Physics

capacitance

capacitance of capacitor is defined as ratio of magnitude of the charge stored on 1 plate to potential diff (voltage) across capacitor if voltage V is applied across plates of capacitor & charge Q collects on it (w/ +Q on + plate & -Q on - plate), then capacitance is given by: C = Q/V SI unit for capacitance is the FARAD (1 F = 1 C/V)

converting between temperature scales

kelvin & celsius scales have diff 0 reference points but the size of their units is the same. size of fahrenheit unit is smaller F = 9/5C + 32 K = C + 273

radiation

transfer of energy by electromagnetic waves through SPACE unlike conduction & convection, radiation can transfer energy through a vacuum

convection

transfer of heat by physical motion of fluid over a material this requires flow, so only liquids & gases can transfer heat through convection

closed systems

capable of exchanging energy, but not matter, w/ the surroundings ex: gas vessels w/ movable pistons most of what will be on MCAT will be closed or approximate a closed system

Hawthrone Effect/ Observer effect

behavior of study participants is altered simply bc they recognize that they're being studied

refraction

bending of light as it passes from 1 medium to another & changes speed speed of light through any medium is always less than its speed through a vacuum (speed of light, 3 x 10^8 m/s). -on MCAT, can use this # for speed of light in air

Metric System

depending on context of question, may be meters, kilograms, & seconds (MKS) or centimeters, grams, & seconds (CGS)

gravitational potential energy

depends on object's position w/ respect to some level identified as the DATUM (ground or 0 PE position) to calculate gravitational PE, U = mgh

coefficient of volumetric expansion

beta constant that characterizes how specific material's volume changes as temp changes it is = to 3x the coefficient of linear expansion for same material. beta = 3*alpha

spherical abberation

blurring of periphery of an image as a result of inadequate reflection of parallel beams at the edge of a mirror or inadequate refraction of parallel beams at edge of a lens this creates area of multiple images w/ very slightly diff image distances at edge of image, which appears blurry

monochromatic light

composed of only 1 color (1 wavelength) so wavelength of monochromatic light can be detected w/o use of diffraction

mirrors & lenses

concave mirrors & convex lenses are both converging & thus have similar properties convex mirrors & concave lenses are both diverging & also have similar properties focal lengths & radii of curvature have simpler sign convention. for both mirrors & lenses, converging species have + focal length & radii of curvature & diverging species have - focal length & radii of curvature

electric circuit

conducting path that usually has 1 or more voltage sources (such as a battery) connected to 1 or more passive circuit elements (such as resistors)

period (T)

if frequency defines # of cycles per second, then its inverse, period (T), is the # of seconds per cycle T = 1/f

randomization

method to control for differences btwn subject groups using an algorithm to place subjects into groups

control / standard

method to verify results POSITIVE CONTROLS are those that ensure a change in the dependent variable when it's expected, control group not exposed to experimental treatment but is exposed to some other treatment known to produce the expected NEGATIVE CONTROLS ensure no change in dependent variable when no change is expected, control group not exposed to experimental treatment or to any other treatment that's expected to have an effect -in drug trials, negative control group is often used to assess for the PLACEBO EFFECT

longitudinal wave

particles of wave oscillates parallel to drxn of propagation/energy transfer ex: sound waves molecules oscillate through cycles of COMPRESSION & RAREFACTION (DECOMPRESSION) along drxn of motion of wave

conservative forces

path independent & do not dissipate energy conservative forces have PE associated w/ them if change in energy around any round trip path is 0 OR if change in energy is = despite taking any path btwn 2 points, then the force is conservative

radioactive decay

naturally occurring spontaneous decay of certain nuclei accompanied by emission of specific particles when balancing nuclear rxns, the sum of atomic # & mass #s must be same on both sides of equation

nearsighted & farsighted

nearsighted people who can see near objects clearly need diverging lens & farsighted need converging lens bifocal lenses are corrective that have 2 distinct regions. 1 that causes convergence of light to correct for farsightedness (HYPEROPIA) & 2nd that causes divergence of light to correct for nearsightedness (MYOPIA) in the same lens -myopia is condition where light rays are focused in front of & not at the retina. this can be corrected with diverging lenses, which spread light rays before they reach the eye > shifts image away from lens hyperopia describes refractive error that results in an individual being unable to see nearby objects. hyperopia is caused by optical power of the eye being insufficient relative to length of eye. the condition is corrected by placing a converging lens in front of the eye, forming an optical system with greater optical power > images of nearby objects shift closer to the lens & onto the retina

fission

process by which large nucleus splits into smaller nuclei spontaneous fission rarely occurs. however through absorption of low energy neutron, fission can be induced in certain nuclei **of special interest are fission rxns that release more neutrons bc these other neutrons will cause chain rxn in which other nearby atoms can undergo fission**. this in turn releases more neutrons, continuing the chain rxn. such induced fission rxns power most commercial nuclear power plants

blackbody

refers to ideal absorber of all wavelengths of light, which would appear completely black if it were at a lower temp than its surroundings

diffraction

refers to spreading out of light as it passes through narrow opening or around an obstacle interference btwn diffracted light rays lead to characteristic fringes in slit lens & double slit systems diffraction & interference are significant evidence for wave theory of light

drag force

resistance force caused by the motion of a body through a fluid, such as water or air acts opposite to the direction of the oncoming flow velocity

equilibrium position

waves oscillate abt this central point the DISPLACEMENT (X) in wave describes how far a particular point on the wave is from the equilibrium position, expressed as a vector quantity

loudness or volume

way that we perceive sound's intensity. perception of loudness is subjective & depends not only on brain function but also physical factors sound intensity on the other hand is objectively measurable

Newton's second law

Fnet = m*a no acceleration will occur when vector sum of forces results in cancellation of those forces net force & acceleration vectors point in same drxn

paramagnetic materials

will be weakly magnetized in presence of external magnetic field, aligning magnetic dipoles of material w/ the external field upon removal of external field, the thermal energy of the individual atoms will cause individual magnetic dipoles to reorient randomly some paramagnetic materials are aluminum, copper, & gold atoms of both paramagnetic & ferromagnetic materials have unpaired electrons so they have a net magnetic dipole moment but the atoms in these materials are usually randomly oriented so that the material itself creates no net magnetic field

insulator

won't easily distribute charge over its surface & won't transfer that charge to another neutral object very well, especially not to another insulator on molecular level, electrons of insulators tend to be closely linked w/ their respective nuclei most nonmetals are insulators experimentally, insulators serve as dielectric materials in capacitors, as well as in isolating electrostatic experiments from the environment to prevent grounding

conductance

Reciprocal of resistance SI unit is SIEMENS (S), sometimes given as siemens per meter (S/m) for conductivity

efficiency

Wout / Win = load*load distance / effort*effort distance often expressed as % by multiplying ratio by 100% efficiency of machine gives measure of amt of useful work generated by machine for given amt of work put into the system % of work put into system that becomes unusable is due to nonconservative or external forces

metallic bond

a bond formed by the attraction between positively charged metal ions and the electrons around them can be visualized as a sea of electrons flowing over & past a rigid lattice of metal cations but is more accurately described as an equal distribution of charge density of free electrons across all neutral atoms w/in metallic mass

open boundaries

allow maximal oscillation & correspond to antinodes. open end of pipe is ex

isovolumetric

also called isochoric no change in volume & therefore no work accomplished. no area in P-V graph

population

complete group of every individual that satisfies the attributes of interest

meters

devices used to measure circuit quantities in the real world AMMETERS, VOLTMETERS, & OHMMETERS

British / Imperial System

foot-pound-second (FPS) uses weight, not mass. slug later used as unit of mass rarely on MCAT

P-V graphs

gas expansion & compression can be represented in graphical form w/ volume on X-axis & pressure on Y-axis work done on or by a system undergoing a thermodynamic process can be determined by finding area enclosed by corresponding P-V curve

exhaustive group of outcomes

group of outcomes is exhaustive if there are no other possible outcomes

adiabatic

no heat exchange

terminal velocity

velocity @ which air resistance is = to gravitational force & no acceleration occurs for object in free fall. this leads to translational equilibrium

frequency (f)

# of wavelengths passing fixed point per second & is measured in HERTZ (HZ) or cycles per second (cps)

resistivity (p, rho)

# that characterizes the intrinsic resistance to current flow in a material SI unit is the oHM-METER (ohm.m)

vectors

#s that have magnitude & drxn include displacement, velocity, acceleration, & force can be notated in bold

scalars

#s that have magnitude ONLY & no drxn include distance, speed, energy, pressure, & mass can be notated in italics

position of median

(n+1)/2 *if mean & median are far from each other, this implies presence of outliers or a skewed distribution

SI Units

**only system required to memorize for MCAT include metric system + 4 other base units length: meter (m) mass (not weight): kilogram (kg) time: second (s) current: ampere (coulomb/second) (A) amt of substance: mole (mol) temp: kelvin (K) luminous intensity: candela (cd)

quartiles

1. to calculate position of first quartile (Q1) in set of data sorted in ascending order, multiply n by 1/4 2. if this is a whole #, the quartile is the mean of the value at this position & the next highest position 3. if this is a decimal, round up to the next whole # & take that as the quartile position 4. to calculate the position of the third quartile (Q3), multiply the value of n by 3/4. again, if this is a whole #, take the mean of this position & the next. if it's a decimal, round up to next whole # & take that as the quartile position the interquartile range is then calculated by: IQR = Q3-Q1 -the interquartile range can be used to determine outliers. any value that falls more than 1.5 interquartile ranges below 1st quartile or above 3rd quartile is considered an outlier

fundamental frequency

1st harmonic lowest frequency (longest wavelength) of standing wave that can be supported by given length of string the possible frequencies are f = nv / 2L the frequency of standing wave given by n = 2 is known as 1st overtone or 2nd harmonic

Kirchoff's laws

2 rules that deal w/ conservation of charge & energy w/in a circuit -charge & energy can't be created nor destroyed in currents & circuits JUNCTION RULE: at any point or junction in a circuit, the sum of currents directed into that point = the sum of currents directed away from that point -this expression of conservation of electrical charge can be LOOP RULE: around any closed loop, sum of voltage sources will always be equal to the sum of voltage (potential drops) bc all energy supplied by source gets fully used up by other elements in the loop -conservation of energy in terms of voltage (J/C) not just energy (J)

observational studies

3 categories 1. COHORT STUDIES are those in which subjects are sorted into groups based on differences in risk factors & then assessed at various intervals to determine how many subjects in each group had a certain outcome -a longitudinal study is an observational research method that follows same subjects over time so cohort study is a form of longitudinal study 2. CROSS-SECTIONAL STUDIES attempt to categorize patients into diff groups at single point in time 3. CASE-CONTROL STUDIES start by identifying the # of subjects w/ or w/o a particular outcome & then look backwards to assess how many subjects in each group had exposure to particular risk factor

speed of light (c)

3.00 x 10^8 m/s for the MCAT, electromagnetic waves also travel in air with this speed, so c = f*lambda -c is speed of light in vacuum & also in air -f is frequency -lambda is wavelength

simple machines

6 devices: inclined plane wedge (2 merged inclined planes) wheel & axle lever pulley screw (rotating inclined plane) all simple machines can be approximated as conservative systems if we ignore the usually small amt of energy lost to external forces such as friction idealized pulley is massless & frictionless & under these theoretical conditions, the work put into the system (exertion of force through distance of rope) = work that comes out of system (displacement of mass to some height). real pulleys/machines don't have idealized conditions & therefore don't achieve 100% EFFICIENCY in conserving energy output to input

temperature

@ any given time, all substances have a particular temperature @ the molecular level, temp is a physical property proportional to the average KE of particles that make up the substance @ macroscopic level, diff in temp determines direction of heat flow. when possible, heat spontaneously moves from materials w/ higher temps to materials w/ lower temps systems to quantify temperature include Fahrenheit, Celsius, & Kelvin scales

static electricity

A buildup of charges on an object, also called static charge buildup most matter is electrically neutral bc a balance of + & - charges ensures relative degree of stability. when charges are out of balance, system can become electrically unstable materials that are normally neutral can acquire net charge as result of friction when you shuffle feet on carpet, negative particles transfer from carpet to feet & when you touch knob, a shock allows excess charge to jump from fingers to knob, which acts as a GROUND, a means of returning charge to the earth STATIC ELECTRICITY is more significant in drier air bc lower humidity makes it easier for charge to become & remain separated

standing waves

A pattern of vibration that simulates a wave standing still produced by constructive & destructive interference of a traveling wave & its reflected wave. more broadly, standing wave will form whenever 2 waves of same frequency traveling in opposite drxns interfere w/ 1 another as they travel through same medium standing waves appear to stand still & aren't propagating bc interference of wave & its reflected wave produce resultant that fluctuates only in amplitude only apparent movement of string is fluctuation of amplitude @ fixed points along length of string. these waves are STANDING WAVES & points in wave that remain @ rest (where amplitude is constantly 0) are known as NODES points midway btwn nodes fluctuate w/ max amplitude & are known as ANTINODES pipes that are open at both ends can also support standing waves & math relating to standing wave wavelength & length of string or open pipe are similar -pipes open @ 1 end & closed @ the other also can support standing waves but bc closed end contains node & open end contains antinode, the math is diff not every frequency of traveling wave will result in standing wave formation. length of medium dictates the wavelengths & thus, the frequencies of traveling waves that can establish standing waves. objects that support standing waves have boundaries @ both ends

capacitors in parallel

Ceq = C1 + C2 + C3... voltage across each parallel capacitor is same & is = to voltage of source

displacement vs. distance

DISPLACEMENT (x or d): change in position in space VECTOR quantity that's straight line & connects object's initial & final positions DISTANCE (d): considers pathway taken & is SCALAR quantity

nonconservative forces

Forces that its work depends on the path. the longer the distance traveled, the larger amt of energy dissipated ex: friction, air resistance, or viscous drag (resistance force created by fluid viscosity) when nonconservative forces are present, total ME is not conserved Wnonconservative = deltaE = deltaU + deltaK work done by nonconservative forces is = to amt of energy "lost" from the system

isobaric

In P-V graph, area under curve is rectangle of length P & width deltaV. work = P*deltaV occurs less than other processes on MCAT

Kelvin scale

Kelvin scale defines 0 K reference point as absolute zero. this temperature is where there is no thermal energy absolute zero sets the freezing point of water at 273.15K (0 celsius) there are no negative temperatures on Kelvin scale bc it starts from absolute 0

mass vs. weight

MASS (m): measure of body's inertia / amt of matter in an object SCALAR quantity Si unit = kilogram, which is independent of gravity so 1 kg of object on earth = 1 kg on moon WEIGHT (Fg): measure of gravitational force on object's mass weight is force & thus a VECTOR quantity w/ units in Newtons (N) Fg = m*g weight of object can be thought of as being applied @ single point in that object called center of mass/gravity *MCAT won't directly test ability to determine center of mass but this calculation may be impt step in problem w/ larger focus

