Condensed MCAT

Isotopic Notation

mass number over atomic number before element Atomic number (Z) = number of protons in nucleus Mass number (A) = number of protons + neutrons

mile to meters to feet

1 mile : 1609 meters 1 mile = 5280 feet *1 inch = 2.5 cm There are about 30.5 cm in a foot

Square root of 2 Square root of 3 Square root of 361 Square root of 256 Square root of 324 Square root of 289

1.414 1.732 19 16 18 17

Planck's constant

6.626 x 10^-34 J*s 4.14X10^-15 eV*s 1 J = 6.242 X 10^18 eV

Error Sources: Bias (3 types) and Confounding

Bias is systematic error, so it doesn't impact precision, but skews data Bias results flaws of data collection Confounding is an error during analysis Most prevalent type of bias = selection bias: Subjects not representative of target population -Could include one gender being more prevalent -Measurement and assessment of selection bias occurs before any intervention Detection Bias: Inconsistent use of knowledge (finding one variable (like hypertension) increases likelihood of finding second variable (diabetes). Both more common in obsession, so physician might use more obese population, inflating true value of secondary measurement Observation bias: Hawthorne effect (Observation bias) -> behavior more likely just because you are being studied -Exercising more when you start taking weight loss drug -Occurs before data analysis, so it is example of bias Confounding: Data analysis error -Third party variables = confounding variables/confounders *Bias is error in data collection, confounding is error in data analysis *Bias is systematic (unidirectional) error that occurs during selection of subjects or measurement and collection of data *Confounding: Association is erroneously drawn between 2 variables because of shared connection to a third variable

Boyles Law and Gay-Lussacs Law

Boyle's Law: P1V1 = P2V2 Pressure and volume have inverse relationship: As one double the other is cut in half Gay-Lussac's Law: P1/T1 = P2/T2 Pressure and temperature have direct relationship: As one is doubled, the other is too

measures of central tendency

Describe the middle of a sample (but how we define the middle can vary): Mean/ arithmetic mean: (equation shown in image): The average, adding up all individual values and dividing the result by the number of values -n = number of data points in the set -Good indicators of central tendency when all values fairly close -Not so good for Outlier -> can shift mean towards one end of the range - Good for normal distribution Median: (n+1)/2 where n is the number of data values -Midpoint: Half of the data points are greater than the value and half are smaller -MUST FIRST LISTED VALUES IN ORDER -Least susceptible to outliers, but not good for large range or multiple modes IF THE MEAN AND MEDIAN ARE FAR APART FROM EACH OTHER, THIS IMPLIES OUTLIERS OR SKEWED DISTRIBUTION -If mean and median are close it implies symmetrical distribution Mode: Number that appears most often in a set of data -There may be multiple or none -Seen as peaks Outliers: result from 1 of 3 causes: 1. True statistical anomaly / anomalous result 2. Measurement error 3. Distribution not approximated by normal distribution (skewed with long tail) *Decision of what should be done with outliers should be made before study begins *When outliers are an indication that data set may not approximate normal distribution, repeated samples or larger samples will generally demonstrate if this is true *Existence of outliers say if mean is appropriate measure

Error Sources

Experimental bias: Usually minimal, experimenter's personal opinions end result in faulty hypothesis from incomplete early data and research collection Instrument error may effect may effect accuracy, precision, or both Accuracy = Validity: Ability of an instrument to measure the true value (scale should say that a 170 lb person weighs 170 lbs) (can be wide range if average comes out to actual number, like 150 and 190 lbs) Precision = Reliability : Ability of instrument to read consistency, or within narrow range (129-131 lbs, narrow range, but not precise because the person actually weighs 170) Bias is a systematic error in data (only an inaccurate/ not valid tool will cause bias, but imprecise tool will still induce error) *Invalid Data leads to bias -> 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 a lack of validity (or accuracy). Unreliable data suffers from random, not systematic, error. Confounding arises from errors in data analysis, not data collection. Random chance can introduce error Random error is hard to avoid, but can be limited with really large sample size An experiment with improperly tared (zeroed) mass balance would have what type of error? This experiment would have inaccuracy (not valid) error but not imprecision error (it is reliable) The scale would reliably read the same weight, but the weight read would not be right. This would lead to bias

