Physics Midterm

Classical physics: standardswhat makes a good standard?

- measureable- communicate to an alien far away so we can speak to a common scientific language- defined by Le Systeme International d'Unites (SI)- base SI units

Standards

time (s)length (m)mass (kg)temperature (K-Kelvin)electric current (A-ampere)amount of a substance (mole (mol))light intensity (candela-cd)

conversion of units: metric units

mega (M, 1,00,000, 10^6)kilo (k, 1000, 10^3)centi (c, .01, 10^-2)milli (m, .001, 10^-3)micro (Greek letter mu, .000001, 10^-6)nano (n, .000000001, 10^-9)

vector notation

put arrow over variable notation

vectors vs scalars

vectors: magnitude, units, and direction (ex: 50 m up, 20 mph north)scalar: only magnitude and units (ex: 40 mph, 60 kg)

x hat

unit vector: has length or magnitude 1 and no units associated with it. Its sole purpose is to indicate the positive x directioncan also change this to being a subscript x (so r subscript x = ...) to describe direction

Position

r arrow, x, yunits: m

displacement

change in r arrow= final position - initial positionunits: mcan also write it as change in x = final x minus initial x (or y)over given time and direction by finding area under velocity vs time curve in that direction and time interval

Average Velocity

displacement divided by the change in timeV subscript av with arrow = change in r arrow divided by change in t or rf-ri/tf-tiunits: m/sfind slope of line on position vs time graph (rise/run)

Instantaneous velocity

V arrowunits: m/smeans at this moment in space what is the object's speeddisplacement divided by the change in time as the change in time becomes infinitesimally smallalso first derivative of position with respect to time (lim as change in 1 approaches zero thing)units: m/sgraphical relationship: measure slope of the tangent line at that point on a position vs time curve

average acceleration

a subscript av with arrowdefined as the change in velocity divided by the change in timeunits: m/s squaredgraphical relationship: find slope between 2 points on velocity vs time curve

instantaneous acceleration

the change in velocity divided by the change in time as the change in time becomes infinitesimally smallunits: m/s squaredgraphical relationship: find slope of the tangent line on velocity vs time area under velocity vs time curvearea under velocity vs time curve (DOUBLE CHECK THIS)

Kinematic Equations

relate different properties of motion with each other when the acceleration is constant (position time curve is parabola, velocity time curve is straight line, acceleration vs time curve is horizontal line) goes t squared -> t

Kinematic Equation 1 (when acceleration is constant)

x [t] = x0 + vx0t +1/2axt squaredin order:position in x direction as a function of timeposition in x-direction at t =0velocity in x direction at t=0constant acc'l in x directiontime

Kinematic Equation 2 (when acc'l is constant)

Vx [t]= Vx0 + axtin order:velocity in x direction as a function of timevelocity at t=0constant acc'ltime

Free Falling Objects (kinematic equations)

motion of object is vertical (use g=9.8 m/s squared as constant acc'l)Procedure: 1. Draw the picture2. Choose coordinate system (x or y)3. Set origins in time and space 4. write initial position (y0), initial velocity (Vy0), and acc'l (ay) in terms of origins (remember to double check negative/positive)5. Write formulas for y[t] and Vy[t] (kinematic)6. Solve the question

Vectors (2-D)

motion in a planedescribed as a raycan describe a vector by an ordered pair in 2-space (1st component describes x-direction, 2nd component describes y direction)

Properties of Vectors: zero vector

u with arrow + 0 with arrow = u with arrow(0,0)

inverse vector

-u with arrowfor every vector u, there exists an inverse vector -u such that u + (-u) =0same length, in opposite direction(-ux, -uy)

vector addition

to add 2 vectors, say a vector v to a vector u we need to place the origin point of v at teh terminal point of uthe sum of u +v is a vector that starts at the origin point of u and ends at termination point of vu +v = (ux+vx, uy+vy)

vector subtraction

add inverse vector -v to uu-v = (ux-vx, uy-vy)

Scalar multiplication

multiply scalar k to vector umakes ray 2x as longnew vector ku has units of the product of the units of k and the units of u with arrow

important to remember: vector addition and subtraction

vectors must have same unitsmagnitude of a vector is the magnitude and units of the vectors without the direction (use absolute value around u with arrow to show magnitude only)