Bernoulli's equation

P is absolute pressure of fluid, rho is density of fluid, v is linear speed, g is acceleration due to gravity, & h is height of fluid above some datum the term 1/2pv^2 is called the DYNAMIC PRESSURE & is the pressure associated w/ the movement of fluid pgh is pressure associated w/ mass of fluid sitting above some position P + pgh gives us STATIC PRESSURE & is the same equation as that for absolute pressure except h is used instead of z Bernoulli's equation states that sum of static pressure & dynamic pressure will be constant w/in a closed container for an incompressible fluid not experiencing viscous drag Bernoulli's is a statement of energy conservation: more energy dedicated toward fluid movement means less dedicated toward static fluid pressure slower air has more pressure & exerts more force

trig functions

SOH CAH TOA values of both sine & cosine range from -1 to 1. values of tangent range from -infinity to infinity sin^-1(opposite/hypotenuse) = theta -inverse trig functions most likely to appear in questions asking for drxn of resultant in vector addition or subtraction

mnemonic: image types w/ single lens or mirror (assuming o is positive)

UV NO IR -Upright images are always Virtual -NO image is formed when object is a focal length away -Inverted images are always Real

force (F)

VECTOR quantity experienced as pushing or pulling on objects & can exist btwn objects that aren't touching SI unit = newton (N)

velocity vs. speed

VELOCITY (v): VECTOR & magnitude measured as rate of change of displacement in a given unit of time SI unit = meters/second average velocity = displacement/time SPEED (v): SCALAR & rate of actual distance traveled in given unit of time avg speed = distance/time

X ray diffraction

X rays diffract within molecules bc the space btwn atoms is comparable to the wavelength of x rays x ray diffraction through a sample of purified & crystallized material can be used to determine its 3D molecular structure & packing

damping / attenuation

a decrease in amplitude of a wave caused by an applied or nonconservative force even after decrease in intensity associated w/ distance, real world measurements of sound will be lower than those expected from calculations bc of DAMPING, or ATTENUATION oscillations are form of repeated linear motion, so sound is subject to same nonconservative forces as any other system, including friction, air resistance, & viscous drag nonconservative forces cause system to decrease in amplitude during each oscillation. amplitude, intensity, & sound level (loudness) are related, so there's corresponding gradual loss of sound harder to hear in confined or cluttered space bc of friction from surfaces to decrease sound waves' amplitudes damping doesn't have effect on frequency of wave, so pitch doesn't change. over small distances, attenuation is usually negligible like nonconservative forces, attenuation is generally negligible on test day. if it's impt for answering a question, the MCAT will make it clear that you should consider the effects of damping/attenuation on an oscillating system

capacitor

a device used to store charge in a circuit. able to hold charge @ particular voltage when 2 electronically neutral metal plates are connected to a voltage source, + charge builds up on the plate connected to positive (higher potential) terminal & - charge builds up on plate connected to - (lower potential) terminal the 2 plate system is a capacitor bc it can store particular charge @ particular voltage capacitor charging stops when capacitor's potential diff reaches that of the battery

standard distribution

a mean of zero and a standard deviation of one normal distribution (bell curve) can be transformed to standard distribution & this new curve can be used to get info abt probability or percentages of populations

positron decay

a nuclear reaction in which a positron is emitted > a proton is converted to a neutron

correlation coefficient

a number btwn -1 & +1 that represents the strength of the relationship value of 0 indicates no apparent relationship

first law of thermodynamics

accounts for conservation of mechanical energy says energy is neither created nor destroyed but merely transferred from 1 form to another this doesn't mean ME will remain constant bc ME only accounts for PE & KE, but not other forms of energy such as thermal energy that is transferred as a result of friction (heat) if frictional forces are present, some ME will be transformed into thermal energy & will be "lost" or dissipated from the system & not accounted for by the equation. this does NOT violate 1st law of thermodynamics bc it's still transformation of some energy from 1 form to another total internal energy of system (sum of its potential & motional energies) is equal to the amount of energy transferred in the form of HEAT to the system, minus the amount of energy transferred from the system in the form of WORK internal energy of a system can be increased by adding heat, doing work on the system, or some combination of both processes change in internal energy calculated with: deltaU = Q - W -Q is energy transferred into system as heat -W is work done by the system

accuracy & precision

accuracy, also called validity, is ability of instrument to measure a true value precision, also called reliability, is ability of instrument to read consistently or w/in a narrow range bias is a SYSTEMATIC error in data that skews data in 1 drxn, only an inaccurate tool will introduce bias, but an imprecise tool will still introduce error -data that is off in a systematic way (reads at a value that is not the true value) will cause bias. this type of data error is an example of lack of validity (or accuracy). unreliable data suffers from random, not systematic, error. -confounding arises from errors in data analysis, not data collection RANDOM ERROR can also introduce error & is usually overcome w/ large sample size

coefficient of linear expansion

alpha constant that characterizes how a specific material's length changes as temperature changes usually has units K^-1 or C^-1. this diff is inconsequential bc the unit size for the scales is the same

weak nuclear force

also contributes to stability of nucleus but is about 1 millionth as strong as strong nuclear force strong & weak nuclear forces constitute 2 of the 4 fundamental forces of nature. the other 2 are electrostatic forces & gravitation

voltmeter

also requires circuit to be active also use magnetic properties of current carrying wires measures voltage drop across 2 points in circuit wired in parallel to these 2 points ideal voltmeter has infinite resistance bc goal of any meter is to minimize its impact on the rest of the circuit

single slit

although it's safe to assume that nonrefracted light travels in a straight line, there are situations where light won't actually travel in a straight line path when light passes through narrow opening (opening w/ size that's an order of light wavelengths), the light waves seem to spread out (diffract) as slit is narrowed, the light spreads out more

instantaneous speed

always = to the magnitude of instantaneous VELOCITY & is avg velocity as change in time approaches 0

inclined planes

another ex of motion in 2D for inclined plane problem, often best to divide force vectors into components parallel & perpendicular to plane force of gravity parallel to plane = mg*sin(theta) force of gravity perpendicular to plane = mg*cos(theta)

adhesion

another force liquid molecules experience an attractive force that molecule of liquid feels towards molecules of some other substance when liquids are placed in containers, a MENISCUS, or curved surface in which liquid "crawls" up the side of the container a small amount, will form when adhesive forces are greater than cohesive forces ***a BACKWARDS (CONVEX) MENISCUS w/ liquid level higher in the middle than at the edges occurs when cohesive forces are greater than adhesive forces. this is less common than a concave meniscus***

sample

any group taken from a population that doesn't include all individuals from the population

natural (resonant) frequency

any solid object, when hit, struck, or disturbed in any way will begin to vibrate. natural frequency is frequency at which a system tends to oscillate if NATURAL (RESONANT) FREQUENCY of object is w/in frequency detection range of human ear, the sound will be audible. natural frequency of most objects can be changed by changing some aspect of object itself frequencies btwn 20 & 20,000 Hz are generally audible to healthy young adults & high frequency hearing generally declines w/ age if applied frequency is not close to natural frequency of a glass, then it will not resonate, & it will not shatter

lenses in contact

are a series of lenses with negligible distances btwn them these systems behave as single lens w/ equivalent focal length given by 1/f = 1/f1 + 1/f2 + 1/f3 + ... bc power is reciprocal of focal length, equivalent power is: P = P1 + P2 + P3 +... ex of lenses in contact is corrective contact lens (either converging or diverging depending on necessary correction) & their powers would be added for lenses not in contact, image of 1 lens becomes object of another lens. image from last lens is considered image of system. microscopes & telescopes are good examples of these systems. magnification for system is: m = m1 x m2 x m3 x ...

gravity

attractive force felt by all forms of matter all objects exert gravitational forces on each other that are small scale, gravity is conservative (path independent w/o dissipating ME) magnitude of gravitational force btwn 2 objects is: Fg = G*m1*m2 / r^2 -G is universal gravitational constant (6.67 x 10^-11 N*m^2 / kg^2) -m1 & m2 are masses of 2 objects -r is distance btwn their centers of mass

intensity

average rate of energy transfer per area across a surface that is perpendicular to the wave in other words, intensity is power transported per unit area SI units of intensity are therefore watts per square meter (W/m^2) & calculated w/ I = P/A -P is power -A is area amplitude of sound wave & its intensity are related to each other. intensity is proportional to square of amplitude -doubling amplitude produces sound wave that's 4x the intensity intensity is also related to distance from source of sound wave. sound waves emanate outward from source in shape of sphere & bc surface area increases as function of square of radius (A = 4pi*r^2), sound waves transmit their power over larger & larger areas the further from the source they travel, so intensity is inversely proportional to square of distance from source

instantaneous acceleration

avg accelerration as change in time approaches 0 in graph of velocity vs. time, tangent to/slope of graph @ any time t is instantaneous acceleration if slope is +, acceleration is + in same drxn as velocity. if slope is -, acceleration is - in opposite drxn of velocity (deceleration)

shock wave

buildup of wave fronts as the distance btwn those wave fronts decreases. this occurs maximally when the object is traveling exactly @ same speed that the wave is traveling (the speed of sound) in special case of Doppler effect, an object producing sound while traveling at or above speed of sound allows wave fronts to build upon 1 another at front of object. this creates larger amplitude @ that point. bc amplitude for sound waves is related to degree of compression of the medium, this creates large pressure differential or pressure gradient. this highly condensed wave is called a SHOCK WAVE & it can cause physical disturbances as it passes through other objects passing of shock wave creates very high pressure followed by very low pressure, which is responsible for phenomenon known as SONIC BOOM which can be heard at any time that object traveling at or faster than speed of sound passes a detector not just at point that speed of sound is exceeded (MACH 1) once object moves past speed of sound, some of the effects of the shock wave are mitigated bc all of the wave fronts will trail behind the object, destructively interfering w/ each other

conductivity

can be divided into 2 categories: -METALLIC CONDUCTIVITY: seen in solid metals & molten forms of some salts -ELECTROLYTIC CONDUCTIVITY: seen in solutions

vector subtraction

can be done by adding vector w/ = magnitude but opposite drxn to 1st vector can also be done w/ component vectors where x-component of resultant vector is diff of x-components of vectors being subtracted

vector addition

can be found w/ tip-to-tail method can also be done w/ component vectors where x-component of resultant vector is sum of x-components of vectors being added

potential difference (voltage)

can be produced by an electrical generator, a galvanic (voltaic) cell, a group of cells wired into a battery, or even a potato

open systems

can exchange both matter & energy w/ environment in open system, not only does matter carry energy, but more energy may be transferred in form of heat or work ex: boiling pot of water, human beings

pipes

can support standing waves & produce sound end of pipe can be open or closed & if open, it can support antinode. if closed, it'll support node 1 end of pipe must be open @ least slightly to allow for entry of air but sometimes these openings are small & covered by musician's mouth & in this case, it functions as closed end pipes that are open @ both ends are OPEN PIPES & those closed at 1 end & open at the other are called CLOSED PIPES an open pipe has antinodes at both ends. if n = 1, length of pipe corresponds to 1/2 wavelength of standing wave. analogous to string except that ends are antinodes instead of nodes same equations for wavelength & frequency # of nodes still tells you which harmonic it is & harmonic is given by # of half wavelengths supported for closed pipe, closed end corresponds to node & open end corresponds to antinode. unlike strings or open pipes, harmonic in closed pipe is = to # of quarter wavelengths supported by pipe -bc closed end must have node & open end must have antinode, there can only be odd harmonics bc an even # of quarter wavelengths would be an integer & a half of half wavelengths -1st harmonic has wavelength 4x length of closed pipe -3rd harmonic has wavelength 4/3 length of closed pipe equation that relates wavelength length of closed pipe is lambda = 4L/n -n can only be odd integers (1,3,5, etc.) frequency of standing wave in closed pipe is: f = nv / 4L -v is wave speed

mutually exclusive outcomes

can't occur at the same time (can't flip both heads & tails in 1 throw) probability of 2 mutually exclusive outcomes coming together is 0%

parallel plate capacitor

capacitance of parallel plate capacitor is dependent on the geometry of the 2 conduction surfaces. C = E0 (A/d) -E0 is permittivity of free space (8.85 x 10^-12 F/m) -A is area of overlap of 2 plates -d is separation of plates **separation of charge sets up a UNIFORM ELECTRIC FIELD btwn the plates w/ parallel field vectors, the magnitude of which can be calculated as:** E = V/d

capacitors in series

capacitors must share voltage drop in loop & therefore can't store as much charge group of capacitors in series acts like 1 equivalent capacitor w/ a much larger distance btwn its plates which means smaller capacitance 1/Ceq = 1/C1 + 1/C2 + ... total voltage is sum of individual voltages, just like for resistors in series

surface tension

causes liquid to form thin but strong layer at liquid's surface surface tension results from COHESION, which is the attractive force that a molecule of liquid feels towards other molecules of the same liquid -cohesion occurs btwn molecules w/ the same properties for molecules below the surface, there are attractive intermolecular forces from all sides & these forces balance out. on the surface, molecules only have strong attractive forces from molecules below them, which pulls surface of liquid toward the center. this establishes tension in plane of surface of water so when there's an indentation on the surface, then the cohesion can lead to a net upward force

secondary batteries

certain type of cell that can be recharged when these batteries are being recharged, an external voltage is applied to drive current toward + end of secondary battery in electrochemical terms, the cells act as a galvanic (voltaic) cell when it discharges & as an electrolytic cell when it recharges

electron capture

certain unstable radionuclides are capable of capturing an inner electron that combines w/ a proton to form a neutron, while releasing a neutrino the atomic # is now 1 less than the original but the mass # remains the same electron capture is a rare process that's perhaps best thought of as a reverse of B-decay

thermal expansion

change in temperature of most solids results in change in their length rising temps cause increase in length & falling temps cause decrease in length amt of length change is proportional to original length of solid & increase in temp according to the equation: deltaL = alpha*L*deltaT -deltaL is change in length -alpha is coefficient of linear expansion -L is original length -deltaT is change in temp mnemonic: its length changes ALOT liquids also experience thermal expansion but only meaningful parameter of expansion is volume expansion. formula for volumetric thermal expansion applies to both liquids & solids: deltaV = beta*V*deltaT -deltaV is change in volume -beta is coefficient of volumetric expansion -V is original volume -deltaT is change in temp

atmospheric pressure

changes w/ altitude & impacts a number of processes like hemoglobin's affinity for oxygen & boiling of liquids when air pressure changes above a large body of water, water level rises or falls to re-establish pressure equilibrium between air & water -****high pressure air forms valleys in water & low pressure air forms hills****

fluids

characterized by their ability to flow & conform to shapes of their containers includes liquids & gases solids DON'T flow & are rigid enough to retain a shape independent of their containers fluids & solids share some characteristics -both can exert forces perpendicular to their surface, although only solids can withstand shear (tangential, parallel to the surface) forces. fluids can impose large perpendicular forces -all fluids & solids are characterized by their density