Pressure

Force per unit area P = F/A Pnet = Fnet/A where P=pressure, F = magnitude of normal force vector, and A is area Measured in pascal (Pa) = newton per square meter (a N/m^2) *If pressure decreases 1 percent and area does not change, the force will be decreased by 1 percent *You can also use millimeters of mercury (mmHg) or torr (which are each to each other) or atm 1.013X10^5 Pa = 760 mmHg = 760 torr = 1 atm Pressure is scalar quantity (magnitude but no direction)

Fundamental unit if charge

Fundamental unit if charge = e = 1.60X10^-19 C -Proton and electron both have this amount of charge (same magnitude), but proton has positive charge and electron has negative, and the proton has much larger mass SI unit for charge = Coulomb (C)

If the P value is greater than alpha (0.05), than we __________ which means the data is................ If the P value is less than alpha (0.05), than we __________ which means the data is................

Hypothesis Testing: Begins with idea about what may be different *Null hypothesis: Always says two populations are equal, or single population can be described by parameter equal to given value *Alternative hypothesis may be nondirectional (not equal) or directional (mean of population A greater than mean of population B) -Z or t-tests -> rely on standard or t distribution *Test statistic determines likelihood that statistic was obtained by random chance (assuming null hypothesis was true) = p-value (compare p-value to significance level (alpha) which is usually = 0.05) If the P value is greater than alpha (0.05), than we fail to reject the null hypothesis, which means the data is not statistically significant (not much of a difference between the populations) If the P value is less than alpha (0.05), than we reject the null hypothesis, which means the data is statistically significant *Higher p-value = higher likelihood that the null hypothesis is true, so don't reject it *Alpha = level of risk we are willing to accept for incorrectly rejecting null hypothesis (type 1 error: likelihood that we report a difference when there isn't one) *A type I error occurs when the null hypothesis is incorrectly rejected. *Type 2 error (B): Incorrectly fail to reject the null hypothesis (there is a difference, but we didn't find it) *Power = 1-B: Correctly reject null hypothesis *Confidence = We did not find a difference, and there wasn't one, so we were correct Confidence Intervals: Determine range of values from sample mean and standard deviation *Usually 95% confidence level, use table to find z or t-score (multiply this by standard deviation int hen add and subtract from mean to get interval) *Wider interval = higher confidence level (95% is common) *As the confidence level increases, a confidence interval becomes wider: To increase the confidence level, one must increase the size of the confidence interval to make it more likely that the true value of the mean is within the range. Therefore, the confidence interval must become wider.

Internal and External Validity (Generalizability)

Internal Validity: Support for causality -> tendency of the same experiment to produce the same results when repeated (supports causality) External validity = Generalizability (ability to take generated information and apply it to larger group) Low generalizability = narrow sample conditions, don't represent target population High generalizability = representative of target population

Exponential Decay

Let n be the number of radioactive nuclei that haven't been decayed yet. The rate of nuclei decay (Δn/Δt) = - λ * n where λ = decay constant Tells us how the number of radioactive nuclei changes with time: Exponential decay: n = n0*e^-λt where n0 = number of undecayed nuclei at time t = 0 Decay constant is related to half life by: λ = ln 2/ (T 1/2) = 0.693 / (T 1/2) Y-axis: Percentage of radioactive nuclei remaining X-axis: Number of half lives

Magnification Equation

Magnification = -I/o -image size/ object actual size If I is negative and o is positive, magnification is positive positive magnification = upright A negative magnification indicates that the image is inverted. Absolute value of m tells you if image is smaller or larger than object | m | > 1 means image is bigger than object | m | = 1 means image = size of object

Positive and Negative Controls An experimenter is attempting to investigate the effect of a new antibiotic on E. coli. He plates cells and administers one milliliter of the antibiotic. Which of the following is an appropriate negative control in this experiment? A. A plate with no cells that was coated with one milliliter of antibiotic. B. A plate with E. coli and no additional treatment. C. A plate with E. coli and one milliliter of isotonic saline. D. A plate of epithelial cells treated with one milliliter of antibiotic.

