00 physics broward 1st week

8/2/2019 00 Physics Broward 1st Week

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for Engineers & Scientists

Ohanian & Markert


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Preliminary Concepts

Physicsthe study of matter (and/or energy?)

Scientific notation: Earth Radius: 6.4 x 106 m

Earth Sun distance: 1.5 x 1011 m

Speed of light: 3.0 x 108 m

Diameter of atom: 1.0 x 10-10 m

Diameter of proton: 2.0 x 10-15 m

When working with scientific figures, round the result

in order to match the least precise figure. What to measure? Position, time and mass (well leave

electric charges & temperature for later) Idealparticles


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Position & Time

Coordinates: needed in order to specify theposition of a particle Establish the origin point

Grid lines: rectangular coordinates

Two-dimensional grids; three-dimensional grids; n-dimensional grids

In order to describe motion, we need the positionof the particle, and the time at which it had that

position Coordinate grid + array of synchronized timing

devices reference frame (position + time)


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Units are needed

in order to record measurements of

position, time, and mass.

The Metric system of units (also called the

International System of Units):

Length: the meter

Time: the second

Mass: the kilogram


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Multiples and submultiples

Kilo 103

Mega 106

Giga

109

Tera 1012

Peta 1015

Exa 1018

Zetta 1021

mili 10-3

micro 10-6

nano 10

-9

pico 10-12

femto 10-15

atto 10-18

zepto 10-21


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The Unit of Length

Originally, the standard METER was a platinum-iridium alloy bar, kept in France. The distancebetween scratch marks located near both ends ofthe bar, was defined as a meter.

It was chosen so that it would be the 1/107 partof the quarter of the polar circunference of theEarth.

Nowadays, the length of the meter is defined in

terms of the speed of light; it is the lengthtraveled by a light wave in vacuum in a timeinterval of 1 / 299,792,458 of a second.


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Other prefixes and unit systems Angstrom = 1 x 10-10 m (Anders Jonas Angstrom, Sweden,

1814-1874) 1 Astronomical Unit = 1.496 x 1011 m (distance from the

Earth to the Sun)

1 parsec (pc) = distance at which 1AU subtends an angle ofone second of an arc (about 3.26 light years, prove it)

1 light-year = distance that light travels in a year British system of units:

Foot = 0.3048 meters

Mile = 5,280 feet = 1,609.38 m

Nautical Mile = 1.151 miles or 1852 m Yard = 3 feet = 0.9144 m

Inch = 1/12 feet = 2.54 cm

Mil = 0.001 inch
http://commons.wikimedia.org/wiki/File:A%C3%85ngstr%C3%B6m.jpg


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Needing help with the parsec numbers?

Parsec: distance

corresponding to a

parallax of one

second

Parallax:

Displacement or

difference in the

apparent position

of an object viewed

along two different

lines of sight
http://en.wikipedia.org/wiki/File:Stellarparallax_parsec1.svg


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The Unit of Time

The SECOND was originally defined as

1 / (60x60x24) or 1/86,400 of a mean solar

day (one complete rotation of the Earth)

Nowadays, the second is defined as the time

needed for 9,192 million vibrations of a

cesium atom (Cesium clocks are really cool!)


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Time Intervals

Age of the Universe 4.0 x 1017 s

Age of the Solar System 1.4 x 1017 s

Age of oldest fossil

1.1 x 1017

s Age of human species 7.9 x 1012 s

From Sun to Earth 5.0 x 102 s

From Moon to Earth 1.3 x 100 s Sound wave 3.8 x 10-3 s
http://en.wikipedia.org/wiki/File:Metric_seal.svg


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The Unit of Mass

The KILOGRAM standard is a cylinder of an alloycomposed of platinum and iridium, kept in France.

Up until now, we still dont have an atomic standard formass.