electrolytic conductivity

depends on strength of solution distilled deionized water has such low ion concentration it may be considered an insulator conductivity in electrolyte solution measured by placing solution as resistor in circuit & measuring changes in voltage across the solution ***concentration & conductivity are directly related*** so this method's often used to determine the ionic concentrations in solutions such as blood 1 caveat is that conductivity in nonionic solutions always lower than in ionic solutions so when concentrations of total dissolved solids does relate to conductivity the contribution of nonionic solids is much less impt than ion concentration

process functions

describe path taken to get from one state to another work and heat

circulatory and respiratory systems

closed loop that has a nonconstant flow rate as a result of valves, gravity, physical properties of our vessels, & the mechanics of the heart nonconstant flow can be measured as a PULSE there's a loss of volume from circulation as a result of a difference btwn osmotic (oncotic) & hydrostatic pressures. this fluid is eventually returned to the circulation as a result of lymphatic flow, but it's problematic for applications of continuity equation blood volume entering the heart is always equal to blood volume leaving the heart during a single cycle as blood flows away from the heart, each vessel has progressively higher resistance until the capillaries, but the total resistance of the system decreases bc the increased # of vessels are in parallel w/ each other. like parallel resistors in circuits, the equivalent resistance is therefore lower for capillaries in parallel than in the aorta return flow to the heart is facilitated by mechanical squeezing of skeletal muscles, which increases pressure in the limbs & pushes blood to the heart & the expansion of the heart, which decreases pressure in the heart & pulls blood in pressure gradients created in the thorax by inhalation & exhalation also motivate blood flow. inspiration & expiration creates pressure gradient not only for the respiratory system, but for the circulatory system as well during inspiration there's negative pressure gradient that moves air into lungs. during expiration, this gradient reverses resistance decreases as total cross-sectional area increases -arterial circulation is primarily motivated by the heart -venous circulation has 3x the volume of arterial circulation & is motivated by skeletal musculature & expansion of the heart air @ the alveoli has essentially 0 speed

coefficient of static friction vs. coefficient of kinetic friction

coefficient of static friction will always be larger than value of coefficient of kinetic friction so max value for static friction always greater than constant value for kinetic friction objects will "stick" until they start moving & then will slide more easily over 1 another

spherical mirrors

come in 2 varieties: concave & convex spherical mirrors have associated center of curvature (C) & radius of curvature (r) -CENTER OF CURVATURE is a pt on the optical axis located at distance = to the RADIUS OF CURVATURE from the vertex of the mirror. it's the center of the spherically shaped mirror if it were a complete sphere if we looked from inside the sphere to its surface, we'd see a CONCAVE surface. if we were to look from outside the sphere, we'd see CONVEX surface mnemonic: conCAVE is like looking into a CAVE for concave surface, C & r are located in front of mirror & for convex, they're behind mirror concave mirrors are called CONVERGING MIRRORS & convex mirrors are called DIVERGING MIRRORS bc they cause parallel incident light rays to converge & diverge after they reflect. the reverse is true for lenses -focal length of converging mirrors & lenses will always be + & focal length of diverging mirrors & lenses will always be -

internal resistance, r(int)

conductive materials such as copper wires act as weak resistors, offering some magnitudes of resistance to current & causing drop in electrical potential (voltage) even sources of emf such as batteries have some small but measurable amount of internal resistance as a result of internal resistance, voltage supplied to circuit is reduced from its theoretical emf value by some small amt actual voltage provided by the cell to a circuit is: V = Ecell - i*rint -V is voltage provided by cell -Ecell is emf of cell -i is current through cell -rint is internal resistance if cell is not driving any current (such as when switch is in open position), then internal resistance is 0, & voltage of cell is equal to emf if current is not 0 & internal resistance is not negligible, voltage will be less than emf **most batteries on MCAT will be considered "perfect batteries" & internal resistance isn't considered

current carrying wires

configuration of magnetic field lines surrounding a current carrying wire will depend on shape of wire 2 special cases common MCAT are long, straight wire & circular loop of wire (w/ particular attention paid to magnetic field @ center of loop)

current

considered the flow of positive charge, even though only negative charges are actually moving any conductive substance may act as a medium through which current can pass electrical current is flow of charge btwn 2 points at diff electrical potentials connected by a conductor such as a copper wire the magnitude of the current is I = Q/deltaT SI unit of current is AMPERE (1 A = 1 C/s) charge is transmitted by a flow of electrons in a conductor & because electrons are negative, they move from point of lower electrical potential to higher potential to reduce electrical potential energy by convention, drxn of current is drxn in which positive charge would flow (from higher to lower potential), so drxn of current is OPPOSITE to drxn of actual electron flow -current flows from +, higher potential end of cell around circuit to -, lower potential end 2 patters of current flow are: -DIRECT CURRENT (DC): in which charge flows in 1 drxn only -ALTERNATING CURRENT (AC): flow changes drxn periodically

diffraction gratings

consist of multiple slits arranged in patterns diffraction gratings can create colorful patterns similar to prism as diff wavelengths interfere in characteristic patterns

isothermal

constant temperature & therefore no change in internal energy

charge

coulomb is SI unit of charge fundamental unit of charge is e = 1.60 x 10^-19 C a proton & electron each have this amount of charge although the proton is + so q = +e while electron is - charged so q = -e even though they have same magnitude of charge, proton has much greater mass than electron electric charge is governed by law of conservation of charge. charge can neither be created nor destroyed

conduction

direct transfer of energy from molecule to molecule through molecular collisions & there must be physical contact btwn objects @ atomic level, particles of hotter matter transfer some KE to particles of cooler matter through collisions metals are best heat conductors bc metallic bonds contain a density of atoms embedded in a sea of electrons, which facilitate rapid energy transfer gases tend to be poorest heat conductors bc there's so much space btwn individual molecules that energy-transferring collisions occur infrequently

rotational equilibrium

exists only when vector sum of all torques acting on object is 0. this is 2nd condition of equilibrium torques that generate clockwise rotation are considered negative object experiencing rotational equilibrium is either not rotating at all (stationary) or rotating w/ constant angular velocity

significant figures

count all #s btwn the first nonzero digit on the left & the last nonzero digit on the right. any digit btwn them is significant including 0 any zeroes to the left of the first nonzero digit are not significant if there are zeroes to the right of the last nonzero digit & there is a decimal point in the number, then they're significant. if there's no decimal point, they're not significant for measurements, the last digit is usually an estimation & is not considered significant when converting btwn standard #s & scientific notation, be sure to maintain the # of significant figures 100.0 = 1.000 x 10^2 100 = 10^2 for multiplication & division, maintain as many digits as possible then round to # of significant digits that's the same as the least number of significant digits in any of the factors, divisors, or dividends for addition & subtraction, decimal points are maintained rather than maintaining significant figures. # may have only as many decimal digits as initial # w/ fewest decimal digits

magnetic field

created by any moving charge, whether a single electron traveling through space or a current through a conductive material SI unit for magnetic field strength is the TESLA (T) where 1 T = 1 N*s / m*C Tesla unit is large so small magnetic field sometimes measured in GAUSS where 1 T = 10^4 gauss

resistors in series

current must pass sequentially through each resistor connected in linear arrangement as electrons flow through each resistor, energy is dissipated & there's voltage drop associated w/ each resistor the voltage drops are additive so for a series of resistors the total voltage drop will be: Vtot = V1 + V2 + V3 +... set of resistors in series can be treated as single resistor w/ resistance equal to sum of individual resistances Req = R1 + R2+ R3 + ... once you know current of whole circuit, can use V = IR to solve for voltage drop across each resistor assuming you know the resistances of the resistor

resistors in parallel

current will divide to pass through resistors separately when resistors are wired in parallel, they're wired w/ common high potential terminal & common low potential terminal. this configuration allows charge to follow diff parallel paths btwn high potential terminal & low potential terminal & electrons have a "choice" regarding which path they will take no matter which path taken, voltage drop experienced by each division of current is the same bc all pathways originate from common point & end at common point within circuit Vbattery = V1 = V2 = V3 voltage is same for all parallel pathways but the resistance of each may differ. electrons prefer path of least resistance & current will be largest through pathways w/ lowest resistance resistors in parallel allows for greater # of conduction paths & reduction in equivalent resistance. can replace all resistors in parallel w/ single resistor that has resistance that's less than resistance of smallest resistor 1/Req = 1/R1 + 1/R2 + 1/R3 +... if current divides into 2 branches & 1 branch has 2x the resistance, it will have 1/2 the current bc voltage drop across branches must be the same (V=IR) when n identical resistors are wired in parallel, total resistance is given by R/n -voltage across each parallel resistor is = & for equal resistances, current flowing through each resistor is also equal

Archimedes' principle

deals w/ buoyancy of objects placed in a fluid a body wholly or partially immersed in fluid will be buoyed upwards by a force equal to the weight of the fluid it displaces. mass of fluid displaced exerts a force equal to its weight against the submerged object buoyant force is always directed upwards & calculated with: Fbuoy = rho(fluid) x V(fluid displaced) x g = rho(fluid) x V(submerged) x g when an object is placed in a fluid, it will sink into the fluid only to the point at which the volume of the displaced fluid exerts a force equal to the weight of the object if object is completely submerged & volume of displaced fluid does not exert buoyant force equal to weight of object, it'll accelerate downward & sink to bottom buoyant force is due to liquid itself, not the object, so if 2 objects placed in fluid displace the same volume of fluid, it'll experience the same magnitude of buoyant force even if the objects themselves have diff masses

acceleration due to gravity (g)

decreases w/ height above earth & increases closer to earth's center of mass near earth's surface, g = 10 m/s^2

specific gravity

density of fluid often compared to that of pure water at 1 atm & 4 degrees C (at this temp & pressure, water has density of exactly 1 g/cm^3) specific gravity = rho / 1 g/cm^3 -rho is density of fluid unitless & # is usually expressed as a decimal. this can determine if object will sink or float in water -specific gravity less than or equal to 1 will float -specific gravity greater than 1 will sink if expressed as %, this directly indicates % of object's volume that's submerged when fluid is pure water -if specific gravity is 0.92, then 92% of its volume is submerged in water & 8% is above -specific gravity of 1 means 100% of object is submerged but it will not sink

chromatic abberation

dispersive effect within a spherical lens depending on thickness & curvature of the lens, there may be significant splitting of white light, which results in rainbow halo around images this phenomenon is corrected for in visual lenses like eyeglasses & car windows w/ special coatings that have diff dispersive qualities from lens itself

harmonic

frequencies that are multiples of fundamental frequency corresponds to # of half wavelengths supported by the string

doppler effect

describes difference btwn actual frequency of sound & its perceived frequency when source of sound & the sound's detector are moving relative to 1 another -it describes APPARENT changes in velocity of waveforms that lead to changes in observed frequency of those waveforms, which are known as Doppler shifts. however, actual velocity of waveforms does not change when doppler shifts occur if source & detector are moving toward each other, the perceived frequency, f', is greater than actual frequency, f if source & detector are moving away from each other, perceived frequency is less than actual frequency f' = f(v+/-vD / v+/-vS) -f' is perceived frequency -f is actual frequency -v is speed of sound in medium -vD is speed of detector -vS is speed of source if you're driving AWAY from ambulance, use lower sign (v-vD) & if ambulance is driving towards you, use top sign (v-vS) doppler effect can be visualized by considering sound waves in front of moving object as being compressed while waves behind object are stretched out doppler effect applies to all waves, including light. if light source is moving toward detector, observed frequency will increase (called blue shift bc blue's @ high frequency end of visible spectrum). if source waves away from detector, causes red shift

electromagnetic spectrum

describes full range of frequencies & wavelengths of electromagnetic waves -wavelengths are often given in mm (10^-3 M), micrometers (10^-6 m), nm (10^-9 m) & Angstrom (10^-10 m) in order from lowest energy to highest energy: radio (10^-9-1m), microwave (1m-1mm), infrared (1 mm-700 nm), visible (700-400 nm), UV (400-50 nm), X ray (50-10^-1 nm) & gamma rays (less than 10^-2 nm) -mnemonic: Roman Men Invented Very Unusual X-Ray Guns changing electric field can cause a change in magnetic field. each oscillating field causes oscillations in the other field completely independent of matter, so electromagnetic waves can even travel through a vacuum

specific heat

describes relationship btwn heat & temperature for a substance specific heat (c) of substance is amt of heat energy required to raise 1 g of substance by 1 degree celsius or 1 unit K. higher specific heat = harder to raise its temp SPECIFIC HEAT OF LIQUID WATER IS 1 CALORIE PER GRAM PER UNIT KELVIN (1 CAL/G*K = 4.184 J/G*K) specific heat for a substance changes according to its phase equation that relates heat gained or lost by object & change in temp of that object: q = m*c*deltaT -m is mass -c is specific heat of substance -deltaT is change in temp in C or K MCAT generally provides specific heat values except for water

electric potential

diff from electric PE. is the ratio of magnitude of the charge's electric PE to the magnitude of the test charge itself V = U/q -V is electric potential measured in VOLTS (V, J/C) even w/o test charge q, we can calculate electric potential of point in space in electric field as long as we know magnitude of source charge & distance from source charge to point in space in field V = kQ/r electric potential is scalar & sign is determined by source charge Q. for + source charge, V is + & for - source charge, V is - for collection of charges, total electric potential at a point in space is scalar sum of electric potential due to each charge bc electric potential is inversely proportional to distance from source charge, a potential diff will exist btwn 2 points that are at diff distances from source charge. if Va & Vb are electric potentials at points a & b, the POTENTIAL DIFFERENCE between them, known as VOLTAGE, is Vb-Va deltaV = Vb-Va = Wab/q

morally relevant differences

differences between individuals that are considered an appropriate reason to treat them differently, such as giving transplant to younger person bc they have longer life expectancy population size often morally relevant in study design bc study that impacts large pop generally has more potential to do good in contrast, race, ethnicity, sexual orientation, & financial status generally not considered morally relevant differences the pop that's most likely to benefit from study may be required to bear greater proportion of the risk bc likelihood of benefit is morally relevant diff

diffraction grate

diffractive array composed of numerous slits w/ near zero width similar to wavelength of incident light like the band patterns produced through single slit diffraction & double slit diffraction, dark bands that result from light passing through a diffraction grate are caused by destructive interference btwn light waves. conversely, light bands are caused by constructive interference btwn light waves compared to other diffractive phenomena, the band pattern caused by grated diffraction is characterized by relatively sharp & narrow peaks. this band pattern occurs bc constructive & destructive interference occurs not only btwn waves emerging from adjacent slits (ex: double slit diffraction) but also btwn waves emerging from slits separated from each other by other slits long wavelength light diffracts more than short wavelength light transmitting polychromatic light composed of light waves with different wavelengths (ex: white light) through a diffraction grate will produce series of multicolored arrays (ex: rainbows) that enables an analysis of wavefront composition **compared to grated diffraction, band patterns produced by single & double slit diffraction are relatively diffuse. therefore, single & double slit diffractions are not helpful in analyzing individual components of light wavefronts