Positive: ensures a change in the dependent variable when it is expected (receives treatment with known result) Negative: ensures no change in the dependent variable when no change is expected (used to assess for placebo effect) Experimental group falls in between these 2 extremes Correct Answer: C Explanation: The purpose of a control is to keep the conditions of two experiments as close as possible to establish causality. In this case, the one milliliter volume addition might have impacted the growth of E. coli; thus, we must control for this by administering an equal volume of a theoretically inert compound to a plate of E. coli.

Measurements of Distribution

Range: An absolute measure of the spread of a data set, while interquartile range and standard deviation provide more information about the distance that data falls from one of the measures of central tendency -Use to determine if something is an outlier -Range: Difference between its largest and smallest values Range = x max - x min -Heavily effected by outliers, but number of data points don't matter -When you can't calculate standard deviation, 1/4 of the range can be used as estimate Interquartile range: Related to median (2nd quartile), and 1st and 3rd quartiles -Divide data sets into 4 parts with each having 1/4 of entire set To find 1st quartile range: Sort in ascending order, multiply n by 1/4 (if this is a whole number, then Q1 = mean of this number and next number up) -If it is a decimal, round UP to the next whole number To find 3rd Quartile range, multiply n by 3/4 and repeat Interquartile range (IQR) = Q3 - Q1 Can be used to find outliers: any value more than 1.5X interquartile range above or below = outlier *1.5 X IQR below Q1 or 1.5X IQR above Q3 Box Plot:Box bounded by Q1 and Q3, Q2 in line in the middle (median) *50% of data between Q1 and Q3, 25% in each box Whiskers = maximum and minimum values of data set (within 1.5X IQR) -> outliers shown outside of whiskers Shows range, median, quartiles, and outliers Useful for large amounts of data

Specific Heat (c)

Relationship between heat and temp = specific heat (c) Specific heat = amount of heat energy required to raise 1 g of substance by 1 deg C or unit K Specific heat of liquid water = 1 calorie per gram unit Kelvin (1 cal/g*K) = 4.184 J/g*K *Specific heat changes by phase

Belmont Report (1979): 3 pillars of research ethics *Inspired by Tuskegee Experiment RJB

Respect,Justice, Beneficence Respect for persons: Honesty between subject and researcher -Informed consent -No coercive influence (Children, pregnant women, and prisoners are considered especially at risk for coercion) -Ability to cease participation -Institutional review boards put in place systematic protections against unethical studies -Confidentiality Justice: Applies to selection of topic and execution of research -Morally relevant differences: Not everyone should be treated exactly the same (age) -Not morally relevant: Race, ethnicity, sexual orientation, financial status (you should not treat people differently because of these) -Justice increases external validity through increasing diversity -Violation of justice: Choosing study participants that are not part of target population More inclusive version of beneficence Maximize good, minimize bad: do things int he least painful way possible -Equipoise: One can't approach research with knowledge that one treatment is superior to another -> providing an inferior treatment= harm

Statistical Significance vs. Clinical Effect

Statistical significance- are results due to random chance? -Refers to low likelihood of experimental findings being due to chance Clinical significance- are results clinically meaningful? Was there a notable or worthwhile change in health status as a result of our intervention Statistical significance does not imply clinical meaningfulness -Refers to usefulness or importance of experimental findings to patient care of patient outcomes

Centripetal Acceleration (ac) Centripetal Force (Fc) Centrifugal force

The acceleration of an object that travels in a circle; always directed towards the center of the circle if the object is in uniform circular motion ac = v^/r Centripetal force generates centripetal acceleration (both vectors, acceleration always in same direction as net force)(this acceleration keeps object in circular pathway) *No more centripetal force = object exits circle path and assumes path along tangent line Fc = m*v^2 / r (equation for centripetal force) F = ma, so centripetal acceleration = v^2 /r where Fc is magnitude of the centripetal force, m is mass, v is speed, and r is the radius of the circular path *Centripetal force Usually the result of gravity, tension, or a normal force Centrifugal Force : FU, I'm out of here. Not real, opposite of centripetal force

