lecture 2 miscellaneous & review forces & acceleration simple harmonic motion waves...

Lecture 2Miscellaneous & ReviewForces & AccelerationSimple Harmonic MotionWaves

Instructor: David Kirkby ([email protected])

Physics of Music, Lecture 2, D. Kirkby 2

Miscellaneous IThe web page describing the Natural Sciences Breadth Requirements is out of date and does not mention this course.

The printed schedule of classes does list this course (on p.20).

To complete your breadth requirement you must complete an additional 2 Natural Sciences classes chosen from:

•Physics 16,17,18,19,20A,20B,20C,20D,21•Earth System Science 1,3,5,11,15•Engineering E5

http://www.reg.uci.edu/registrar/soc/ns.html


Miscellaneous III have put 2 copies of the textbook on reserve at the Science Library.

The bookstore was out of stock of the textbook yesterday, but now have another 20 copies on the shelf.

Online demonstrations are written in Java and require a recent Java plug-in to work with your browser. They work with the Mozilla browser (in the “Internet Apps” folder) of the PCs in the NACS Engineering Gateway computer lab.

You should have received an email sent to the course list yesterday. If not, check your email setup.


Review of Lecture 1Organizing principle for our study of sound:

Sound = Source + Propagation ( + Detection )

Sound travels from a source as a periodic disturbance of a medium (usually air).

Sound propagates through a medium without the particles of the medium themselves actually traveling from the source to the detector.

Some of the properties of air relevant to sound are its temperature, density and pressure.


Sources of sound usually rely on solid moving parts that are made to vibrate with the same frequency and amplitude as the sound they produce.

Sound detectors usually have solid moving parts that react to disturbances in the air around them.

A sound is characterized by its frequency (or period), speed, wavelength and amplitude.

Speed = wavelength x frequency

(this is just another version of speed = distance/time)


ForceA force is a push or a pull applied to an object.

Applying a force to an object can:•Distort its shape, and / or•Change its motion

For simplicity, we often think in termswith idealized objects (like billiard balls)whose shapes cannot be distorted.

For these idealized objects, a net forceon an object necessarily changes itsmotion.


Example: GravityAn object near the Earth experiencesa force due to gravity. The size of thisforce is proportional to its mass.

Gravity

Cassini orbiter near Saturn

The force of gravity also applies inspace, where the distance betweenmassive objects now becomes important.


Example: Elastic Forces An elastic object (spring, rubber

band, diving board, etc) exerts a restoring force when it is compressed or stretched. The size of this force is proportional to how much the object has been compressed or stretched.

resistscompression

resistsstretching


Example: Inelastic ForcesAn inelastic object (string, rod, etc) transmits forces between 2 other objects. (But no real objects are truly inelastic).

Transmits forcesbetween hand to ball

Transmits forcesbetween dogs


Example: FrictionOne object sliding against another can experience friction. Friction exerts a force that resists the sliding object’s motion. The size of the friction force is approximately proportional to the size of the force pushing the 2 objects together.


Combined Forces, VectorsThere are generally several forces acting on an object, each in different directions.

The only thing that matters for the object’s motion is the combined, or net force.

Forces are combined as vectors.

Vectors are just arrows. You add 2 vectors together by lining them up head to tail.

Many quantities in physics are vectors: force, acceleration, velocity.


Example: Addition of Velocity VectorsA kayaker’s velocity has two components: one due to his paddling and the other due to the current.

What is his actual direction of travel?

Directionof current

Directionof paddling


AccelerationAcceleration is the rate of change of velocity (speed).

E.g., pushing the acceleratorpedal on a car increases itsspeed.

Acceleration is measured inm/s2 (why?)

The space shuttle acceleratesat about 30 m/s2, or about3x the acceleration due toGravity (“3g”).


Can the speed be zero if the acceleration is not zero(ie, the speed is changing)?

Can the acceleration be negativewhen the velocity is positive?


Newton’s LawThe way in which an object’s motion changes as a result of the net force applied to it is described by Newton’s Second Law:

Force = mass x acceleration

Or, using the Physicist’s standard symbols:

F = m a

We can also turn this around: a = F/m

Isaac Newton, 1642-1727


Newton’s 2nd Law: ExampleBoth of these cars have a 5 liter engine and so transmit the same force to the drive wheels…

But the Crown Victoria has a lot more mass! Which is morefun to drive?

Crown Victoria Mustang

F

mFm

a =a =


Example: Addition of Force VectorsCan the net force be zero when two or more forces are applied?

aerodynamic lift

gravity

a = F / m = 0

because F = 0

Helicopter hovers!


Pressure RevisitedNow that you know something about force, we can define pressure more precisely:

pressure = force / area

Or equivalently, force = pressure x area

Pressure decreases when aforce is distributed overa larger area.

It is harder to pop a balloonwith 100 nails that with1 nail.


Pressure ExampleThe force of an egg hitting the floor only depends on its mass and how high it fell from.