magnification (m)

dimensionless value that's the ratio of the image distance to the object distance m = -i/o magnification also gives ratio of size of image to size of object orientation of image (upright or inverted) can be determined bc a - magnification signifies an INVERTED image while a + magnification signifies an UPRIGHT image if |m| > 1, the image is smaller than the object (reduced). if |m|>1, the image is larger than the object (enlarged). if = 1, image is same size as object

bimodal

distribution containing 2 peaks w/ valley ini between bimodal distribution might have only 1 mode if 1 peak is significantly higher than the other, which is still considered bimodal if there's sufficient separation of the 2 peaks or sufficiently small amt of data w/in valley region, bimodal distributions can often be analyzed as 2 separate distributions

ohmmeter

doesn't require circuit to be active & often have their own battery of known voltage & then function as ammeters through another point in the circuit bc only 1 circuit element is being analyzed, Ohm's law can be used to calculate resistance by knowing the ohmmeter's voltage & the current created through another point in the circuit -measures RESISTANCE

closed boundaries

don't allow oscillation & correspond to nodes. closed end of pipe & the secured ends of a string are both considered closed boundaries

transverse waves

drxn of particle oscillation is PERPENDICULAR to the PROPAGATION (movement) of wave ex: electromagnetic waves or holding string & moving it up & down for any waveform, energy's delivered in drxn of wave travel so for a transverse wave, the particles are oscillating perpendicular to drxn of energy transfer

field lines

electric field vectors may be represented using field lines **field lines are imaginary lines that represent how a + test charge would move in presence of a source charge. point out from + charge and point in at - charge** field lines are drawn in drxn of actual electric field vectors & also indicate relative strength of electric field @ given point in space of field. **where field lines are closer together, field is stronger** field lines of single charge never cross each other **bc every charge exerts its own electric field, a collection of charges will exert net electric field @ point in space that is = to vector sum of all electric fields** if test charge w/in field is +, then force is in same drxn as electric field vector of source charge. if test charge is -, the force will be in drxn opposite to field vector of source charge

alpha decay

emission of alpha-particle, which is a ^4 2 nucleus that consists of 2 protons, 2 neutrons, & 0 electrons alpha particle is very massive compared to a beta particle & carries double the charge alpha particles interact w/ matter very easily, so they don't penetrate shielding (such as lead sheets) very extensively emission of an alpha particle means that the atomic # of the daughter nucleus will be 2 less than that of the parent nucleus & the mass number will be 4 less

beta decay

emission of beta particle, which is an electron & is given the symbol e- or B- electrons don't reside in the nucleus, but they're emitted by the nucleus when a neutron decays into a proton, a B-article, & an antineutrino. bc electron is singly charged & 1836x lighter than a proton, the beta radiation from radioactive decay is more penetrating than alpha radiation **in some cases of induced decay (POSITRON EMISSION), a POSITRON is released, which has mass of electron but carries + charge. position is given symbol e+ or B+.** a neutrino is emitted in positron decay as well -neutrino & antineutrino not tested on MCAT during B- decay, a neutron is converted into a proton & a B- particle (Z = -1, A = 0) is emitted. hence, atomic # of daughter nucleus will be 1 higher than that of parent nucleus & the mass # will not change during B+ decay, a proton is converted into a neutron & a B+ particle (Z = +1, A = 0) is emitted. hence, atomic # of daughter nucleus will be 1 lower than that of parent nucleus, & the mass # will not change. in both kinds of beta decay, there needs to be conservation of charge. if negative charge (B-) is produced during negative beta decay, a neutron is converted into a proton to maintain charge. conversely if positive charge B+ is produced in positive beta decay, a proton is converted into a neutron to maintain charge

potential energy

energy associated w/ given object's position in space or other intrinsic qualities of the system ex: gravitational, elastic, electrical, & chemical PE

second law of thermodynamics

energy is constantly being dispersed. energy spontaneously disperses from being localized to becoming spread out if it's not hindered from doing so entropy of system can decrease as long as the entropy of its surroundings increases by AT LEAST as much entropy of an isolated system increases for all real (irreversible processes)

kinetic energy

energy of motion objects w/ mass that are moving w/ some speed have associated kinetic energy K = 1/2 mv^2 Si unit = Joule KE is related to SPEED, not velocity. an object has the same KE regardless of drxn of its velocity vector

translational equilibrium

exists only when vector sum of all forces acting on object is 0. this is called the first condition of equilibrium an object experiencing translational equilibrium will have constant speed (which could be 0 or nonzero) & constant drxn

strong nuclear force

energy stored in nucleus can be emitted under specific circumstances ***actual mass of every nucleus (other than hydrogen) is slightly smaller than sum of masses of all protons & neutrons w/in it. this difference is called MASS DEFECT*** characterization of the equivalence of matter & energy embodied by the equation: E = mc^2 where E is energy, m is mass, & c is speed of light **mass defect is result of matter that's been converted to energy. bc of large exponent on speed of light, small amount of mass will yield huge amount of energy** when protons & neutrons (neucleons) come together to form nucleus, they are attracted to each other by strong nuclear force, which is strong enough to more than compensate for repulsive electromagnetic force btwn protons -although strong nuclear force is strongest of the 4 fundamental forces, it only acts over extremely short distances. -**the bonded system is at lower energy level than unbonded constituents & this diff in energy must be radiated away in form of heat, light, or other electromagnetic radiation before mass defect becomes apparent** -**this energy, called BINDING ENERGY, allows nucleons to bind together in nucleus**. given strength of strong nuclear force, the amt of mass that's transformed into dissipated energy will be measurable fraction of initial total mass. the binding energy per nucleon peaks at element iron, which implies that iron contains most stable nucleus. in general, intermediate sized nuclei are more stable than very large or small nuclei

third law of thermodynamics

entropy of perfectly organized crystal @ absolute 0 is 0

perpendicular bisector of the dipole

equipotential line halfway between +q and -q bc angle btwn this plane & dipole axis is 90 degrees, cos(90) = 0, so the electrical potential at any point along this plane is 0 the magnitude of the electric field on the perpendicular bisector of the dipole can be approximated as E = kp / r^3 the electric field vectors at the points along the perpendicular bisector will point in the drxn opposite to p as defined directionally by physicists in electric dipole, electric potential is 0 anywhere on any perpendicular bisector of dipole axis & at infinity

confidence intervals

essentially reverse of hypothesis testing w/ confidence interval, determine range of values from sample mean & standard deviation. rather than finding a p value, begin w/ desired confidence interval (95% is standard) & use table to find its corresponding z or t score. when we multiply z or t score by standard deviation & then add & subtract this # from the mean, we create a range of values. we're 95% confident that true mean value is within this range.

electric field

every electric charge sets up a surrounding electric field just like every mass creates gravitational field electric fields make their presence known by exerting forces on other charges that move into space of the field whether the exerted force through electric field is attractive or repulsive depends on whether the stationary TEST CHARGE q (the charge placed in the electric field) & the stationary SOURCE CHARGE Q (which actually creates the electric field) are opposite or like charges electric fields are produced by source charges (Q). when test charge (q) is placed in electric field (E), it will experience an electrostatic force (Fe) equal to qE E = Fe/q = kQ / r^2 -E is electric field magnitude in newtons per coulomb -Fe is magnitude of force felt by test charge q -k is electrostatic constant -Q is source charge magnitude -r is distance btwn charges with this equation there are 2 ways to calculate magnitude of electric field @ particular place in space 1. place test charge q at some point w/in electric field, measure force exerted on that test charge, & define electric field @ that point in space as ratio of force magnitude to test charge magnitude (Fe/q) -disadvantage of this method is that test charge must be present 2. just need to known magnitude of source charge & distance btwn source charge & pt in space @ which we want to measure electric field (kQ / r^2) electric field is vector quantity w/ a direction. the direction is that positive test charge would feel repulsive force & would accelerate away from a + source charge. if source charge is - then test charge would experience attractive force & accelerate toward - source charge -therefore + charges have electric field vectors that radiate outward (point away) from charge & - charges have electric field that radiate inward (point toward) charge

pitot tube

example of Bernoulli's equation specialized measurement device that determines speed of fluid flow by determining diff btwn static & dynamic pressure of fluid at given points along tube common app of Bernoulli's eq. on MCAT is the VENTURI FLOW METER. the avg height of tube remains constant, so pgh term is constant at points 1 & 2 (these 2 points of tubes of liquid above them) if cross-sectional area decreases from point 1 to 2, linear speed must increase according to continuity equation as dynamic pressure increases, absolute pressure must decrease at point 2. w/ lower absolute pressure, the column of fluid at point 2 will be lower, this is called VENTURI EFFECT

kinetic friction (fk)

exists btwn sliding object & surface upon which it slides tire that's rolling along road doesn't experience kinetic friction bc tire isn't sliding against pavement fk = µk*N as opposed to static friction equation, this friction will always have constant value rather than a range

static friction (fs)

exists btwn stationary object & surface which it rests 0 ≤ fs ≤ µs*N -coefficient of static friction is UNITLESS quantity that's dependent on 2 materials in contact -normal force is component of force btwn 2 objects in contact that's perpendicular to plane of contact

work-energy theorem

expression of relationship btwn work & energy. direct relationship btwn work done by all forces acting on object & change in KE of that object net work done by forces acting on object will result in equal change in object's KE Wnet = deltaK = Kf-Ki allows us to calculate work w/o magnitude of forces acting on object or displacement through which forces act work-energy theorem can be applied to changes in other forms of energy

electrical conductor

facilitates electrical current (movement of charge) whereas electrical insulators inhibit current although some electrical conductors are also thermal conductors, mechanisms of thermal & electrical conductivity are not the same

polarizers

filters often used in cameras & sunglasses which allow only light w/ an electric field pointing in a particular drxn to pass through. if light beam passes through polarizer, it'll only let through that portion of light parallel to axis of polarizer. if 2nd polarizer is then held up to the first, the angle btwn the polarizers' axes will determine how much light passes through. when polarizers are aligned, all the light that passes through the first polarizer also passes through 2nd. when 2nd polarizer is turned so that its axis is perpendicular, no light gets through at all

plane mirrors

flat, reflective surfaces that cause neither convergence nor divergence of reflected light rays bc light doesn't converge at all, plane mirrors always create virtual images. in a plane mirror, the image appears to be the same distance behind the mirror as the object is in front of it. plane mirrors create appearance of light rays originating behind the mirrored surface. bc reflected light remains in front of the mirror but the image appears behind the mirror, the image is virtual plane mirrors can be conceptualized as spherical mirrors with an infinite radius of curvature

incompressible fluid

fluids with volumes that can't be reduced by any significant degree through application of pressure

lengths f, o, i, and r

focal length (f) is the distance between the focal point (F, point at which rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed) & the mirror for all spherical mirrors, f = r/2 where radius of curvature (r) is distance btwn C & the mirror the distance btwn the object & mirror is o, the distance btwn image & mirror is i. the relationship btwn these 4 distances is: 1/f = 1/o + 1/i = 2/r -units for these lengths are not important but they need to have the same units -on MCAT< will mostly use equation to calculate the image distance for all types of mirrors & lenses plane mirrors can be thought of as spherical mirrors w/ infinitely large focal distances so for a plane mirror, r = f = infinity & i = -o. virtual image is at a distance behind the mirror = to the distance of the object in front of the mirror

circular current carrying wire

for circular loop of current carrying wire of radius r, the magnitude of the magnetic field at the center of the loop is given as: B = u0*I / 2r

FINER method

for evaluating a research question, need to determine if it'll add to scientific knowledge in a practical way & w/in reasonable time period Feasible? Interesting? Novel? Ethical? Relevant?

Pascal's principle

for incompressible fluids, a change in pressure will be transmitted undiminished to every portion of the fluid & the walls of the containing vessel 1 application: hydraulic systems

straight current carrying wire

for infinitely long & straight current carrying wire, we can calculate magnitude of magnetic field produced by current I in the wire @ a perpendicular distance r from the wire as: B = u0*I / 2*pi*r -B is magnetic field @ distance r from wire -u0 is PERMEABILITY OF FREE SPACE, 4pi x 10^-7 T*m / A -I is the current straight wires create magnetic fields in the shape of concentric rings to determine direction of field vectors, use a right hand rule -point thumb in direction of current & wrap fingers around current carrying wire. your fingers mimic circular field lines curling around the wire

lensmaker's equation

for lenses where thickness can't be neglected, the focal length is related to the curvature of the lens surfaces & index of refraction of the lens by the LENSMAKER'S EQUATION 1/f = (n-1) (1/r1 - 1/r2) -n is index of refraction of lens material -r1 is radius of curvature of 1st lens surface -r2 is radius of curvature of 2nd lens surface

harmonic series

formed by all possible frequencies that string can support for strings attached at both ends, the # of antinodes present tell you which harmonic it is

circulation motion frequency & period

frequency = revolutions per second & has units of hertz (Hz) or s^-1 period is the inverse of frequency, so it is the seconds required to make 1 revolution & has units of seconds to convert to velocity, multiply frequency (revolutions per second) by circumference (meters per revolution) to yield velocity in meters/second v = 2*pi*r / period v = 2*pi*r*frequency

angular frequency (w)

frequency is related to angular frequency which is measured in radians per second & is often used in consideration of simple harmonic motion in springs & pendula w = 2*pi*f = 2pi/T

independent events

have no effect on 1 another & can occur in any order w/o impacting 1 another their probabilities are never expected to change for independent events, the probability of 2 or more events occurring at the same time is the product of their probabilities alone P (A and B) = P(A) x P(B) probability of at least 1 of 2 events occurring is the sum of their initial probabilities minus the probability that they will both occur P (A or B) = P(A) + P(B) - P (A and B) *in probability, when using the word AND, multiply the probabilities & when using the word OR, add the probabilities & subtract the probability of both happening together

ferromagnetic materials

have unpaired electrons & permanent atomic magnetic dipoles that are normally oriented randomly so material has no net magnetic dipole **however unlike paramagnetic materials, ferromagnetic materials will be strongly magnetized when exposed to magnetic field or under certain temperatures** common ferromagnetic material include iron, nickel, & cobalt bar magnets are ferromagnetic w/ a north & south pole. **field lines exit north pole & enter south pole** bc magnetic field lines are circular it's impossible to have a monopole magnet. if 2 bar magnets interact, opposite poles will attract while like poles repel

range

heavily affected by outliers in cases where it's not possible to calculate the standard deviation for a normal distribution bc the entire data set isn't provided, it's possible to approximate the standard deviation as 1/4 of the range

fluorescence

if 1 excited fluorescent substance w/ ultraviolet radiation, the electron in the fluorescent substance returns to the original state in 2 or more steps by returning in 2 or more steps, each step involves less energy so at each step, a photon is emitted w/ lower frequency (longer wavelength) than the absorbed ultraviolet photon. if wavelength of this emitted photon is w/in the visible range of electromagnetic spectrum, it will be seen as light of particular color corresponding to that wavelength

zeroth law of thermodynamics

if 1 object is in thermal equilibrium w/ 2nd object which is in thermal eq. w/ a 3rd object, then 1st & 3rd objects will also be in thermal eq. this is transitive property in thermal systems when brought into contact, no net heat will flow btwn these objects. heat flows btwn objects NOT in thermal equilibrium thermal contact doesn't necessarily imply physical contact bc objects can be in thermal contact across space

charge movement

if allowed, charges move spontaneously in direction to decrease electric PE for + test charge, this means moving from high electric potential to lower electric potential -the voltage, deltaV = Vb-Va is negative in this case bc q is + for a + test charge & thus, Wab must be -, which represents decrease in electric PE - test charge spontaneously moves from lower to higher electric potential. voltage in this case is + bc q is - for - test charge. Wab must also be - to represent decrease in electric PE again + charges spontaneously move in drxn that DECREASES their electric potential (- voltage) & - charges move in direction that INCREASES their electric potential (+ voltage). in both cases, electric potential energy is decreasing mnemonic: the "plus" end of a battery is the high potential end & the "minus" end of a battery is the low potential end. positive charges move from + to - (definition of current) while - charges move from - to +