Magnitude of vector

write magnitude of u with arrow to be utake square root of ux squared + uy squared

uniform circular motion

uniform" means constant: the speed remains the same as the object travles in a circlespeed is the magnitude of the velocity vectorv arrow at any given point is tangential to the circle because the direction of velocity is changing (even if the magnitude of v isn't) then the object is acceleratingacc'l= final velocity minus initial velocity divided by final time minus initial timedistance traveled on the circle is R (the change in certain Greek letter that shows the angle between the two radii at the final velocity point and initial velocity pointan object in uniform circular motion is accelerating with a magnitude of (v) sqaured/R and a direction towards the center of the circle (R is radius)to find v: distance/time distance for circle: 2 pi R

2 ways an object accelerates

1. maintain direction, but change speed- same/opposite direction as velocity -tangential acceleration2. maintain speed, change direction- associated with uniform circular motion- perpendicular to velocity -centripetal-acceleration = sum of these two

Universal Scientific Law

one that holds true everywhere in the universeNewton says natural state of an object is not to be at rest nor is it to be in uniform circular motion

Newtons 1st Law of MOtion

in an inertial frame of reference, an object in motion will continue in motion traveling in a straight line at a constant speed and an object at rest will remain at rest unless compelled to change by an external net force.constant velocity -> velocity is not changing -> acceleration is zeroNewton says the natural state of an object is to not accelerate

inertial frame of reference

the observer of the object is not acceleratingex: plane accelerates, can rolls backward: seems like violation of 1st law, but can't apply it to this because you are accelerating and are therefore not an inertial frame of reference

Newton's second law of motion

in an inertial frame of reference, an object will accelerate in teh same direction as a net external force with a magnitude of acceleration proportional to the net external force and inversely proportional to its mass. we get sum of the forces (with arrow) = mass times a (with arrow)

net force

sum of all the forces acting on an objectdo vector addition to find net force if more than one

balanced forces

if sum of forces equals zero vector

unbalanced forces

if sum of forces does not equal zero

units of force

Newtons (N)

Newton's third law of motion

if one object exerts a force on another object, then the 2nd object exerts a force on the 1st object that is equal in magnitude and opposite in direction

force: gravity near the surface of the earth

w with arrowmagnitude = mgdown towards center of the earthcan use for freely falling objects: g=9.8 m/s squaredcan also be called the weight of the object

normal force

N with arrowforce of surface on an objectperpendicular to the surface in the direction of the objectex: object is not moving, velocity is zero, no net force: forces balanceddoesn't always act up (think of ball on ramp)

tension force

think of ball on a stringT with arrowdirection: away from the object in direction of string

static friction

f subscript s with arrowforce of friction acting on object when NOT in motion such that the sum of the forces on the object = 0force between surface and surface of the objectdirection: such that sum of the forces = zero vector (parallel to surface)magnitude of static friction is less than or equal to mu subscript s times magnitude of the normal force mu subscript s is the coefficient of static friction and it depends on the material of the object (between zero and one)

applied force

F subscript app with arrowex: someone pushing on a wall

kinetic friction

f subscript k with arrowmagnitude: mu k times magnitude of the normal forcedirection: acts in opposite to velocityonly applies when object is moving

spring force

force of spring on an objectF subscript s with arrowmagnitude: k times the magnitude of the change in positiondirection: acts toward its equilibrium point where it is at its natural lengthdirectly proportional to the displacement from the equilibrium point (linear behavior)restoring force

Drag force

D with arrowDirection: if fluid is still, in opposite direction of object's velocityforce of air passing by an object, if the air is still then the drag force will be the opposite direction of an object's velocitycauses an object to slow down

Buoyant force

upward force on an object equal to the weight of the displaced fluidB with arrowMagnitude: = weight of displaced fluiddirection: up

pin force

P with arrowdirection: any directionforce of an object by a pin

contact forces

force on an object requires the object to be in contact with creator of the force (normal, kinetic friction, static friction, pin, spring, tension, buyont, and drag)

field force

gravity from gravitational field created by earth

Kepler's 1st law of planetary motion

planets travel around sun in ellipse with sun as one foci

kepler's second law

a ray from planet to sun sweeps out equal area for equal timesallows for planet to be in uniform circular motion

kepler's third law of motion

a planet's distance from teh sun (given by the semi-major axis length) cubed is proportional to the time it takes to complete an orbit squaredT^2 is proportional to R^3description of motion in the solar system