Whether the shell breaks on not depends on how much area that force is distributed over…

Pressure = Force / Area Pressure = Force / Areahttp://www.sciencejoywagon.com/physicszone/lesson/02forces/pressure/pressure.htm

http://www.sciencejoywagon.com/physicszone/lesson/02forces/pressure/pressure.htm








Simple Physical SystemsWe will now study some examples of simple physical systems. These examples are chosen because they have features in common with the way sounds are generated:

•Pendulum•Spring

We will see how the motions of these systems relate to the forces applied to them and learn that these are all examples of Simple Harmonic Motion (S.H.M.)


Example: Object on a SpringA spring is a very elastic object with a natural “resting” position.

We usually idealize the spring as having no mass, but the object having mass (otherwise a = F/m is infinite!)

Suppose a spring is fixed at one end and has a free mass connected to the other end are resting on a table.

What are the forces on the mass?


Restoring force: the object is pulled towards the spring’s resting point.

Resting point

Spring compressed

Resting position

Stretched


Example: PendulumA pendulum consists of a string attached to a fixed pivot at one end and a mass at the other end.

We usually idealize a string as having no mass and being inelastic.



Tension: the inelastic stringpulls the mass towards thefixed pivot.

Gravity: the mass is pulledtowards the Earth.


Example: Uniform Circular MotionImagine a mass tied to the end of a string that you spin around in a circle above your head.


Tension: the string pulls the mass in towards the middle of the circle.

A central force (e.g., Gravity) can also pull an object in towards a central point and results in the same uniform circular motion.


What do these examples have in

common ?


Simple Harmonic MotionThis demonstration of the motion of springs and pendulums shows that they share a common periodic behavior.

We call this periodic motion Simple Harmonic Motion(or S.H.M. for short).

A S.H.M. is described by its:•Frequency (or period)•Speed•Wavelength•Amplitude

http://positron.ps.uci.edu/~dkirkby/music/html/demos/SimpleHarmonicMotion/index.html


Aside on TrigonometrySimple harmonic motion can be described mathematically using trigonometry, as:

y(t) = A sin ( 2 f t)

Or just as well, as:

y(t) = A cos ( 2 f t)

It is no coincidence that S.H.M. is a very common physical motion and that most calculators devote keys to sin & cos!


What is a Wave?We have already seen one example of a wave: sound.

Now we are going to generalize this concept…

A wave is a periodic (repetitive) disturbance of some medium that travels from one point to another without the medium itself being transported.

All waves can be described in terms of their:•Frequency•Wavelength•Speed•Amplitude


Example 1: SoundSound waves are usually disturbances of air.

Sound waves that we can hear have frequencies roughly in the range of 20 Hz - 20,000 Hz.

Higher frequencies correspond to higher-pitched (more treble) sounds.

The speed of sound in air is about 345 m/s.


Example 2: LightLight waves are a disturbance of electric and magnetic fields. They do not require a physical medium and can be transmitted through empty space.

Light is part of a continuum ofelectromagnetic waves that alsoinclude X-rays, ultra-violet,infra-red and radio waves.


The frequencies we can see correspond to about 1015 Hz!

Light travels at about 300,000,000 m/s.


Example 4: Water WavesWater waves are a complex disturbance of the surface of a body of water due mostly to wind.

Water waves travel at speeds in the range 1-10 m/s. They travel faster in shallow water.


Longitudinal & Transverse WavesVisit this site to see particle simulations that compare longitudinal and transverse waves:

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html











Solid objects can support both longitudinal and transverse waves, because they are elastic along all their axes.

Liquids and gases can only support longitudinal waves, because they offer no resistance to sideways forces (also known as shear forces).

Sound is a longitudinal wave.

Light is a transverse wave.

What about water waves?


Water waves combine both longitudinal and transverse wave motions.

The result is that water particles follow circular paths:












But water is a liquid! How can it support transverse waves?

The answer is that the transverse component of water waves is not due to its resistance to shear forces, but due to the force of gravity on the mass of the water.


S.H.M. and WavesWhat is the connection between Simple Harmonic Motion and Waves?

The source of waves is often a disturbance created by a solid object undergoing S.H.M.

Wave detectors are often solid objects that respond to local disturbances by undergoing S.H.M.

We will be identifying lots of examples of S.H.M. when we look at sound sources and detectors later in the course…


SummaryForce is a push or a pull on an object.

Acceleration is the rate of change of velocity.

Newton’s Second Law: F = m x a

Pressure: P = F / A

Examples of Simple Harmonic Motion: spring, pendulum, uniform circular motion.

Examples of waves: sound, light, water.


Review QuestionsCan an object be at rest when two forces are acting on it?

Does motion require a force?

Can the speed be zero if the acceleration is not zero?

What are the common features of all Simple Harmonic Motion?

What are the common features of all waves?

What properties do waves and Simple Harmonic Motion have in common?


Problem Set #1Due at the beginning of class next Thursday, 10 Oct.

First part of homework is to complete the online survey. This will only work from a computer setup for sending email (eg, using Outlook on Windows).

If you have trouble with the online survey, write your answers on a printed copy and hand that in with your homework next week.

The last 2 questions involve some hands-on measurements and will take more time.

lecture 2 miscellaneous & review forces & acceleration simple harmonic motion waves...

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