IV & DV

if change in independent variable always precedes change in dependent variable & change in dependent variable doesn't occur in absence of experimental intervention, the relationship is said to be ***causal NOT just correlational*** on graph, independent variable is on x axis & dependent variable on y

kinetic energy of ejected electron

if frequency of photon of light incident on metal is at threshold frequency for the metal, the electron barely escapes from the metal, but if the frequency of incident photon is above threshold frequency of metal, the photon will have more than enough energy to eject a single electron & the excess energy will be converted to KE in ejected electron KE of ejected electron is: Kmax=hf-W where W is the WORK FUNCTION, the minimum energy required to eject an electron & is related to the threshold frequency of that metal by: W=h*fT this formula solves for maximum KE of electron rather than exact KE bc actual energy can be anywhere btwn 0 & Kmax, depending on specific subatomic interactions btwn photon & metal atom Kmax is only achieved when all possible energy from photon is transferred to ejected electron

slit lens system

if lens is placed btwn narrow slit & screen, a pattern is observed consisting of bright central fringe w/ alternating dark & bright fringes on each side central bright fringe (maximum) is 2x as wide as bright fringes on sides, & as slit becomes narrower, the central maximum becomes wider location of dark fringes (minima) is given by the formula: asin(theta) = n*lambda -a is width of slit -theta is angle btwn line drawn from center of lens to dark fringe & axis of lens -n is integer indicating # of the fringe -lambda is wavelength of incident wave bright fringes are halfway btwn dark fringes

wavelength of standing wave

if string is secured @ both ends & is immobile at these points, they're considered nodes if standing wave has only 1 antinode btwn 2 nodes at ends, the length of the string corresponds to 1/2 wavelength of this standing wave if there are 2 antinodes btwn ends, there must be 3rd node btwn the antinodes & length of the string = 1 wavelength of standing wave length L of string must be equal to some multiples of half-wavelengths equation that relates wavelength lambda of standing wave & length L of string it supports is lambda = 2L/n -n is positive, nonzero integer (1,2,3,etc.) called the HARMONIC

traveling wave

if string's fixed at 1 end & moving up & down, wave will form & propagate toward fixed end it's TRAVELING WAVE bc wave is moving. Traveling waves are observed when a wave is not confined to a given space along the medium when wave reaches fixed boundary, it's reflected & inverted. if free end of string's continuously moved up & down, there will be 2 waves: original wave moving down string toward fixed end & reflected wave moving away from fixed end. these waves will interfere w/ each other

free fall

if there's no air resistance & only force acting on object to make it fall is gravitational force, then object would fall w/ constant acceleration, acceleration due to gravity, & would not reach terminal velocity @ max height, velocity = 0 v = v0 + a*t deltax = vo*t + a*t^2/2 v^2 = v0^2 + 2ax x = vt

real & virtual images

images created by a mirror can be either real or virtual image is real if light actually converges at position of the image image is virtual if light only appears to be coming from position of the image but does not actually converge there distinguishing features of real images is the ability of the image to be projected onto a screen

dependent events

impact 1 another, such that the order changes the probability bc probability of 2nd event depends on 1st event

base & derived units

in each measurement system, there are base units & derived units base units: standard units around which the system is designed derived units: created by associating base units w/ each other. ex: newton = kg*m / s^2

power in circuits

in electric circuits, energy is supplied by cell that houses spontaneous oxidation-reduction rxn, which when allowed to proceed (by closing of switch, for example), generates flow of electrons **these electrons have electrical PE & convert that energy into KE as they move around circuit, driven by emf of cell** current delivers energy to various resistors, which convert this energy to some other form, depending on particular configuration of resistor rate at which energy is dissipated by resistor is power of resistor & can be calculated: P = IV = I^2*R = V^2 / R -I is current through resistor -V is voltage drop across resistor -R is resistance of resistor

linear motion

in linear motion, object's velocity & acceleration are among the line of motion so moving object continues in straight line falling objects exhibit linear motion w/ constant acceleration. 1D motion *MCAT tends to restrict kinematics problems to those that involve motion w/ constant acceleration. most common presentations of linear motion problems involve objects, such as balls, being dropped to the ground from some starting height

medical core ethical tenets

in medicine, there are 4 core ethical tenets BENEFICIENCE: obligation to act in patient's best interest NONMALEFICENCE: obligation to avoid treatments or interventions in which the potential for harm outweighs the potential for benefit respect for patient AUTONOMY, or the responsibility to respect patients' decisions & choices about their own healthcare jUSTICE: responsibility to treat similar patients w/ similar care & to distribute healthcare resources fairly in research, these 4 principles are replaced by slightly modified set. 3 necessary pillars of research ethics: -respect for persons -justice -slightly more inclusive version of beneficience (cause net positive change that doesn't have to be related to study goals, like financial incentives)

Half-life (t1/2)

in sample of radioactive particles, half life of sample is time it takes for 1/2 of the sample to decay in each subsequent half life, 1/2 of the remaining sample decays so that the remaining amount asymptomatically approaches 0

natural process

in thermodynamics, a process which would occur as expected in nature

nuclear reactions

include fusion, fission, & radioactive decay & all involve either combining or splitting nuclei of atoms. bc binding energy per nucleon is greatest for intermediate sized atoms (they're most stable), when small atoms combine or large atoms split, a great amount of energy is released

type II error

incorrectly fail to reject null hypothesis likelihood that we report no diff btwn 2 pops when 1 actually exists probability of type II error sometimes symbolized by beta probability of correctly rejecting a false null hypothesis (reporting a diff btwn 2 pops when 1 actually exists) is referred to as POWER & is equal to 1-beta

type I error

incorrectly rejecting null hypothesis probability of correctly rejecting a true null hypothesis is referred to as CONFIDENCE

parameter

info that's calculated using every person in a population

gamma decay

is the emission of gamma rays, which are high energy/frequency photons. they carry no charge & simply lower the energy of parent nucleus w/o changing the mass # or atomic # high energy state of parent nucleus may be represented by an asterick

Newton's third law

law of action & reaction FAB = -FBA to every action, there's always an equal & opposite rxn physical contact is not necessary

Newton's first law

law of inertia Fnet = m*a = 0 a body @ rest or in motion w/ constant velocity will remain that way unless net force acts upon it

normal

lie drawn perpendicular to boundary of medium all angles in optics are measured from the normal, not the surface of the medium

particle theory of light

light is not continuous wave but acts as discrete bundles of energy called photons photoelectric effect is strong support for particle theory of light

color of objects

light that contains all the colors in equal intensity is perceived as white the color of an object that does not emit its own light is dependent on the color of light that it reflects, so an object that appears red absorbs all colors of light except red. red object under green illumination will appear black bc it absorbs the green light & has no light to reflect

equipotential line

line on which potential @ every point is the same. the potential diff btwn any 2 points on equipotential line is 0 on paper, equipotential lines may look like concentric circles surrounding a source charge but in 3D, these are spheres surrounding source charge no work is done when moving test charge from 1 point on equipotential line to another. work is done when moving test charge from 1 line to another but depends only on potential diff of 2 lines & not on pathway taken btwn

sound

longitudinal wave transmitted by oscillation of particles in deformable medium so sound can travel through solids, liquids, & gases but not a vacuum speed of sound is given by v = root (B/rho) -B is bulk modulus, a measure of the medium's resistance to compression (B increases from gas to liquid to solid) -rho is density of medium bc bulk modulus increases disproportionately more than density as 1 goes from gas to liquid to solid, sound travels fastest through solid & slowest through gas. speed of sound is fastest in solid w/ low density & slowest in very dense gas speed of sound in air @ 20 degrees C is approximately 343 m/s sound's produced by mechanical disturbance of particles in material along sound wave's drxn of propagation. particles don't travel along wave but they do vibrate/oscillate abt equilibrium position, which causes small regions of compression to alternate w/ small regions of rarefaction (decompression) -alternating regions of increased & decreased particle density travel through material, allowing sound wave to propagate sound involves vibration of material particles, so source of any sound is ultimately a mechanical vibration of some frequency & can be produced by vibrating solids or fluids. the pitch (frequency) @ which the air column w/in instrument vibrates is determined by length of air column, which can be changed. human voice can produce sound by passing air btwn vocal cords, & air vibrates. male vocal cords are larger & thicker than females, so male voice typically lower in pitch

UV-Vis spectroscopy

looks at absorption of light in visible & ultraviolet range absorption spectra may be represented as color bar w/ peak areas of absorption represented by black lines. can also be shown as graph w/ absolute absorption as function of wavelength changes in molecular structure can have dramatic shifts in absorption patterns of substance -indicators like phenophtalein has clear appearance in acidic substance (doesn't absorb any visible light) & is bright pink in basic state (absorbs all but longer wavelengths of visible light). most indicators contain large organic compounds that have strikingly diff absorption patterns based solely on protonation state of compound. these compounds often have conjugated double bonds or aromatic ring systems that allows absorption of light from photons in visible range

pitch

lower frequency sounds have lower pitch sound waves w/ frequencies below 20 Hz are called INFRASONIC WAVES & those w/ frequencies over 20,000 Hz are ULTRASONIC WAVES

diamagnetic materials

made of atoms w/ no unpaired electrons & have no net magnetic field these materials are slightly repelled by magnet & can be called weakly antimagnetic diamagnetic materials include common materials you wouldn't expect to get stuck to a magnet: wood, plastics, water, etc. but the atoms in these materials are usually randomly oriented so that the material itself creates no net magnetic field

translational motion

occurs when forces cause object to move w/o any rotation simplest pathways may be linear or parabolic & any problem regarding translational motion can be solved using free body diagrams & Newton's 3 laws

fusion

occurs when small nuclei combine to form larger nucleus

propagation speed (v)

of wave can be calculated w/ v = f*lambda

magnetic force

magnetic fields exert forces only on other moving charges, charges that do not "sense" their own fields. they only sense the field established by some external charge or collection of charges assume presence of fixed & uniform external magnetic field charge must have perpendicular component of velocity in order to experience magnetic force. if charge is moving parallel/antiparallel to magnetic field vector it won't experience magnetic force bc sin(0) & sin(180) = 0 to determine direction of magnetic force on moving charge, position right thumb in drxn of velocity vector then put fingers in drxn of magnetic field lines. palm will point in drxn of force vector for positive charge & back of hand points in drxn of force vector for - charge for straight wire, magnitude of force created by external magnetic field is FB = I*L*B*sin(theta) -I is current -L is length of wire in field -B is magnitude of magnetic field -theta is angle btwn L & B same right hand rule can be used for current carrying wire in field as for a moving point charge. just remember current is considered the flow of + charge

large amplitude on objects

many objects can't withstand large amplitude of oscillation & will break or crumble. w/ steady, loud tone when object resonates (oscillated w/ max amplitude), it's possible for object to shatter

amplitude (A)

maximum magnitude of displacement in wave, which is displacement from equilibrium position to top of crest or bottom of trough

mode

may be multiple modes in a data set or if all #s appear equally, there can even be no mode for set

sinusoidal wave

may be transverse or longitudinal & its individual particles oscillate back & forth w/ displacement that follows sinusoidal pattern MCAT's primarily concerned w/ these waves

mechanical advantage

measure of increase in force accomplished by using a tool. inclined planes make it easier to lift objects bc they distribute the required work over a larger distance, decreasing required force for a given quantity of work, any device that allows work to be accomplished through smaller applied force is said to provide mechanical advantage mechanical advantage is ratio of magnitudes of force exerted on object by simple machine (Fout) to force actually applied on simple machine (Fin) for ramp, MA = hypotenuse / height dimensionless ratio

linear speed

measure of linear displacement of fluid particles in a given amount of time while flow rate is constant, linear speed of fluid changes relative to cross-sectional area product of linear speed & cross sectional area is equal to flow rate, which must be constant throughout system, so Q = v1A1 = v2A2 this is the CONTINUITY EQUATION & tells us fluids flow quicker through narrow passages

entropy

measure of spontaneous dispersal of energy @ a specific temp, how much or how widely spread out energy becomes in a process it's not only "disorder" but degree to which energy is spread out through system, up to & including the universe liquid & solid waters @ 0 celsius have same KE but liquid has more microstates, so energy is dispersed over larger # of microstates in liquid water so it has higher entropy & is less organized than ice equation for calculating change in entropy is: deltaS = Qrev / T -Qrev is heat gained or lost in reversible process -T is temperature in kelvin units of entropy are usually J/mol*K when energy is distributed into a system @ a given temp, its entropy increases. when it's distributed out of system @ a given temp, entropy decreases bc energy spontaneously disperses & entropy increases bc of this, entropy of universe is increasing. universe is closed, expanding system, so entropy of universe is always increasing. universe is progressively & irreversibly spreading out energy this doesn't mean energy can never be localized or concentrated, but concentration of energy won't happen spontaneously. work usually must be done to concentrate energy

threshold frequency (fT)

minimum frequency of light that causes ejection of electrons threshold frequency depends on type of metal being exposed to the radiation. the photoelectric effect is an "all or nothing" response so if frequency of incident photon is less than threshold frequency (f < fT) then no electron will be ejected bc photons don't have sufficient energy to dislodge electron from its atom but if frequency of incident photon is greater than threshold frequency (f > fT) then electron will be ejected & maximum KE of ejected electron will be = to diff btwn hf & hfT (also called the work function)

z or t tests

most common hypothesis tests & rely on standard distribution or closely related t-distribution from data collected, a TEST STATISTIC is calculated & compared to table to determine the likelihood that that statistic was obtained by random chance (under assumption that null hypothesis is true). this is our P VALUE -when we compare our p value to a SIGNIFICANCE LEVEL (ALPHA), 0.05 is commonly used. if p value > alpha, we fail to reject null hypothesis which means there's not a statistically significant diff btwn the 2 pops -value of alpha is the level of risk we're willing to accept for incorrectly rejecting null hypothesis