Field Lines

The direction of electric field always goes from positive to negative *E field lines will always point in the direction a force would be exerted on a positive charge field lines for a positively charged particle will always point away from the particle in a radial pattern, regardless of the direction in which the particle is moving. This is because field lines point in the direction a positive test charge would move in that field (Positive to negative).

Normal and Skewed Distribution

The mean, median and mode are all the same at the center of the distribution Basis of the bell curve Approximately 68% of the distribution is within one standard deviation of the mean, 95% within 2, and 99% within 3 Counterpart of normal distribution is standard distribution Standard distribution = normal distribution with a mean of 0 and a standard deviation of one When the spread of data is not symmetrical meaning the data clusters to one end. The mode is located at the highest point, then the median and finally the mean. (mean is more susceptible to outliers, mode really isn't affected by outliers, and median can be (so it is in the middle)) The direction of skew is determined by tail, not the bulk of distribution: The visual shift in data opposite direction of skew -Negatively skewed distribution has tail on left (negative side) -Positively skewed distribution has tail on right Bimodal Distribution: 2 or more peaks 2 peaks with valley in between = bimodal -Technically, you can have bimodal distribution with only one mode if one peak is slightly higher than the other, but even when peaks are different sizes, we still call it bimodal -Can sometimes be measured separately, but don't have to be

4 core ethical tenets

beneficence: Obligation to act in patients best interest nonmaleficence: Obligation to avoid things where potential harm outweighs good autonomy: Respect Patient's decisions justice: Responsibility to treat people fairly and and distribute care

3 Types of Observational Studies

cross-sectional, case-control, cohort Cohort: Form of longitudinal study (follows the same subject over time) -> subjects sorted into different groups based on exposures and then followed to see if they end up with the outcome (following equal number of smokers and non-smokers for 20 years to see who develops more lung cancer) (better when exposure is rare) Cross-sectional: Single point in time: exposure and outcome ascertained together Case-control: Working backwards: start with outcome, work back to see if they had exposure (better when outcome is rare) Often look for connections between exposure and outcome -> but CANNOT demonstrate causality (but tendency toward casualty can be shown with Hill criteria)

Hill's Criteria

describe the components of an observed relationship that increase the likelihood of causality in the relationship -First criteria has to be present -More criteria = more likelihood -Not proven, can determine correlation, not causation *Correlation quantified with correlation coefficient between -1 and +1 (-1 = strong negative correlation, 0 = no correlation, +1 = strong positive correlation ) Temporality: Exposure (independent variable) must be before outcome Strength: More variability in outcome variable explained by variability in study variable Dose-Response Relationship: Proportional relationship Consistency : Similar in multiple settings Plausibility: Reasonable mechanism, supported by literature Consideration of alternative explanations : Confounders Experiment : Can an experiment be performed to determine casualty 100% Specificity: Change in outcome only produced by change in independent variable Coherence : Consistent with current state of knowledge

Ln(x) Natural Log of X

log (x) * 2.303 Natural log = log base e (as opposed to usual log base 10) e = 2.72

