;

antinode, velocity, wavelength.

o A transverse wave is one where the displacement created is vertical

If we have a transverse wave on a string, what force causes the vertically-displaced portions of ;

the string to oscillate "up and down"?

o The tension on the string acts as a restoring force to bring it back to the middle, but it

overshoots and goes to a maximum amplitude on the other side

Explain how longitudinal waves work.;

o Longitudinal waves are those where the displacement is longitudinal - i.e. along the

length of the wave

It is a series of compressions and stretches (aka rarefactions);

Discuss how sound is a longitudinal wave. What implications does this have for the necessary ;

conditions for hearing sound?

o Sound waves are simply longitudinal waves in air - and the analog of "compressions"

and "rarefactions" are regions of high and low air pressure

o The implication is that we must have air in order to hear sound - because to hear sound

is simply for our ear to detect the pattern of air pressure changes

Recall the demo where a bell in a vacuum was rung, and no sound was heard;

How are the speed, frequency, and wavelength of a wave related? What implication does this ;

have for sound in different mediums?

o Speed = frequency x wavelength

o The implication is that sound travels at different speeds in different mediums, and so

when sound passes from one medium to another, the speed will change: thus either

frequency or wavelength must change

Frequency does NOT change, and so wavelength does - thus the sound we hear ;

is different

Give an example of a wave traveling through different mediums.;

o If we pluck a guitar string, first the string vibrates in the form of a characteristic wave,

and then it causes the air around it to vibrate - and we hear that in our ear

Doppler Effect

Explain what the Doppler Effect is. Give an example.;

o It is the phenomenon where a sound will sound different if its source is traveling either

toward you or away from you than it would if the source was stationaryo This is why the siren from a police car or fire truck will appear to change in tone if you

are standing on the side of the road and the car comes towards you, passes you, and

continues on away from you

How does the Doppler Effect work?;

o It is because the sound waves are either compressed (coming towards you) or expanded

(going away from you), and thus the altered wavelengths are perceived differently

How do sonic booms work?;

o This is an extreme application of the Doppler Effect whereby the source of sound

created is so loud that the waves are compressed so much that they all arrive at

essentially the same time at a single spot, and an extremely loud sound is created

Oscillations & Resonance

Explain how a pendulum is an example of a simple harmonic oscillator.;

o It is because if we pull the mass to the left or right then let go, the tension in the string

will cause the mass to swing back in the direction of the equilibrium position, and in fact

surpass it and go to an extreme on the other side

o The force that does this (and is definitive of simple harmonic oscillation) is a "restoring

force": a restoring force always tries to bring the mass to equilibrium

Discuss the relationship which the restoring force has to the object's distance from the ;

equilibrium point. What implication does this have for the period of a given pendulum?o The restoring force is linearly proportional to the object's distance from equilibrium: the

further away the object is, the stronger the force is which wants the object to return

It consists of the force created by the tension of the string and gravity;

o The implication is that for a given pendulum, its period will always be the same…

Regardless of how far away you initially bring the pendulum;

And also regardless of what the MASS of the swinging object is;

o The ONLY FACTOR that can change the pendulum's period is the length of the string

Explain how pendulum clocks work.;

o There is a circle with 30 teeth (a gear), and an apparatus attached to a pendulumo The apparatus is positioned such that every time the pendulum completes an oscillation

(period = 2 seconds), the apparatus clicks past one "tooth"

o Thus, every time the gear completes a full revolution, we know that it has been one

minute (60 seconds)

Describe the motion of a mass on a spring, and why it is a harmonic oscillator.;

o Firstly, there is an equilibrium point - where the spring is neither stretched nor

compressed

o If we (for instance) pull the mass such that we are not at the equilibrium point and the

spring is stretched, we will feel tension because the restoring force in the spring wants

to return the mass to the equilibrium point

o It is a harmonic oscillator because if we release the mass, it will accelerate back towards

the equilibrium position and overshoot it to the other side, compressing the spring and

creating another restoring force that pushes the mass again back to the equilibrium

position from the other side

How do we adjust the frequency of these things?;