projectile motion

motion (velocities & accelerations) in 2 dimensions (usually horizontal & vertical) are independent of each other & must be analyzed separately objects in projectile motion on earth only feel acceleration of gravity in vertical drxn, so vy will change @ rate of g but vx will be constant bc we assume air resistance is negligible so no measurable force acts along x axis multiplying velocity in x drxn w/ total time can find horizontal distance traveled assuming air resistance is negligible, amt of time object takes to get to max height = time it takes for object to fall back down to starting height can find time to max height by setting final velocity to 0 then multiply this time by 2 to get total time as long as object ends @ same height it starts as *gravity is unique bc it's used as a constant AND a vector in calculations. remember gravity has a drxn

thin film interference

multicolored arrays generated by reflection events that occur w/in a system composed of 2 layers of semitransparent media. relative intensity of colors seen within multicolored array depends on constructive & destructive interference among waveforms of polychromatic (variable wavelength) light interference that occurs within thin film system results from differences in travel path of light. some light that is incident on the 2 media system will reflect off the surface of the first medium & some light will transmit through first medium before reflecting off media interface when light reflected off surface of first medium constructively interferes w/ light reflected off media interface, an observer perceives bright light. conversely, when they destructively interfere, observer perceives darkness thin film interference is influenced by the THICKNESS of the film bc light waves of a specific wavelength (ie, color) that interfere constructively or destructively at 1 film thickness may no longer interfere in same fashion at diff thickness -surface tension & other effects that locally distort the surface of fluid may also cause multicolored arrays to appear on surface as light that emerges from adjacent segments of thin film varies in color composition

skewed distribution

negatively skewed distribution has tail on the left (more negative side). -bc mean is more susceptible to outliers than median, the mean of negatively skewed distribution will be lower than the median in positively skewed distribution, mean > median **drxn of skew is determined by its tail, not the bulk of the distribution

work

not a form of energy itself but a PROCESS by which energy is transferred from 1 system to another (other transfer of energy is called heat) transfer of energy by work or heat is only way by which anything occurs energy transferred through work when something exerts forces ON or AGAINST something else W = F . d = F*d*cos(theta) -W is work -F is magnitude of applied force -d is magnitude of displacement through which force is applied -theta is angle btwn applied force vector & displacement vector bc work is dot product, only components of forces parallel or antiparallel to displacement vector will do work & transfer energy SI unit = Joule

isolated system

not capable of exchanging energy or matter w/ their surroundings, so the total change in internal energy is 0 isolated systems are very rare ex: bomb calorimeter attempts to insulate rxn from surroundings to prevent energy transfer ex: the entire universe can be considered an isolated system bc there are no surroundings

hypothesis testing

null hypothesis says there's no difference, populations are equal alternative hypothesis may be nondirectional (pops aren't equal) or directional (mean of pop A is greater than mean of pop B)

rotational motion

occurs when forces applied against object in such a way as to cause object to rotate around fixed pivot point, also known as the fulcrum application of force some distance from fulcrum generates torque, or the moment of force distance btwn applied force & fulcrum is the lever arm it's torque that generates rotational motion, not mere application of force itself. this is bc torque depends on magnitude of force but also on length of lever arm & angle @ which force is applied. torque = r x F = rFsin(theta) -r is length of lever arm -F is magnitude of force -theta is angle btwn lever arm & force vectors

circular motion

occurs when forces cause object to move in circular pathway in uniform circular motion, instantaneous velocity vector is always tangent to circular path, so object has tendency (inertia) to break out of its circular path & move in linear drxn along tangent. in uniform circular force, no work is done bc displacement & force are always perpendicular this doesn't happen bc of centripetal force that always points radially inward in all circular motion, we can resolve forces into radial & tangential components. in uniform circular motion, tangential force is 0 bc there's no change in speed of object centripetal force generates centripetal acceleration (in same drxn as force) & this acceleration keeps object in circular pathway. when centripetal force no longer acts on object, it exits circular path & assumes path tangential to circle @ that pt centripetal force can be caused by tension, gravity, electrostatic forces, or other forces Fc = m*v^2 / r -Fc is magnitude of centripetal force -m is mass -v is speed -r is radius of circular path

radioactive decay on MCAT

on MCAT, be prepared to answer 3 general types of radioactive decay problems: 1. the integer arithmetic of particle & isotope species 2. radioactive half life problems 3. use of exponential decay curve & decay constants when approaching radioactive decay problems on MCAT, start by balancing # of protons (the atomic #). often, wrong answer choices will simply have error in # of protons & can be eliminated before even checking mass #s

other units

on small scale, diff units may be given that are easer to work w/ Angstroms (1 A = 10^-10 m) nanometer (1 nm = 10^-9 m)

Hill's Criteria of Causality

only 1st criterion is necessary for relationship to be causal but it's not sufficient. the more criteria that are satisfied by a relationship, the likelier that the relationship is causal -hill's criteria doesn't provide an absolute guideline on whether a relationship is causal, thus ***for any observational study, the relationship should be described as CORRELATION*** -temporality -strength -dose-response relationship -consistency -plausibility -consideration of alternative explanations -experiment **expriment will always establish clearer causal link than an observational study -specificity -coherence (w/ current state of scientific knowledge)

visible region

only part of electromagnetic spectrum perceived as light by the human eye diff wavelengths are perceived as diff colors, w/ violet at 1 end of the spectrum (400 nm) & red at the other (700 nm)

air resistance

opposes motion of object. its value increases as speed of object increases, so object in free fall will experience growing drag force as magnitude of its velocity increases eventually, drag force = in magnitude to weight of object, & the object will fall w/ constant velocity called terminal velocity

resistance

opposition w/in any material to the movement & flow of charge ***materials that offer almost no resistance are called conductors & those that offer high resistance are called INSULATORS*** ***conductive materials that offer amounts of resistance btwn these 2 extremes are called RESISTORS***

plane polarized light

or linearly polarized light light in which the electric fields of all waves are oriented in the same drxn (their electric field vectors are parallel) their magnetic field vectors are also parallel but convention dictates that the plane of the electric field identifies the plane of polarization. unpolarized light has random orientation of its electric field vectors electric fields of unpolarized light waves exist in all 3 dimensions. the drxn of the wave's propagation is surrounded by electric fields in every plane perpendicular to that drxn -polarizing light limits the electric field's oscillation to only 2 dimensions

boiling point

phase change from liquid to gas (BOILING, EVAPORATION, or VAPORIZATION) or gas to liquid (CONDENSATION) occurs @ boiling point corresponding heat of transformation is called HEAT OF VAPORIZATION MCAT will provide heat of vaporization

melting point

phase change from liquid to solid (FREEZING or SOLIDIFICATION) or solid to liquid (MELTING or FUSION) occurs @ melting point the corresponding heat of transformation is called the HEAT OF FUSION MCAT will provide heat of fusion

total internal reflection

phenomenon in which all the light incident on a boundary is reflected back into original material, resulting in angle of incidence greater than the critical angle total internal reflection occurs as light moves from medium with higher refractive index to medium with lower one

gas system in cylinder w/ piston

piston is movable when gas expands, it pushes up against piston, exerting force that causes piston to move up & volume of system increases when gas is compressed, piston pushes down on gas, exerting force that decreases volume of system work has been done when volume of system has changed due to applied pressure

system

portion of the universe that we are interested in observing or manipulating the rest of the universe is considered SURROUNDINGS

energy density

pressure can be thought of as a ratio of energy per cubic meter, or energy density (J/m^3) systems @ higher pressure have higher energy density than systems @ lower pressure

echolocation

process that Doppler effect can be used by animals, where animals emitting sound serves as both source & detector of sound sound bounces off surface & is reflected back to animal. time it takes sound to return & change in frequency of sound can determine position of objects & speed they're moving

reversible reaction

process that can spontaneously reverse course the key is to make sure that process goes so slowly requiring an infinite amt of time so that the system is always in equilibrium & no energy is lost or dissipated no real processes are reversible. we can only approximate reversible processes freezing & melting of water in real life are irreversible (once frozen, ice isn't expected to spontaneously melt) in physics while still being CHEMICALLY reversible

unnatural process

process which does not undergo naturally predicted changes in heat/energy over time

dipole moment (p)

product of charge & separation distance p = qd has SI units of C.m dipole moment is a vector but its drxn is defined differently by physicists & chemists -physicists define vector along line connecting charges (dipole axis) w/ vector pointing from - charge toward + charge -chemists usually reverse this convention, having it point from + charge toward - charge. sometimes chemists draw crosshatch @ tail end of dipole vector to indicate that tail end is + charge

work input

product of effort & effort distance

work output

product of load & load distance

timbre

quality of sound determined by natural frequency/frequencies of object some objects vibrate @ single frequency producing pure tone. others vibrate @ multiple frequencies that have no relation to 1 another. these objects produce sounds that we don't find musical & these sounds are called NOISE still other objects vibrate @ multiple natural frequencies (a FUNDAMENTAL PITCH & multiple OVERTONES) that are related to each other by whole number ratios to produce a richer tone

Snell's law

refracted ray of light obeys Snell's law as they pass from 1 medium to another: n1sinθ1 = n2sinθ2 -n1 & theta1 refer to medium from which the light is coming -n2 & theta2 refer to medium into which the light is entering theta is also measured w/ respect to normal from snell's law when light enters medium with higher index of refraction (n2 > n2), it bends toward the normal (theta2 < theta1). opposite is true if it's the other way around bc it'll bend away from the normal

coulomb's law

quantifies magnitude of electrostatic force (Fe) btwn 2 charges Fe = k*q1*q2 / r^2 -Fe is magnitude of electrostatic force -k is Coulomb's constant -q1 & q2 are the magnitudes of the 2 charges -r is the distance btwn the charges COULOMB'S CONSTANT (also called electrostatic constant) is a # that depends on units used in equation. -in SI units, k = 1 / 4*pi*E0 = 8.99 x 10^9 N*m^2 / C^2 E0 is the PERMITTIVITY OF FREE SPACE, 8.85 x 10^-12 C^2 / N*m^2 drxn of force may be obtained by remembering that unlike charges attract & like charges repel. the force always points along line connecting centers of the 2 charges coulomb's law looks similar to gravitational force equation but w/ diff constant & using charge rather than mass

circular polarization

rarely seen natural phenomenon that results from interaction of light w/ certain pigments or highly specialized filters circularly polarized light has uniform amplitude but continuously changing drxn which causes helical orientation in propagating wave helix has avg electrical field vectors & magnetic field vectors that lie perpendicular to 1 another, like other waves, w/ maxima that fall on border of helix circular polarization occurs when 2 wave forms w/ equal amplitude & perpendicular linear polarization propagate 90 degrees out of phase to 1 another (ie, 1 waveform yields zero displacement when the other waveform is yielding a peak or trough) > only 90 degree phase shift yields both positive. negative oscillations along each axis & the symmetry necessary to produce a circular polarization pathway

power

rate at which energy is transferred from 1 system to another always measure of rate of energy consumption, transfer, or transformation per unit time P = W/t = deltaE / t -P is power -W is work which is = to change in energy -t is time over which work is done SI unit for power = watt (W) which is J/s

acceleration (a)

rate of change of velocity that object experiences as result of some applied force VECTOR quantity SI unit = m/s^2 deceleration: acceleration in drxn opposite the initial velocity avg acceleration = change in velocity/change in time

pressure

ratio of force per unit area P = F/A SI unit is pascal (Pa) 1 Pa = 1 N/m^2 other common units of pressure are millimeters of mercury (mmHg), torr, & the atmosphere pressure is scalar w/ no direction Fnet = Pnet * A = (Pfinal - Pinitial)*A

density

ratio of mass to volume scalar w/ no direction density = mass/volume SI units for density are kg/m^3, but can also use g/mL or g/cm^3 mL & cm^3 are the same volume DENSITY OF WATER is 1 g/cm^3 = 1000 kg/m^3

real & virtual sides

real & virtual are on opposite sides when comparing mirrors & lenses real side is where light actually goes after interacting with lens or mirror or mirrors, light is reflected & therefore stays in front of mirror, so real side for mirror is in front of mirror & virtual side is behind for lenses, bc light travels through lens & comes out on other side, real side is on opposite side of lens from original light suorce & cvirtual side is on same side of lens as original light source although object of single lens is on virtual side, this doesn't make the object virtual. objects are real with a + object distance unless they're placed in certain multiple lens systems in which 1 of the lens becomes object for another which is rarely on MCAT

reflection

rebounding of incident light waves at boundary of a medium light waves that are reflected are not absorbed into 2nd medium but bounces off boundary & travels back through 1st medium law of reflection is: theta1 = theta2 when theta1 is incident angle & theta 2 is reflected angle, both are measured from the normal

heat

refers to transfer of thermal energy from hotter object w/ higher temp (energy) to colder object w/ lower temp (energy) heat can never spontaneously transfer from cooler to warmer object w/o work being done on system SI unit for heat is joule (J) heat can also be measured in calorie (cal), nutritional Calorie (Cal), or British thermal unit (BTU) 1 calorie is amt of heat required to raise 1 g of water 1 degree celsius 1 Calorie is amt of heat required to raise 1 kg of water by 1 degree celsius 1 Calorie = 1000 calories objects don't need to be touching to be in thermal contact & transfer heat. 3 ways heat can transfer energy: CONDUCTION, CONVECTION, & RADIATION

lenses

refract light while mirrors reflect it when working w/ lenses, there are 2 surfaces that affect the light path. light's refracted twice as it passes from air to lens & from lens back to air on MCAT, lenses generally have negligible thickness. bc light can travel from either side of a lens, a lens has 2 focal points, w/ 1 on each side. the focal length can be measured in either drxn from the center. for thin spherical lenses, the focal lengths are equal, so we speak of just 1 focal length for the lens as a whole converging lens are always thicker at center & diverging lens are always thinner at center basic formulas for finding image distance & magnification for spherical mirrors also apply to lenses eye is complex refractive instrument that uses real lenses. cornea acts as primary source of refractive power bc change in refractive index from air is so significant. then light passes through adaptive lens that can change its focal length before reaching vitreous humor. it's further diffused through layers of retinal tissue to reach rods & cones

scientific notation

significand & an exponent significand must be w/ an absolute value in the range [1, 10), so any real number btwn -10 & -1 not including -10 or btwn 1 & 10 not including 10 exponent can be any number