Rules of Logarithms

loga(1) = 0 * Lowercase a means it is the base log a(A) = 1 log (A X B) = log A + Log B log (A / B) = log A - Log B log (A^B) = B *log A log (1/A) = - log A "p" is shorthand for -log, so pH is -log [H+] and pKa is -log (Ka) The most common bases used are base 10 (common logarithm) or base e (natural logarithm) e = Euler's number = 2.7183 log e = ln Converting common Logs to natural logs: log x = ln x / 2. 303 When estimating the logarithm of a number, use scientific notation. If the value is written in proper scientific notation, it will be in the form of: n x 10^m. log (nX10^m) = log (n) + log (10^m) = m + log (n) Because n is a number between 1 and 10, its logarithm will be a decimal between 0 and 1 because (log 1 = 0 and log 10 =1). The closer n is to 1, the closer log n will be to 0. The closer n is to 10, the closer it will be to 1. TO estimate, just move the decimal of n so that: log (nX10^m) = log (n) + log (10^m) = m + log (n) = m + 0.n This is similar to calculating negative logarithms and negative exponents for pH -log ( n X 10^-m) = m - 0.n Estimate log 7,426,135,420 log (7.5 X 10^9) (count everything but the number in front of the decimal) log (7.5) + 9 -> 0.75 + 9 = about 9.75

Equation for heat energy/heat transfer/that relates the heat gained or lost by object and change in temp:

ΔQ = mc*Δ T (looks like MCAT) Δ Q = heat gained or lost m = mass c= constant (specific heat) Δ T = change in temp in deg C or K

Change in entropy:

ΔS = Q of rev (Qrev) / T where ΔS = change in entropy (units = J/ mol* K), Qrev = heat gained or lost in a reversible process, and T is temp in kelvin *When energy is distributed into system at given temp, entropy increases (energy out of system = entropy decrease)

Atmospheric Pressure

- Remember: Temperature will not change until liquid is completely vaporized -The boiling point of a liquid depends on the atmospheric pressure. Higher the atmospheric pressure, higher the boiling point. At the top of Mount Everest, water boils at a much lower temperature than 100, because the atmospheric pressure there is much less than that at sea level. (This also means that it takes a longer time to cook food at the top of Everest than at sea level.) Pressure cookers cook food in lesser time because the temperature of boiling water inside it is much higher than 100 degrees due to increased pressure. - At higher elevation atmospheric pressure decreases hence the boiling point decreases Changes with altitude Below sea level = more than 1 atm of pressure Above sea level (in the mountains) = less than 1 atm (decimal, like .93 atm or something

Linear Motion Equations

-Falling objects exhibit linear motion with constant acceleration -Velocity and acceleration vectors are parallel or antiparallel Equations: v= v0 + at x = v0t + at^2/2 v^2 = v0^2 + 2ax x = v(with line over it)*t where x v and a are displacement (when motion is vertical use y instead), velocity, and acceleration vectors v0 is initial velocity v with line over it = average time With free fall problems, air resistance is assumed negligible so object falls with constant acceleration of gravity (9.8 m/s^2) (Will not reach terminal velocity) -This is called free fall *The only force acting on both free fall and projectile motion is gravity

Torque

-Torque (measured in N*m) generates rotational motion (primary motivator for rotational movement that combines force, lever arm, and angle between), depends on the force and length of the lever arm and angle at which force is applied T = r X F = rFsin(theta) where r is length of lever arm, F is magnitude of force, and theta is angle between the lever arm and force vectors *Occurs in the absence of net torques *Constant angular velocity (usually 0 on MCAT) sin90 =1 , so torque is greatest when force is applied 90 degrees (Perpendicular) to lever arm sin0 = 0 so there is no torque when force applied parallel to lever arm Rotational Equilibrium exists only when vector sum of all torques = 0 (second condition of equilibrium) Torque clockwise = negative, counterclockwise = positive *either the object is not moving at all (more common) or object rotating with constant angular velocity Torque 1 = torque 2 r1F1*sin(theta1) = r2F2*sin(theta2) r1*mg*sin90 = r2*mg*sin90 r1m1=r2m2

Laminar Flow Poiseuille's Law

-smooth and orderly (smooth lines around object) -often modeled as layers of fluid that flow parallel to each other Upward force = buoyant force, downward force = gravity *If the maximum buoyant force is larger than the force of gravity on the object, it will float. This is true if the object is less dense than the fluid it is in *NOTE: Layers may not have same linear speed (layer closest to wall may be slower) Calculate the rate of flow for Laminar flow with Poiseuille's Law Q = Flow = (pi*r^4*Δ P) / (8nL) Where Q is rate of flow, r is radius of tube, ΔP is pressure gradient, n (eta) is viscosity, L is length of pipe *Relationship between radius and pressure gradient is inverse and exponential (more radius = less pressure assuming constant flow rate) Fluids with low viscosity and laminar flow can be approximated to be conservative systems (total mechanical energy of system is constant if we discount small viscous drag forces that occur in all real liquids)