o Bigger mass = lower frequency

o Stiffer spring = higher frequency

Explain what the concept of resonance is.;

o The "resonance frequency" is the frequency at which an oscillator "naturally" likes to

oscillate

o We can increase the amplitude of the oscillations if we add energy to the system at a

frequency identical to this natural, "resonant" frequency

How does resonance apply to shock absorbers in cars?;

o Well, here we want to REDUCE the amplitude of the oscillations (so we will go up and

down less)

o So the shock absorbers are designed to compress and expand at a frequency DIFFERENT

than the one at which the car is bouncing up and down - this will reduce the amplitude

of the movement and make the ride more comfortable

How does resonance apply to pushing a child on a swing?;

o Here the relevant principle is that of pushing the child right when he gets to the apex of

his swing - because when we do that, we are adding energy at the same frequency as

the one at which he is oscillating

o That is why we can get him swinging very high in a relatively short time if we do this (as

opposed to, say, pushing him back before he has reached the height of his swing)

How does resonance apply to breaking a wine glass with sound?;

o It applies because if we play sound at a certain frequency, it will cause the air to (of

course) also move at a certain frequency

o Now, the sides of the wine glass also vibrate (ever so subtly) in response to the airo If we get the air to vibrate at the resonant frequency of the wine glass, the oscillations

of the glass will increase until the glass breaks

How can water have an effect on resonance?;

o [I forget which demo this was, but] if water was the medium in which energy was being

added to some system at that system's resonant frequency, the water could potentially

dampen its effects

Standing Waves and Sound

Explain how a standing wave on a string works.;

o If we have a string that is stationary at both ends, we can pluck it and cause a wave to

be created at (one of) the string's resonant frequency

o The wave travels down to one end and is reflected -- and this pattern maintains itself for

some period of time

o We say it is a "standing" wave because a pattern of oscillation is produced such that

there appears to be no movement

Explain the concept of harmonics.;

o A string has many harmonics, and they are simply the term used for the frequencies

associated with the natural "standing wave" conformations which the string can assumeo Yes, that is right: a string can have more than one type of standing wave - theoretically,

any number of wavelengths within the string is possible as long as the ends stay as

nodes

Why is a sound heard when we rub the top of a wine glass with our finger?;

o Because due to friction, when we rub our finger we are actually dragging it to some

degree, and causing the glass to deform slightly

o This deformation creates a wave in air which produces the sound we hearo Continuously rubbing the finger adds energy (helps the glass deform more) and thus

makes the sound louder

Why is a sound produced when we hit the end of a metal pole on the ground?;

o Because (again) the metal deforms ever so slightly, and we get a wave in air that makes

the sound

Explain why sound can be created by blowing into an organ pipe. What happened when we put ;

this tube over a flame from a Bunsen burner, and why?

o Blowing into a pipe creates a longitudinal standing wave using the air inside the tube

One end is closed (a node, where compression can take place) and the other is ;

open (an anti-node)

The standing wave goes at a frequency that we can hear, and that is the sound ;

we perceive

o Note that the fundamental wavelength is TWICE the length of the tube, because only

one end is a node

o When we put this over a flame, we could see the flame moving around in the air

because of the changes in air pressure coming out of the pipe

Explain why sound can be created by blowing across the mouth of a beer bottle.;

o It is because when we blow, we are activating a mass-spring system such that the air in

the neck of the bottle moves up and down due to the force we provide with our breath

(by "pushing it down") vs. the restoring force of the air in the wide part of the bottle

that pushes it back up

o The frequency produced by this oscillation is perceived by our ears

How do we show that sound is a compression/rarefaction wave?;

o Recall that we had a tube of (some gas), with holes in the top…and also a flame

o We created a longitudinal sound wave in the tube, and where the regions of pressure

were low (i.e. the nodes), the flames shot up higher because it was a stable

environment for the flames to work

Explain how a loudspeaker works.;

o There is an electromagnet, which consists of two magnets that can move towards or

away from each other depending on the current in the coil

o As the magnets move, they cause a paper cone to move, and this causes a pressure

wave in air that we perceive as sound

What happens when we mix up the red and black wires in a stereo system? What is the name ;

for this phenomenon?

o When we do that, we send the wrong signals to the speakers, and so the air pressure

waves created cancel each other out by the time they reach us, and we perceive a very

soft noise - this is called "destructive interference"

o When the wires are correctly plugged in, the sound waves created are the same as each

other, so "constructive interference" occurs and we hear a loud sound

From Textbook

Chapter 9

Topic 3

Sunday, October 08, 2006

12:28 AM

Topic 3: Balloons, Bubbles, and Pressure

From Lecture

Ideal Gas Law: Pressure, Density, Temperature, etc.