Avogadros number: 6.02214 x 1023 atoms (ormolecules) per mole, and the atomic mass of achemical element

Common Atomic Masses: 12grams for Carbon, 1g for

Hydrogen, 16g for Oxygen Atomic mass unit: 1 u = Mass of a Carbon-12 atom / 12

1 u = 1.66 x 10-27 Kg
http://en.wikipedia.org/wiki/File:Metric_seal.svghttp://en.wikipedia.org/wiki/File:Metric_seal.svghttp://commons.wikimedia.org/wiki/File:Avogadro_Amedeo.jpg


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Other Units

1 avoirdupois pound = 0.45359 Kg

1 ounce = 1/16 pound = 28.35 g

1 Metric Ton = 103 Kg

1 Ton (1,000 lb) = 907 Kg

1 troy pound = 0.82286 avoirdupois pound

1 troy pound = 12 troy ounces

1 troy ounce = ( 192 / 175 ) * avoirdupoisounce
http://commons.wikimedia.org/wiki/File:Avogadro_Amedeo.jpg


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Derived Units

Base units: the meter, the second, and the

kilogram

Derived units are constructed by a

combination of the base units.

Area (meters squared); volume (meters

cubed)

Density (Kg / meters3)

Speed (meters / seg)


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Warm-up Exercises

Conversion of Units

Always check unit consistency

Ratios of two quantities with identical dimension

or units will have no dimensions at all; they arecalled dimensionless quantities.

Basic trigonometrical functions of the righttriangle; law of sines; law of cosines

Basic algebra: equation systems, quadraticequations


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Lets solve

Page 22, Nos. 13 15

Page 23

Nos. 26 & 27

Nos. 36 38

Page 25, Nos. 68 & 69

And for homework: Group 1 odd numbers between 70 & 84

Group 2 even numbers between 69 & 83

i


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Just in case.


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Chapter 3: Vectors

Displacement of a particle: a change of itsposition

The arrow drawn from an initial point P1 to a

final point P2 is called the displacement vector. A displacement vector is defined by its length

and direction.

Velocity, acceleration, and force are vectors.

Length, time, mass, temperature, and energyare scalars.


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Operations involving vectors Vector addition: two displacements carried out in

succession, result in a net displacement, which isregarded as the vector sum of the individualdisplacements.

The sum of two vectors is called the resultantof thesevectors. Visual technique: triangle or parallelogram.

The Commutative Law applies to vector addition The magnitude of the resultant of two vectors Is

usually less than the sum of the magnitudes of thevectors.

The negative of a given vector A is a vector of thesame magnitude, but opposite direction.

The subtraction of two vectors A and B is defined asthe sum of A andB.


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Lets go 3-D

In space, the vector is the diagonal

of the box formed.

The position vector and other vectors are expressed interms of unit vectors: i (used for the x axis) j (used for the y axis)

k (used for the z axis)

The magnitude of the unit vectors is (of course) 1.

Vectors expressed in terms of unit vectors: A = 2i + 3j 2k

A = (2 ; 3 ; -2)


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The Position Vector

Any point in a plane can be specified by tworectangular coordinatesxand y, and thedisplacement vector from the origin to the point.

The displacement vector joining the origin to anygiven point is called theposition vector.

x and y are the components of the positionvector, and they will be represented with Ax andAy.

The addition or subtraction of two vectors can beperformed by adding or subtracting theircomponents.


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Vector Multiplication

Dot Product: also called the scalar product, is theproduct of the magnitudes of the two vectors andthe cosine of the angle between them.

Notation: A . B = |A|*|B|*Cos(A,B)

When will it be positive, negative or cero?

A . B = AxBx + AyBy + AzBz+

The dot product of a vector and a unit vector, will

give the first vectors component in thatdirection.

Dot product is commutative


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Cross Product

Also called the vector product, because the result ofthis multiplication is another vector.