Calorie (C = 1000 c)

1 Cal = 1000 cal = 4184 J

1 V =

1 J/C = 1 N*m/C Remember V = Ed, so if you are given a quantity in N/C and a quantity in Volts, dividing voltage by electric field (in N/C) will give us distance in meters

ATM to Pascals

1 atm = 101,325 Pa

3 System types

A system is a portion of the universe that we are interested in observing or manipulating. The rest of the universe = surroundings 3 main types: Isolated systems: not capable of exchanging energy or matter with surroundings (total change in internal energy = 0) -Rare, bomb calorimeter, entire universe (because nothing surrounds the universe) *Calorimeters (like coffee cup calorimeters) are our best approximations of isolated systems, where neither energy nor matter is exchanged with the environment Closed Systems: Capable of exchanging energy but not matter (gases in vessels with moveable pistons Open system: Exchange both matter and energy with environment -Matter carries energy, and more may be transferred in the form of heat or work -Boiling pot of water, human beings, unconfined combustion reactions

Alpha and Beta Decay and Gamma Decay *note: mass number is top number

Alpha Decay: Emission of an alpha (a) particle, which is a (4 over 2) He nucleus thats has 2 protons, 2 neutrons, and no electrons -Alpha particles do not have any electrons, so they carry a charge of +2 -> they interact with matter very easily and do not penetrate shielding (like lead sheets) extensively -Very massive compared to beta particle and carries twice the charge -Emission of a particle means that the atomic number of the daughter nucleus will be two less than parent nucleus and the mass number will be four less Beta Decay Emission of a Beta (B) particle (electron: Given by symbol e- or B-) *Even though electrons don't reside in nucleus, they are emitted by the nucleus when a neutron decays into a proton, a Beta particle and antineutrino (v with line over it) *Don't worry about neutrino and antineutrino for MCAT -Electron almost 2000 X lighter than proton, so beta radiation from radioactive decay is more penetrating than alpha radiation Induced decay (positron emission) -> positron released (has the mass of electron but carries positive charge)(e+ or B+). Neutrino (v) emitted here as well (O15 (parent) -> N15 and B+) During B- decay (image shown), neutron converted into proton and B- particle (Z=-1, A = 0) -Atomic number of daughter nucleus will be one higher than parent nucleus, and mass number will not change *Remember, Z = atomic number = number of protons (Add one) *A = mass number = protons + neutrons (does not change) During B+ decay (image same but B+ instead of B- on far right and Z-1 instead of Z+1), proton converted into a neutron and a B+ particle (Z = +1, A=0) is emitted. Atomic number of daughter nucleus will be one lower and mass number won't change In both types of beta decay there needs to be conservation of charge. If negative charge (B-) is produced, a neutron needs to be converted to proton. If positive charge (B+) is produced, proton converted to neutron to maintain charge *NEGATIVE BETA DECAY PRODUCES NEGATIVE BETA PARTICLE AND POSITIVE BETA DECAY PRODUCES POSITIVE BETA PARTICLE In alpha decay, an element loses two protons. In positron decay, a proton is converted into a neutron. Gamma decay has no impact on the atomic number of the nuclide. Therefore, two alpha decays and two positron decays will yield a daughter nuclide with six fewer protons than the parent nuclide. Gamma Decay: Emission of γ rays (gamma rays), which are high frequency, high energy photons They don't carry a charge and lower energy of parent nucleus without changing mass or atomic number High energy state of parent shown with asterisk No changes occur in mass number or atomic number, only a γ ray is emitted *Note: Gamma radiation produces electromagnetic radiation (rather than nuclear fragments), so it can be detected on an atomic absorption spectrum Alpha Decay: Emits (4 over 2) He, ΔZ (atomic number = number of protons) = +2 and ΔA= +4 (mass number) Beta-Negative decay: Emits electron (B- or e-) and antineutrino (v with line over it), ΔZ = +1 and ΔA = 0 (stays same) Beta-Positive decay: Emits positron (B+ or e+) and neutrino (v with line over it), ΔZ = -1 and ΔA = 0 (stays same) Gamma Decay: Emits gamma ray (y), ΔZ and ΔA don't change Electron Capture: Emits nothing, but absorbs electron from inner shell), ΔZ=-1 and ΔA= 0 (no change)