Discuss the structural differences between a solid and a liquid.;

o A solid is structural and arranged in a periodic manner, such that if we know the location

of one molecule, we can infer the location of all other molecules in that structure

o Conversely, the molecules in gas are much farther apart from each other, and there is

no defined structure

What happened when we ran an air hose through liquid nitrogen? Why?;

o We caused some of the gases in the air to condense into liquids, while some others

remained as gas

o The result was that a combination of gas and liquid came out the other end

o This is a property of gases - at certain temperatures, the molecules come together close

enough that the substance takes on the consistency of a liquid

Explain how the concept of pressure applies to a gas.;

o Recall that pressure = force / area

o And the individual molecules in some sample of gas push against the walls of their

container, and create pressure

Explain how a steam engine works.;

o It's all about this pressure principle - you evaporate water and now we have lots of

steam in a confined space

o Thus it will create pressure against the walls, and this pressure can be used to crank an

engine

Why does a balloon make a loud sound when it pops?;

o It is because there is a sudden release of pressure from the gas molecules which were

previously inside, pushing out against the fabric of the balloon

When this pressure is suddenly released, a loud sound is made;

o Note that the pressure inside is (definitely) greater than the pressure outside because

the pressure inside needs to keep the balloon stretched out

Explain gaseous temperature on a molecular level.;

o Temperature of some sample of gas is related to how quickly the molecules of gas are

moving around

o Note that if they move around faster, they will bump into the walls with more force and

thus create greater pressure as well - that's why if a gas is in a container than can

expand, heating the gas will cause the container to expand

How do we apply the molecular explanation of temperature to making bombs and popcorn?;

o Both things involve the principle of heating something up so that it expands so much

and so rapidly that an "explosion" is caused

Either the bursting of the kernel into a piece of popcorn;

Or the bomb exploding;

Explain gaseous density on a molecular level.;

o Density is just how many gas molecules there are in a given area

o Again, when the density is higher, the pressure will be higher because more gas

molecules will be hitting the sides of the container

How does this apply to using a straw?;

o We are basically sucking the air out of the straw, meaning that there is less pressure

available to push the liquid down

o Thus liquid is able to come up the straw and into our mouth :)

What does the Ideal Gas Law tell us?;

o PV = nRT, or P = number density x R x T

o Pressure is proportional to density of particles times temperature

Atmospheric Pressure and Buoyancy

Explain the "box" model of atmospheric pressure.;

o If we are talking about the atmospheric pressure acting on a single person, imagine that

the column of air above him is divided into boxes

o Gravity acts (as it always does) on these boxes, and so there is a downward force on the

person created by all this air

However, there are also air boxes which push up to counteract this (that is why ;

we are not crushed)

o As we get higher on this "pile" of boxes, there is more air pushing up and less air

pushing down, so the air pressure we experience is less

Why was it hard to pull those rubber disks apart when the air was removed from inside them?;

o Because removing the air meant that the air pressure in the "container" was reduced to

zero, all the air from outside wanted to get in so that pressure could equilibrateo This air created a force which opposed the efforts to pull the discs apart

Why does it not hurt to lie on a bed of nails?;

o Because the pain which we traditionally think nails cause is due to pressure, which

(recall) is related to force and area

o In this case, we are spreading out the area of the pressure source by putting many nails,

and thus the total pressure is not too bad

What would happen if the cabin of an airplane became de-pressurized, and I failed to put on my ;

o All the intestinal gas we have (which is now kept at a certain density because of the

atmospheric pressure from outside) would now be subjected to less atmospheric

pressure, and so it would expand (very uncomfortable!)