Newton's universal law of gravitation

how it works near surface of the earthexplains kepler's laws of planetary motionmagnitude of F subscript g with arrow = G subscript m times M over r squaredG = 6.67 x 10^11 m^3/kgs^2think of mass at the center of the earth...this comes out to be about 9.8 m/s^2

how it helps explain Kepler's laws

1. planets travel in elliptical orbitif planet is moving in a circle and the force acting on the planet is towards the center (same direction as planet's acc'l) the planet is in circular motion2. ray from planet to sun sweeps out equal are for equal timesonly way for areas to be equal is for speed of the planet to be constant because the distance from the sun is never changing3. distance form sun ^3 proportional to the time it takes for planet to complete orbit ^2apply newton's 2nd law of motion F=maFg= maGMsunm/R^2 = m v^2/R...eventually get T^2 proportional to R^3

electric force

force between two charged particles

3 fundamental particles

1. electron: charge of -1.6 x 10^-19 C (Coulomb), has the smallest mass2. proton: charge of +1.6 x 10^-19C, fairly large mass compared to electron3. Neutron: neutral charge: no net charge, mass close to protonelectrons orbit nucleus, made up of protons and neutrons, electrons = protonsnumber of electrons determines the "chemistry" of the element

Attractive Force

when two particles are unlike charges, line connecting them

Repulsive force

two like charged particles repels them acting in the opposite direction

Electric force formula

magnitude of Fe with arrow = k times the magnitude of q1 times q2 divided by r^2 q is a charged particlek is a universal constant: 8.99 x 10^9 Nm^2/C^2

Insulator

electrons don't move easilyex: diamond: carbon has 4 electrons on its outer shellelectrons form bonds between carbon atoms and there are no free electrons to roam

Conductor

electrons move easilyAl: 12 electrons tightly bound to nucleus, extra are not, which means the extra one moves more freely

Franklin experiment: rabbit fur and glass rod

put glass rod by rabbit fur, electrons move to rod: fur has net positive charge and rod has net negative chargemove negative rod by metal, the electrons will move to the opposite side, making it half negative and half positivethe positive side of the metal then is attracted to the negative rodLOOK UP HIS EXAMPLE FROM CLASS

Field Lines

representation of the direction of a force emulating from an object creating the fieldmass will create gravitational force on 2nd masscharge create electric force on 2nd chargeORmass will create gracitational field and another mass will feel a force from gravitational fieldcharge creates electric field and another charge will feel force from electric field

field lines: gravitational force

mass creates gravitational field with field lines emulating into the surrounding space directed toward the massDenote field lines by G with arrowwhen placed in a gravitational field, a mass will feel a force in direction on the gravitational field such that Fg=mG

Electric Field lines

a pos charge creates electric field lines emulating from and directed away from the chargea neg charge creates field lines emulating from and directed toward the chargeE with arrow = electric fieldFe = electric forcein precense of electric field, a positive charge will feel an electric force in the same direction as electric field linesneg will feel it in opposite direction as field lines

Rules for drawing electric field lines for different configuration of charges

1. There should be a minimum of 4 lines off of each charge2. # of lines proportional to charge: if +q charge has 4 lines, +2q charge has 8 lines3. Draw in stubs off each charge (pointing in for neg charges and out for pos)4. Then begin drawing lines towards infinity. As you meet other lines, lines pointing in teh same direction can meet, lines point in the opposite direction run parallel to each other towards infinitylines NEVER cross 5. If net charge of configuration = 0 make all lines meet (b/c no electric force from a neutral charge once you get far away from it)

Magntism: old model

used to think "poles" created magnetic forceNorth and South Poles acted like chargesmagnetic field lines go away from N pole toward S polepoles then would feel a force from magnetic fieldnorth pole would feel a magnetic force i nthe direction of the magnetic field and a south pole would feel a magnetic force in the opposite direction of the magnetic field

New Model: Magnetism

north and south poles don't seem to exist independent of each other magnetism for magnetic fields:a moving charged particle creates a magnetic fielda moving charged particled feels a force from a magnetic fieldB with arrow FB with arrow is magnetic force