The voltage across the terminals of an isolated 3μF capacitor is 4V. If piece of ceramic have dielectric constant k=2, placed between plates, what is new charge, capacitance, and voltage. A 3μF capacitor is connected to a 4V battery (no longer isolated). If piece of ceramic have dielectric constant k=2, placed between plates, what is new charge, capacitance, and voltage.

Charge: Adding dielectric has no effect on charge in isolated capacitor (no new charge, same as before) Q = CV -> 3μF * 4 = 12 μC Capacitance: C'= kC C' = 2*3μF = 6 μF New Voltage: V = Q/C, so V' = Q'/C' V = 12 μC/ 6 μF = 2 V Next question: Capacitance: C' = kC C' = 2*3μF = 6 μF Voltage: Voltage held constant by battery, so it stays sat 4 V Charge: Q = CV -> Q' = C'V' Q' = 6 μF * 4V = 24 μC

__________ mirrors and ____________ lenses are both converging ___________ mirrors and __________ lenses are both diverging

Concave mirrors and convex lenses are both converging Convex mirrors and concave lenses are both diverging *For diverging lens (concave) and mirrors (convex) -> focal length is negative

Lenses for Vision Correction

Converging lenses are needed for people who are farsighted (reading glasses) -Farsightedness = hyperopia -Objects farther away are seen clearly, while objects up close are blurry -Always thicker at center Diverging lenses (standard glasses) are needed by people who are nearsighted -you can see objects clearly Up Close, but objects farther away are blurry -Always thinner at center -nearsightedness = myopia Bifocal lenses are corrective lenses that have two distinct regions The eye has an optical power of around 60 diopters Most contact lens wearers have prescriptions between 0.25 and 8 diopters (+ and -), so even at tis worst the human eye can maintain its optical power at about 87% of maximum

Convex and Concave Mirrors

Convex, diverging: image still right side up but distoreted, smaller, wider field of vision (security mirrors and passenger side car mirrors) -Parallel light reflected in multiple directions (larger vision field) Concave and convex mirrors produce images by reflection, and concave and convex lenses produce images by refraction Images from mirrors can be real (light actually converges at the position of image) or virtual (light only appears to come from the position of the image but does not actually converge there) *Real images can be projected onto screen Convex: Passenger side mirror: Diverging, everything appears smaller and farther away) Concave Mirrors: Make-up mirror: everything appears bigger and closer (Converging) -Can produce real, inverted images or virtual, upright images depending on where object is relative to focal point ConCAVE: like looking into cave because it curves inward (thinnest in middle) = Converging (light rays converge after they reflect) All spherical mirrors: f = r/2 where the radius of the curvature (r) is distance between C and the mirror Distance between object and mirror = o Distance between image and mirror = i f = r/2 1/f = 1/o + 1/i = 2/r All values have the same units If the image has a positive distance (i> 0) it is a real image (in front of mirror) If the image has a negative distance ( i<0) it is virtual and located behind the mirror

In some forms of otosclerosis, the stapedial foot plate, which transmits vibrations from the bones of the middle ear to the fluid within the cochlea, can become fixed in position. This limits the displacement of the stapedial foot plate during vibration. Based on this mechanism, which of the following symptoms would most likely be seen in an individual with otosclerosis? A. An increase in the perceived volume of sounds B. A decrease in the perceived volume of sounds C. An increase in the perceived pitch of sounds D. A decrease in the perceived pitch of sounds

Correct Answer: B Explanation: Saying that the stapedial footplate has limited displacement during vibration is another way of stating that the amplitude of the vibration has been decreased. Because amplitude is related to intensity, and intensity is related to sound level, the perceived sound level (volume) will be decreased as well. Pitch, described in choices (C) and (D), is related to the frequency of a sound, not its amplitude.