What is Archimedes' Principle of Buoyancy?;

o "An object partially or wholly immersed in a fluid is acted on by an upward buoyant

force equal to the weight of the fluid it displaces."

What phenomenon was observed with the Playdoh boat, and why did this happen?;

o This is a demonstration of Archimedes' Principle: when it was shaped like a real boat,

the volume of water it displaced was greater than the volume of water it displaced

when we condensed it into a ball

o Thus when we had the greater volume of water, the buoyant force supporting the boat

(equivalent to the weight of this greater volume) was big enough to support the boat's

weight

o But when we had the smaller volume of water, the buoyant force was less, while the

boat was the same weight - but this time it was insufficient to hold the boat up

Why do we float higher in the Dead Sea than in our bathtubs?;

o It is because salt water is denser, so the weight of the volume of water we displace is

greater than the same volume in regular water

o Thus this greater weight means there is a greater buoyant force keeping us up

How does our weight change when we are in water?;

o Our weight is essentially equivalent to the normal force that needs to be produced by

the surface we are standing on in order for us to not fall through

o When we are in water, this normal force is reduced because the downward force

produced by gravity on our body is (partially) counteracted by the buoyant force

Balloons

How does a hot air balloon work?;

o We have to think about PV = nRT, and the relationships which that equation representso The idea is that we use a fire to warm the air inside the hot air balloon…and this

increases the kinetic energy of the molecules, causing one of the following things to

happen:

All molecules remain in the area and pressure increases (molecules hitting the ;

wall more frequently and at greater speeds)

Some molecules leave the area and pressure remains the same (molecules hit ;

the wall at the same rate even though they are moving faster, because there

are fewer molecules)

o Since it is an open system, pressure cannot be different and so the latter option occurs.

This reduces the density of the balloon to the point where it rises (can you explain this

using Archimedes' Principle?)

Why did a balloon float when put at the top of a tube with dry ice at the bottom, yet outside the ;

tube it sinks?

o This is again an application of Archimedes' Principle: remember that the buoyant force

depends on the weight of the air you have displaced

o In regular air, this weight is not sufficient to keep the balloon afloat (it does have SOME

weight!)

However, the gas evaporating from the dry ice is "heavy", so the buoyant force ;

created is enough to keep the balloon afloat

What is the source of the energy that causes a balloon to fly around the room when you ;

suddenly let the air out of it?

o It's because when we were blowing up the balloon, we added energy to the system

because the elastic material resisted stretching

Why do helium balloons act as they do?;

o Again, it's all about buoyancy. Think about the weight of the air displaced by the

balloon. Now think about the weight of the balloon (plus, of course, the helium inside)

o If the balloon is lighter, of course it will rise...

Bubbles

How does soap work?;

o It is made up of molecules where one end of the molecule is hydrophobic (and thus can

interact with oil) and the other is hydrophilic (and thus can interact with water)

This is why soap is good at removing oil - because it can cluster around the oil ;

droplet, then the whole thing can be washed away with water

How did he create that sheet of bubbles?;

o He created a very sheet-like balloon-like structure where there was water in the middle,

and then soap on either side such that the hydrophilic end of the molecules were

touching the water

Hydraulic Pump

Explain the principle behind the hydraulic pump.;

o This takes advantage of the principle that within a body of fluid, the pressure is the

same everywhere

o So we can supply a lot of pressure at one location in the fluid with a medium force but

very small area

At the other end of the fluid, we can put a pump with very large area, meaning ;

that having equivalent pressure in this area would mean having an even greater

force

o The "catch" is that the bigger weight will much less further than the smaller weight

because work must always be equal, and work = force x distance…thus if we have small

force and big distance, the other end will have large force and small distance

Basically, this allows us to move heavy things with little but prolonged effort, ;

instead of much but instantaneous effort

From Textbook

Section 5.1

Topic 4

Sunday, October 08, 2006

12:28 AM

Topic 4: Electricity

From Lecture

Current

Describe how electrons move in solids.;

o Think of the crystal lattice model of solids which was shown in class

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