A x B produces another vector: Perpendicular to A and B

With a magnitude equal to the product of the magnitudesof the two vectors times the sine of the angle betweenthem

For the direction of the resulting vector, use the right-hand rule

A x B = - B x A

i x i = 0; j x j = 0; k x k = 0

i x j = k ; j x k = i ; k x i = j


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Now, we exercise

Page 88; Section 3.2: 12 to 15



Homework: Review problems (pg 91)

Group 1: 66, 68, 70, 74, 76

Group 2: 67, 69, 71, 73, 75

For everyone: 72, 77, 78

END OF SESSION 1 (I wonder if were onschedule or not?)


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Motion along a straight line We will assume that the straight line coincides

with the x axis. Therefore, the x coordinate is afunction of time x=f(t).

Average velocity is defined as the change ofposition divided by the time interval

If we use a x vs t graph, the definition ofaverage velocity is the same as the slopebetween the two points (t1, x1) and (t2,x2)

Are average speedand average velocitythe

same? Discuss. Can the average velocity be negative? If so, how

do we interpret this result?

Velocity unit: meters / seg


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Chapter 2: Motion

Mechanics: the branch of Physics that studiesbodies in motion. Two major divisions: Kinematics (position, velocity, and acceleration)

Dynamics (force)

As a first approach, we will study translationalmotion of a particle (leaving rotational andinternal motions for later).

Average speed = total distance traveled / timetaken

Motion and speed are relative to the frame ofreference with respect to which it is calculated.


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Instantaneous velocity

Defined from a graphical point of view as theslope of the tangent that touches the plot at aspecific time.

Can the average velocity be equal to theinstantaneous velocity? Discuss.

Using a mathematical approach:v = lim (Dx/Dt)

Dt0

And that takes us to the calculus definition:v = dx / dt


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Acceleration

The average acceleration is defined as the change ofvelocity divided by the change of timea = (v2 v1) / (t2 t1)

Units : meters / seg2

If a vehicle is speeding up while moving in the negativedirection, what happens to its acceleration? And if itsslowing down?

Instantaneous acceleration is equal to the slope of the

tangent drawn on the plot of velocity vs. time. It is also the first derivative of the velocity, hence:

a = (d/dt)(dx/dt) = d2x/dt2


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Motion with constant acceleration

Constant acceleration implies a constant slope in theplot of velocity vs. time (feel free to graph this)

From the previous graph, we can determine that theacceleration (slope) is:

a = (Vf V0)/t; therefore

Vf= V0 + at (Eq. 1)

The average velocity, at a constant acceleration, is theaverage of two values: initial and final velocity:

v = (Vf+ V0)/2; or

v = V0 + at/2


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More motion (at constant acceleration)

The new position x will be equal to the initial positionx0 plus the product of the average velocity multipliedby time:

x = x0 + vt; therefore,

x = x0 + v0t + at2

/2 (Eq. 2) If we isolate t from Eq. 1 and replace it in Eq. 2, we will

find a direct relationship between position and velocity(go ahead, find it):

(x x0) = (vf2 v0

2) /2a (Eq. 3)

In free fall, the acceleration is a constant usuallydenoted by g, and it is equal to 9.81 m/s2

Standard gs, terminal velocity


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Exercises, exercises, exercises

Solve the challenging ones for: Speed (pg 58)

Average velocity (pg 60)

Acceleration (pg 61)

Motion with constant acceleration (pg 62)

Acceleration of free fall (pg 64)

Integration of equations of motion (pg 65)

Ah, homework! Review problems (pg 66) Group 1: odd numbers between 110 and 120

Group 2: even numbers between 111 and 119 PLUS119


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Ch. 4: Motion in 2D and 3D

Two-dimensional motion consists of two one-dimensional motions occurring simultaneously.

To describe translational motion of a particle in aplane, we will use an x coordinate and a y coordinate.

Average and instantaneous velocity for the x and ycomponents are defined as seen in Chapter 2. Andapplying Pythagoras, we can obtain the instantaneousspeed.