PE in capacitor

regardless of geometry of capacitor (parallel plate or otherwise), function of capacitor is to store amt of energy in the form of charge separation @ a particular voltage PE stored in capacitor is U = 1/2 CV^2 stored energy in capacitor is only useful if it's allowed to be discharged. charge can be released from plates either by discharging across the plates or through some conductive material w/ which the plates are in contact

streamlines

representations of molecular movement that indicate pathways followed by tiny fluid elements (sometimes called fluid particles) as they move velocity vector of fluid particle will always be tangential to the streamline at any point streamlines never cross each other streamlines indicate some but not all pathways for the fluid & can assume fluid is incompressible so the rate at which a given volume or mass of fluid that passes 1 point must be same for all other points in closed system

viscosity

resistance of a fluid to flow increased viscosity of a fluid increases its VISCOUS DRAG which is a nonconservative force that's analogous to air resistance thin fluids like gases, water, & dilute aqueous solutions have low viscosity so they flow easily. objects can move through these fluids w/ low viscous drag thick fluids move more slowly & objects can move through these fluids but w/ more viscous drag all fluids (except for superfluids not tested on MCAT) are viscous to some degree. those w/ lower viscosities behave more like ideal fluids, which have no viscosity & are INVISCID. more viscous fluid "lose" more energy while flowing SI unit for viscosity is pascal-second (Pa.s = N*s/m^2) assume conservation of energy in low viscosity fluids w/ laminar flow **unless otherwise stated, assume viscosity is negligible, allowing Bernoulli's equations to be an expression of energy conservation for flowing liquids

resistors

resistance of resistor is dependent on resistivity, length, cross-sectional area, & temperature R = p*L / A -R is resistance of resistor -p is resistivity -L is length of resistor -A is its cross-sectional area resistance is directly proportional to its length. longer resistor = electrons have to travel longer greater distance through resistant material inversely proportional to cross sectional area bc the area increases the # of pathways through the resistor, called CONDUCTION PATHWAYS (current doesn't follow continuity equation for incompressible fluids) most conductors have greater resistance at higher temps bc increased thermal oscillation of atoms in conductive material produces greater resistance to electron flow on MCAT, most common resistors you will see outside of generic, unlabeled resistors are light bulbs, although all appliances function as resistors -you may also see resistance applied atypically as in resistance to air flow in lungs or to blood moving in circulatory system. same mathematical relationships useful for both

resultant

resultant of vectors is sum or diff of 2 or more vectors to find the resultant, 1. resolve the vectors to be added into their x & y components 2. add the x components to get the x component of the resultant (Rx) & do the same to get Ry 3. find magnitude of resultant by using Pythagorean theorem 4. find drxn (theta) of resultant by using relationship theta = tan-1 (Ry/Rx)

electric dipole

results from 2 equal & opposite charges being separated a small distance d from each other can be transient (as in the case of moment to moment changes in electron distribution that creates London dispersion forces) or permanent (as in the case of molecular dipole of water or carbonyl functional group) for points in space relatively distant from dipole: V = k*q*d*cos(theta) / r^2 in absence of electric field, the dipole axis can assume any random orientation. when electric dipole is placed in uniform electric field, each of the equal & opposite charges of the dipole will experience force exerted on it by the field. bc the charges are equal & opposite, the forces acting on the charges will also be equal in magnitude & opposite in direction, resulting in a situation of translational equilibrium there will be however a net torque about the center of dipole axis that can be calculated from: T = pEsin(theta) -where p is magnitude of dipole moment (p=qd) -E is magnitude of uniform external electric field -theta is angle the dipolle moment makes w/ the electric field this torque will cause dipole to reorient itself so its dipole moment p aligns with electric field E for dipole at some angle in external electric field, there will be translational equilibrium but not rotational equilibrium. this is bc forces are in opposite directions but the torques are in the same direction dipole in electric field will experience torque until it comes to rest oriented w/in the field, at which point the angle btwn the plane of the dipole & electric field is 0 degrees. once this point is reached, inverting the electric field has no impact on dipole bc it will now have an angle of 180 degrees, the sine of which is still 0

detection bias

results from educated professionals using their knowledge in an inconsistent way. bc prior studies have indicated that there's a correlation btwn 2 variables, finding 1 of them increases the likelihood that researcher will search for 2nd

turbulent flow

rough & disorderly turbulence causes formation of EDDIES, which are swirls of fluid of varying sizes occurring typically on downstream side of obstacle/object obstructing laminar flow ***in unobstructed fluid flow, turbulence can arise when speed of fluids exceeds certain CRITICAL SPEED*** significant amount of energy is dissipated from the system as a result of increased frictional forces **calculations of energy conservation such as Bernoulli's equation can't be applied to turbulent flow systems so MCAT always assumes laminar flow for these questions

free body diagrams

should be drawn for any problem in which you must perform calculations on forces

sign conventions for lenses

sign conventions slightly change for lenses for both lenses & mirrors, + magnification represents upright images & - magnification means inverted images. + image distance means image is real & located on real R side & - image distance means image is virtual & on virtual (V) side

electric potential energy

similar to gravitational PE, is a form of PE dependent on relative position of 1 charge w/ respect to another charge or to a collection of charges electric PE is work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge U = kQq / r deltaU = work = kQq/r if the charges are like charges, then PE is + & if charges are unlike, PE is -. negative PE gets increasingly negative as charges are brought closer together & this decrease in energy represents an increase in stability. for positive PE, the closer the charges are, the less stable they'll be. like charges are more stable farther apart bc the electric PE becomes a smaller + number

pulleys

simple machine provide mechanical advantage in same way as inclined plane, reduces necessary force at cost of increasing distance to achieve given value of work or energy transference pulleys allow heavy objects to be lifted using much-reduced force. simply lifting object requires a force = mgh (its change in gravitational PE) if displacement occurs over distance = to displacement, then force required to lift object = mg if distance through which displacement is achieved is GREATER than displacement (an indirect path), then applied force < mg if crate needs to be lifted by 2 ropes & crate is momentarily stationary in midair, then it's in translational equilibrium. the weight (the LOAD) is balanced by total tension in the ropes & tensions in the ropes are = to each other (if they weren't =, the pulley would turn until tensions were = on either side) > each rope supports 1/2 the crate's total weight & only half the force (EFFORT) is required to lift the crate this decrease in effort is the mechanical advantage & it comes at expense of distance to lift an object to a certain height in the air (LOAD DISTANCE), 1 must pull through length of rope (EFFORT DISTANCE) = to 2x the displacement. if crate must be lifted 3 meters, then both sides of supporting rope must be shortened by 3 meters, so you need to pull through 6 meters of rope increasing # of pulleys decreases tension in each segment of rope & leads to increase in mechanical advantage. for ex, if load divided among 6 lengths of rope, effort required is now only 1/6 of total load. need to pull through length of rope that's 6x desired displacement & efficiency will decrease due to added weight of each pulley & additional frictional forces

laminar flow

smooth & orderly often modeled as layers of fluid that flow parallel to each other characterized by smooth flow lines around object layers won't necessarily have the same linear speed w/ laminar flow through pipe or confined space, possible to calculate rate of flow using POISEUILLE'S LAW Q = pi*r^4*deltaP / 8*eta*L -Q is flow rate (volume flowing per time) -r is radius of tube -delatP is pressure gradient -n (eta) is viscosity of fluid -L is length of pipe

regression analysis

software programs use BINARY (yes vs no, better vs worse), as well as CONTINUOUS (amt of weight lost, percent improvement), or CATEGORICAL VARIABLES (state of residence, SES) to create a regression model REGRESSION ANALYSIS may demonstrate linear, parabolic, exponential, logarithmic, or other relationships

systems of equations

solve w/ substitution & elimination methods answers w/ the variables x & y are reported as coordinates on the Cartesian plane (x, y). systems can have many variables, but it's unlikely you'll encounter system w/ more than 3 variables (x, y, z) on MCAT

metallic conductivity

some materials allow free flow of electron charge w/in them & these materials are called electron conductors metal atoms easily lose 1 or more outer electron bc metals have lowest ionization energies so it's easy for them to lose electrons & electrons can then move around in larger collection of metal atoms this makes most metals good electrical & thermal conductors

confounding

sometimes called confounding bias or omitted variable bias, is a **data analysis error** data may or may not be flawed but an incorrect relationship is characterized. a "third party" variable that may affect both identified variables are called CONFOUNDING VARIABLES, or CONFOUNDERS

interference effects on sound volume

sound volume can vary periodically due to interference effects. when 2 sounds of slightly diff frequencies are produced in proximity, volume will vary @ rate based on diff btwn 2 pitches being produced frequency of this periodic increase in volume can be calculated by the equation: fbeat = |f1-f2| -f1 & f2 represent the 2 frequencies that are close in pitch -fbeat represents resulting beat frequency

superconductor

special class of materials & when cooled to very low temperatures, the resistivity of the material completely dissipates & drops to 0 major exception to rules of internal resistance

semilog graphs

specialized representation of log data set curved nature of log data is made linear by change in AXIS RATIO. in semilog graphs, 1 axis (usually x axis) maintains traditional unit spacing & other axis assigns spacing based on a ratio, usually 10, 100, 1000, & so on. the multiples may be of any number as long as there is consistency in the ratio in some cases, both axes can be given a diff axis ratio to create a linear plot. when both axes use a constant ratio from point to point on axis, this is termed a LOG-LOG GRAPH. the axes on a graph will determine which type of plot is being used

abberations

specific types of errors that spherical mirrors & lenses are subject to bc they're imperfect

elastic potential energy

springs & other elastic systems act to store energy every spring has characteristic length @ which it's considered relaxed or @ equilibrium when spring is stretched or compressed from its equilibrium length, the spring has elastic potential energy U = 1/2 kx^2 where k is SPRING CONSTANT (measure of stiffness of spring) & x is magnitude of displacement from equilibrium

standard deviation

standard deviation can also be used to determine whether a data point is an outlier. if a data point falls more than 3 standard deviations from the mean, it's an outlier standard deviation relates to normal distribution as well. on normal distribution, approximately 68% of data points fall w/in 1 standard deviation of the mean, 95% fall w/in 2 standard deviations, & 99% fall w/in 3 standard deviations

equipoise

studies comparing 2 potential treatment options shouldn't approach research w/ knowledge that 1 treatment is superior to the other -if it becomes evident that 1 is better, stop trials bc providing inferior treatment is net harm

hydrostatics

study of fluids at rest & the forces & pressure associated with standing fluids

fluid dynamics

study of fluids in motion MCAT presents simplified version, making assumptions such as rigid-walled containers & uniform density of liquids

dynamics

study of forces & torques

electrostatics

study of stationary charges & forces that are created by & which act upon these charges charged subatomic particles: protons (+) & electrons (-) opposite charges exert ATTRACTIVE forces while those w/ same sign exert REPULSIVE forces. unlike force of gravity which is always attractive, electrostatic force can be repulsive or attractive depending on signs of charges interacting although these particles are very tiny, they still have mass so equations such as the KE equation can still be used when solving problems w/ charged particles

selection bias

subjects used for study aren't representative of target population measurement & assessment of selection bias occurs before any intervention

total mechanical energy

sum of an object's PE & KE E = U + K -E is total ME -U is PE -K is KE

lorentz force

sum of electrostatic and magnetic forces charges often have both electrostatic & magnetic forces acting on them @ the same time & the sum of these electrostatic & magnetic forces is known as the LORENTZ FORCE

energy

system's ability to do work or make something happen

hydraulic systems

take advantage of near-incompressibility of liquids to generate mechanical advantage in hydraulic lift, closed container w/ incompressible liquid -left side has piston of cross-sectional area A1 & when it is pushed down, it exerts force of magnitude F1 & generates pressure P1 -piston displaces volume of liquid equal to A1*d1 (cross-sectional area x distance = volume) -the liquid is incompressible so same volume of liquid must be displaced on right side w/ second piston & much larger surface area A2 -pressure generated from piston 1 is transmitted undiminished to all points w/in the system including A2 -bc A2 is larger than A1 by some factor, the magnitude of the force F2 exerted against A2 must be greater than F1 by the same factor so P1 = P2 according to Pascal's hydraulic machines generate output force by magnifying input force by factor equal to the ratio of corss-sectional area of larger piston to that of smaller piston energy is still conserved in this process -bc the factor by which d1 is larger than d2 is equal to the factor by which F2 is larger than F1, there's no additional work done or unaccounted for bc the greater force F2 is moving through smaller distance d2, so just need to exert small force over small area through large distance to generate much larger force over larger area through smaller distance when applying to Pascal's principle, the larger the area, the larger the force, although this force will be exerted through a smaller distance

guage pressure

the difference between absolute pressure and atmospheric pressure difference between absolute pressure inside the tire & the atmospheric pressure outside the tire amount of pressure in a closed space above & beyond atmospheric pressure Pgauge = P - Patm = (P0 + rho*g*z) - Patm -when P0 = Patm, then Pguage = rho*g*z at a depth z

wavelength (lambda)

the distance from 1 maximum (CREST) of wave to next

critical speed

the speed above which flow of a fluid will be turbulent depends on physical properties of fluid, such as its viscosity & diameter of the tube ***when critical speed for fluid is exceeded, fluid demonstrates complex flow patterns & laminar flow occurs only in thin layer of fluid adjacent to the wall, called the BOUNDARY LAYER*** the flow speed immediately at the wall is 0 & increases uniformly throughout the layer beyond the boundary layer, the motion is highly irregular & turbulent for fluid flowing through tube of diameter D, critical speed can be calculated as: Vc = Nr*eta / rho*D -Nr is dimensionless constant called the Reynolds number -eta is viscosity of fluid -rho is density of fluid REYNOLDS NUMBER depends on factors such as size, shape, & surface roughness of any objects w/in the fluid

electromotive force (emf)

the voltage when no charge is moving btwn the 2 terminals of a cell that are at diff potential values not actually a force but a potential diff (voltage) & as such, has units of joules per coulomb ( 1 V = 1 J/C), not Newtons Emf can be thought of as a "pressure to move" that results in a current

irreversible reaction

thermodynamic process that's extraordinarily unfavorable in reverse, usually as a result of changes in entropy

state functions

thermodynamic properties that are a function of only the current equilibrium state of a system state functions are independent of the path taken to get to a particular equilibrium state include pressure, density, temp, volume, enthalpy, internal energy, Gibbs free energy, & entropy

power of lens (P)

this is measured in DIOPETERS, where f (the focal length) is in meters & is given by the equation P = 1/f P has the same sign as f, therefore, + for converging lens & - for diverging lens

image for a lens

to find where image is for a lens, draw the following rays & find a point where any 2 intersect. this point of intersection marks tip of image: -ray parallel to axis > refracts through focal point of front face of lens -ray through or toward focal length before reaching lens > refracts parallel to axis -ray to center of lens > continues straight through w/ no refraction if rays don't appear to intersect, extend them to same side of lens from which light came, creating virtual image

sound level (beta)

to make range of sound that average human ear can hear, use logarithmic scale called the sound level measured in DECIBELS (dB) beta = 10 log (I/I0) -I is intensity of sound wave -I0 is threshold of hearing (1 x 10^-12 W/m^2) which is used as reference intensity when intensity of sound is changed by some factor, 1 can calculate new sound level w/ betaf = betai + 10*log(If/Ii) -If/Ii is ratio of final intensity to initial intensity

blinded experiment

to remove bias from perception of subject & investigator due to what group the subject is in SINGLE BLIND EXPERIMENT: only patient or assessor (person making measurements/evaluations) is blinded DOUBLE BLIND EXPERIMENTS; investigator, subject, & assessor all don't know the subject's group w/o blinding, the placebo effect would greatly reduce in control group but still present in treatment group

absolute (hydrostatic) pressure

total pressure exerted on an object that is submerged in fluid P = P0 + rho*g*z -P is absolute pressure -P0 is INCIDENT or AMBIENT PRESSURE (pressure at the surface) -rho is density of the fluid -g is acceleration due to gravity -z is depth of the object P0 does not always stand for atmospheric pressure hydrostatic pressure for liquids is linear bc as depth changes, the density of the liquid remains constant. gases, however, have densities that change according to forces applied to them bc they are compressible while liquids are not

electromagnetic waves

transverse waves bc the oscillating electric & magnetic field vectors are perpendicular to the drxn of propagation electric & magnetic fields are also perpendicular to each other electromagnetic waves can vary in frequency & wavelength but in vacuum, all electromagnetic waves travel at same speed called SPEED OF LIGHT. electromagnetic waves can travel in vacuum!!