Apply the same strategy to define average accelerationand instantaneous acceleration.

Remember: velocity and acceleration are vectors, andcan be separated into their x and y components.


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Projectile Motion

The only acceleration experienced by a bodythat has been launched, is gravity (verticalacceleration).

Therefore, the x component of acceleration isZERO, and the y component of acceleration is-g (-9.81 m/s2).

So we have linear uniform motion for the xaxis, and motion with constant accelerationfor the y axis.


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Uniform Circular Motion

Defined as motion with constant speed along acircular path

The velocity vector at any instant is tangent to the

path (or to the circle). All the velocity vectors have same magnitude but

different direction; therefore, circular motion isaccelerated motion.

The acceleration vector points inward along theradius, toward the center of the circle (centripetalacceleration). Why?


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Exercises

They begin on page 121, as usual practice the

exercises with an asterisk (they should be the

most challenging ones).

And finally, homework:

Review problems, page 127: everyone solves

exercises 102 to 105.


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Chapter 5: Newtons Laws of Motion

Dynamics: the study of forces and their effects

on the motion of bodies

Under ideal frictionless conditions, a body in

motion will continue to move forever

Newtons First Law establishes: In the

absence of a net external force, a body at rest

remains at rest, and a body in motion

continues to move at constant velocity. Inertia: the tendency of a body to continue in

its initial state of motion


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Considerations for the Law of Inertia

The Law of Inertia is not valid in all reference

frames; specifically, in a reference frame that

has an accelerated motion relative to another.

The reference frames in which the 1st Law is

valid, are called inertialreference frames.

The velocity of the particle is relative to the

reference frame; acceleration is absolute(regardless of the reference frame)

d


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Newtons 2nd Law

Force: any push or pull exerted on a body;

such a push (or pull) has magnitude and

direction

As Sir Isaac would have said: An external

force acting on a body, gives it an acceleration

that is in the direction of the force and has a

magnitude directly proportional to the

magnitude of the force and inverselyproportional to the mass of the body

a = F / m and therefore, F = ma

h d l


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Weight, Contact Force and Normal Force

Mass is an intrinsic property of the body; weight

is an extrinsic property of a body (measuring thepull of gravity on it, and gravity depends on

location).

Gravity requires no perceptible medium for its

transmission. Common forces require contact.

Contact force: the push that the surface of a body

exerts on the other adjacent surface. If the two

bodies are solid: Friction force: sliding surfaces

Normal or compression force: perpendicular press

between surfaces


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Mass and Force

Mass is a measure of the resistance that the body

offers to changes in its velocity.

Force: a vector applied to a specific mass, that

generates acceleration

In the International Unit system, the unit of force isthe Newton (the force that will give a mass of 1 Kg an

acceleration of 1 m/s2

In the British system, the unit of force is the pound-

force (lbf), and its equal to 4.482 N.

Weight is a force, proportional to the mass of the

body being weighed.


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Newtons 3rd Law

Quoting Sir Isaac: Whenever a body exerts a

force on another body, the latter exerts a force

of equal magnitude and opposite direction on

the former.

Action-reaction forces need not to be normal

to the surface

Not all two forces of equal magnitudes andopposite directions are an action-reaction pair.


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Final relevant concepts

Free-body diagram: the body is presented free

from its surrounding environment, and the

environment is reduced to the forces it exerts over

the body. Tension: the force with which a cable pulls on what is

attached to it. The direction of the tension is along

the cable.

The transmission of the magnitude of the tension

without change occurs even if the cable is led around

pulleys


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Exercises (as usual)

The Problems section begins on page 162.

You should practice the exercises marked with

the asterisks (the challenging ones).

1st part of homework for week No. 2: Review

problems for everyone! (starting on page 168)

Exercises 78 to 81

Exercises 91 to 94


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I wonder if were still running late

00 physics broward 1st week

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