friction

type of force that always opposes movement of objects & causes it to slow down or become stationary. 2 types: static friction & kinetic friction

infrared (IR) spectroscopy

used in organic chemistry to determine chemical structure bc diff bonds will absorb diff wavelengths of light

doppler ultrasound

used to determine flow of blood within the body by detecting frequency shift associated w/ movement toward or away from receiver.

cross product (A x B)

used to generate 3rd vector (determine both magnitude & drxn) A x B = |A| |B| sin(theta) resultant of cross product always perpendicular to plane created by 2 vectors. to find drxn of resultant C: 1. point thumb in drxn of vector A 2. extend fingers in drxn of vector B 3. palm is plane btwn vectors A & B so drxn of palm pts in drxn of resultant C *MCAT is 2D so vector of interest usually into or out of screen *ORDER OF VECTOR MULTIPLICATION MATTERS IN DETERMINING DRXN OF RESULTANT VECTOR. A X B DOESN'T = B X A. POINT THUMB TOWARDS 1ST VECTOR BEING MULTIPLIED

Dot Product (A*B)

used to generate scalar quantity like work A*B = |A| |B| cos(theta)

ammeter

used to measure current @ some point w/in a circuit using ammeter requires circuit to be on or the current will be 0 ammeters are inserted in series where current is being measured & uses magnetic properties of current-carrying wire to cause visible needle movement for calibrated display of current if there's particularly high current, this will overwhelm the ammeter & a special low resistance shunt is used in parallel w/ the ammeter to allow a reading ideally an ammeter will not change circuit mathematics when inserted into circuit. to do so, it must have extremely low resistance ideal ammeters have 0 resistance & no voltage drop across themselves

box and whisker plot

used to show range, median, quartiles, & outliers for set of data bounded by Q1 & Q3, while Q2 (median) is line in middle of box. ends of whiskers correspond to max & min values of data set outliers can be presented as individual points w/ ends of whiskers corresponding to largest & smallest values in data set that are still w/in 1.5 x IQR of median

logarithms

used with scales w/ extremely large scale MCAT mostly deals w/ base ten logarithms (common logarithms) log 1000 = 3 bc 10^3 = 1000 log 1 = 0 bc 10^0 = 1

ray diagram

useful for getting approximation of where an image is. on MCAT, ray diagrams helpful for quick determination of type of image that will be produced by object some distance from the mirror (real vs virtual, inverted vs upright, magnified vs reduced) when drawing ray diagram, 3 impt things to draw -for concave mirror, ray that strikes mirror parallel to AXIS (the normal passing through center of mirror) is reflected back through focal point -a ray that passes through focal point reaching point of intersection w/ axis is reflected back at the same angle, measured from the normal any time an object is at the focal point of a converging mirror, the reflected rays will be parallel & thus the image will be at infinity a single diverging mirror forms only a virtual, upright, & reduced image, regardless of position of object. the further away the object, the smaller the image to find where image is for a mirror, draw the following rays & find point where any 2 intersect. point of intersection marks tip of image. if rays you draw don't appear to intersect, extend them to other side of mirror, creating a virtual image -ray parallel to axis > reflects back through focal point -ray through focal point > reflects back parallel to axis -ray to center of mirror > reflects back at same angle relative to normal

x ray diffraction

uses bending of light rays to create model of molecules x ray diffraction is often combined w/ protein crystallography during protein analysis dark & light fringes don't take on linear appearance, but rather a complex 2D image

ultrasound

uses high frequency sound waves outside range of human hearing to compare relative densities of tissues in the body ultrasound machine consists of transmitter that generates pressure gradient, which also functions as a receiver that processes the reflected sound. bc speed of wave & travel time is known, the machine can generate a graphical representation of borders & edges w/in the body by calculating the traversed distance. ultrasound machines calculate distance based on travel time of reflected sound ultrasound relies on reflection so interface btwn 2 objects is necessary to visualize anything. most ultrasound transmitters & receivers don't function simultaneously bc 1 objective of system is to reduce interference most modern ultrasound machines also have a Doppler mode ultrasound can be used therapeutically. ultrasound waves create friction & heat when they act on tissues, which can increase blood flow to site of injury in deep tissues & promote faster healing. focused ultrasound also has range of applications

Ohm's law

voltage drop btwn any 2 points in circuit can be calculated w/ Ohm's law: V = IR -V is voltage drop -I is current -R magnitude of the resistance equation applies to single resistor w/in a circuit, any part of a circuit, or to an entire circuit (provided 1 can calculate the equivalent resistance from all resistors in circuit) -as current moves through set of resistors in a circuit, the voltage drops some amount in each resistor

flow rate

volume per unit time constant for closed system & independent of changes in cross-sectional area

weight

weight of any volume of given substance w/ known density can be calculated force of gravity = rho*V*g -rho is density of object -V is volume -g is gravity

dielectric material

when a dielectric material, such as air, glass, plastic, etc. is introduced btwn plates of capacitor, it increases the capacitance by a factor called the DIELECTRIC CONSTANT (K) which is a measure of a material's insulating ability -any relevant dielectric constants will be given on MCAT capacitance due to dielectric material is C' = kC -C' is new capacitance w/ dielectric material -C is original capacitance when dielectric is placed in isolated, charged capacitor (charged capacitor disconnected from any circuit) the voltage across the capacitor decreases bc dielectric material shields opposite charges from each other. by lowering voltage across charged capacitor, the dielectric has increased the capacitance of capacitor by factor of dielectric -decrease in voltage > increase in capacitance when dielectric is placed in charged capacitor w/in a circuit (still connected to voltage source) the charge on capacitor increases. voltage must remain constant bc it must be = to that of the voltage source. by increasing amt of charge stored on capacitor, the dielectric has increased capacitance of capacitor by factor of dielectric constant -increased stored charge > increased capacitance

vector * scalar

when a vector's multiplied by a scalar, its magnitude will change & its drxn will be either parallel or antiparallel to original drxn (will be in opposite drxn if vector's multiplied by negative #)

exponents

when adding or subtracting numbers with exponents, the true value must be calculated before addition or subtraction can be performed 3^2 + 3^2 does not = 6^2, but rather 9 + 9 = 18 -however if base & exponent are the same, we can add the coefficients 3^2 + 3^2 = (1 + 1)3^2 = 2 x 3^2 = 18 in cases of multiplication & division, exponents can be manipulated directly as long as the base # is the same. when multiplying 2 #s w/ the same base, the exponents are added X^A x X^B = X^A+B in division, we subtract the exponent of the denominator from exponent in numerator to find exponent in quotient as long as all bases are the same X^A / X^B = X^(A-B)

phase difference

when analyzing waves that are passing through same space, can describe how "in step" or "out of step" the waves are by calculating the PHASE DIFFERENCE 2 waves w/ same frequency, wavelength, & amplitude & pass through same space at same time are IN PHASE if their respective crests & troughs line up -when waves are perfectly in phase, the phase difference is 0 if 2 waves travel through space in way that crests of 1 wave coincide w/ troughs of other, then they are out of phase & phase diff would be 1/2 of a wave, expressed as lambda/2 or 180 degrees bc 1 cycle = 1 wavelength = 360 degrees waves can be out of phase w/ each other by any other fraction of a cycle as well

load & effort

when considering simple machines, load & effort are both forces load determines necessary output from the output force & mechanical advantage, we can determine necessary input force

work in a gas

when gas expands, work is done BY gas & work is POSITIVE when gas compresses, work is done ON the gas & work is NEGATIVE

conductor

when given a charge, the charges will distribute approximately evenly upon the surface of the conductor conductors are able to transfer & transport charges & are often used in circuits or electrochemical cells conductors often conceptualized as nuclei surrounded by sea of free electrons that are able to move rapidly throughout the material & are only loosely associated w/ the + charges conductors are generally metals although ionic (electrolyte) solutions are also effective conductors

heat equation for phase change

when heat energy is added to or removed from system experiencing a phase change, amt of heat added or removed can't be calculated w/ q = mcdeltaT bc there's no temp change q = mL -q is amt of heat gained or lost from material -m is mass of substance -L is HEAT OF TRANSFORMATION or LATENT HEAT of substance

speed of light through a medium

when light is in any medium besides a vacuum, its speed is less than c. for a given medium, n = c/v where c is speed of light in vacuum, v is speed of light in medium, & n is dimensionless quantity called the INDEX OF REFRACTION of the medium for vacuum, index of refraction is 1 & for air, n is essentially = to 1 bc speed's extremely close to c for all other materials, index of refraction will be greater than 1

photoelectric effect

when light of sufficiently high frequency is incident on a metal in a vacuum & the metal atoms emit electrons electrons liberated from metal by photoelectric effect produce net charge flow per unit time, or CURRENT if light beam's frequency is above threshold frequency, light beams of greater intensity produce larger current in this way. the higher the intensity of the light beam, the greater the # of photons per unit time that fall on electrode, producing a greater # of electrons per unit time liberated from the metal -when light beam's frequency is above threshold frequency, the magnitude of the resulting current is directly proportional to the intensity & amplitude of the light beam only electrons are ejected, not protons or neutrons bc of weak hold that metals have on their valence electrons due to low ionization energies

rectilinear propagation

when light travels through a homogenous medium, it travels in a straight line

critical angle (thetac)

when n2 < n1, eventually, a special incident angle called the critical angle is reached, for which refracted angle theta2 = 90 degrees at critical angle, refracted light ray passes along interface between 2 media critical angle can be derived from snell's law if theta2 = 90 degrees such that thetac = sin-1 (n2/n1)

thermal equilibrium

when no net heat flows btwn 2 objects in thermal contact, their temperatures are equal & they are in thermal equilibrium

forced oscillation

when periodically varying force is applied to a system, the system will then be driven @ a frequency = to the frequency of force if frequency of applied force is close to that of natural frequency of system, then amplitude of oscillation becomes larger -the amplitude is increasing bc the FORCE FREQUENCY is nearly identical to natural frequency system is RESONATING if frequency of periodic force is = to natural (resonant) frequency of system. amplitude of oscillation is @ max if frictionless, periodically varying force would continually add energy to system & amplitude would increase indefinitely -no system is frictionless so there's always some damping, which results in finite amplitude of oscillation

rounding

when rounding number to be multiplied, round 1 number up & 1 number down to compensate. when rounding numbers to be divided, round both numbers in same drxn to compensate

phase changes

when substance is undergoing phase change, heat that's added or removed from system doesn't result in change in temp phase changes occur @ constant temp & temp will not begin to change until all of the substance has been converted from 1 phase to another phase changes are related to changes in PE, not KE (even though adding heat raises temp of system bc particles in system have greater avg KE) molecules of water in ice aren't truly frozen & can't move. molecules can rotate, vibrate, & wiggle around. the bonds are free to bend & stretch. molecules are in relatively stable positions bc of H bonds btwn them, but they still have fairly significant amt of KE the PE is quite low bc of the stability provided by relative closeness of 1 molecule to another & by the H bonds when heat energy is added, it causes water molecules to move away from each other by breaking free of H bonds. molecules are held less rigidly in place & now have greater degrees of freedom of movement & avg PE increases increased freedom of movement permits greater # of MICROSTATES of water molecules although molecules gain additional drxns & forms of motions, the amt of up & down & side to side motion must decrease, keeping avg KE of liquid water at 0 Celsius the same as solid water @ 0 C liquid water has greater # of microstates due to increased freedom of movement but its avg KE is same as solid water at same temp

dispersion

when various wavelengths of light separate from each other if source of white light is incident on 1 of the faces of a prism, the light emerging from the prism is spread out into fan shaped beam bc violet light has smaller wavelength than red & is bent to greater extent. **SMALLER WAVELENGTH MEANS GREATER ANGLE OF REFRACTION** due to their diff speeds while inside the prism, various wavelengths of light are refracted to diff degrees. bc red experiences least amount of refraction, it's always at top of spectrum while violet is always at bottom as light enters medium w/ diff index of refraction, wavelength changes but frequency of light does not **FREQUENCY DOES NOT CHANGE WHETHER LIGHT REFLECTS, DIFFRACTS, ETC. BC IT ONLY DEPENDS ON THE SOURCE**

principle of superposition

when waves interact w/ each other, the displacement of resultant wave at any point is sum of displacements of the 2 interacting waves when waves are perfectly in phase, the displacements always add together & amplitude of resultant = sum of amplitudes of 2 waves. this is CONSTRUCTIVE INTERFERENCE when 2 waves are perfectly out of phase, the displacements counteract each other & amplitude of resultant wave is diff btwn amplitudes of interacting waves. this is DESTRUCTIVE INTERFERENCE if waves aren't perfectly in phase or out of phase, PARTIALLY CONSTRUCTIVE or PARTIALLY DESTRUCTIVE interference can occur. 2 waves nearly in phase will mostly add together & is not quite sum of 2 amplitudes. 2 waves almost perfectly out of phase don't quite cancel but wave's amplitude is much smaller than that of either wave

multiple slits

when waves interact w/ each other, the displacements of the waves add together in process called INTERFERENCE diffracted rays of light emerging from 2 parallel slits can interfere w/ 1 another. when monochromatic light (light of only 1 wavelength) passes through the slits, an interference pattern is observed on screen behind the slits regions of constructive interference btwn 2 light waves appear as bright fringes (maxima) on screen & regions where light waves interfere destructively, dark fringes (minima) appear positions of dark fringes (minima) on screen can be found from equation: dsin(theta) = (n + 1/2)*lambda -d is distance btwn 2 slits -theta is angle btwn line drawn from midpoint btwn 2 slits to dark fringe & normal -n is integer indicating # of the fringe -lambda is wavelength of incident wave

conservation of mechanical energy

when work done by nonconservative forces is 0 or when there are no nonconservative forces acting on the system, total mechanical energy of the system (U + K) remains constant, sum of KE & PE remains constant deltaE = deltaU + deltaK = 0

exponential decay

where n0 is # of undecayed nuclei at time t = 0 & lamba is the decay constant