Which of the following describes the image formed by an object placed in front of a convex lens at a distance smaller than the focal length? A. Virtual and inverted B. Virtual and upright C. Real and upright D. Real and inverted

Correct Answer: B Explanation: The image produced by a convex lens can be either real or virtual. It is real if the object is placed at a distance greater than the focal point, and virtual if the object is placed at a distance less than the focal point (between the focal point and the lens). Remember that for a single mirror or lens, an image that is real must be inverted and one that is virtual must be upright. In this question, the object is placed in front of the focal point, so the image must be virtual and, therefore, upright. We could also determine this from the optics equation. If f > o, then 1/f - 1/o is negative, and i is therefore negative (virtual).

Which of the following are able to produce a virtual image? I. Convex lens II. Concave lens III. Plane mirror A. I only B. III only C. II and III only D. I, II, and III

Correct Answer: D Explanation: All images produced by plane mirrors will be virtual, so statement III is true. The same goes for diverging species (convex mirrors and concave lenses), so statement II is true. Converging species (concave mirrors and convex lenses) can produce real or virtual images, depending on how far the object is from the species, so statement I is also true.

Current Voltage Electromotive force (emf) Conductivity

Current: Movement of positive charge through conductive material over time (amperes: C/S) Voltage: Potential difference between two points (V: J/C) *VOLTAGE CANT BE MORE THAN EMF Electromotive force (emf): Potential difference of the voltage source for a circuit, usually a battery (also measured in Volts) Conductivity: Reciprocal of resistance, measure of permissiveness to current flow (measured in Siemens (S))

Sign conventions for lenses

For both lenses and mirrors, positive m = upright image and -m = inverted image For both, positive image distance means image is real (located on real (R) side) whereas negative distance means the image is virtual The difference is, for mirrors and lenses, the "Real" sides (where light actually goes) are opposite -For mirrors, the real side is where light is reflected back, so its on the same side as the object (in front of mirror) -For lenses, they don't actually reflect light, so the real side is on the other side of the lens (light is reflected through) (virtual side is on the same side as the light source) BUT just because the object of a single lens is on the virtual side does not make it virtual (objects are real, with positive distance) For both mirrors and lenses, focal length and radii of curvature relationships are same Converging species have positive focal lengths have radii of curvature (Concave mirrors and convex lenses) Diverging species have both negative (Convex mirrors and concave lenses) *remember, lenses have to focal lengths and two radii of curvature *For thin lens, where thickness is negligible, the sign of focal length and radii of curvature are given based on first surface the light passes through

Electromagnetic Spectrum

From longest wavelength / lowest energy / Lowest frequency: Long radio waves, AM radio waves, FM radio waves, Microwaves, Infrared, Visible light spectrum (red to violet), ultraviolet, X-rays, gamma (y) rays Frequency goes from 300 kilohertz (smallest frequency = radio waves) to 3X10^21 Hz (biggest = gamma rays) If a light ray has a frequency of 5.0X10^14, wavelength = c/f = 3X10^8 / 5.0X10^14 = 6X10^-7 meters (600 nm), so its within visual light spectrum Visible light spectrum from 400-700 nm, full spectrum goes from about 10^-16 meters to 10^8 meters Can be measured in mm (10^-3 m), micrometers (10^-6), nm (10^-9) and A (angstrom, A with little circle over it = 10^-10 m) Violet has the shortest wavelength (around 400) and red has the highest (around 700) Lowest Energy/frequency = highest wavelength Light that contains all colors in equal intensity = white The color of an object that does not omit its own light is dependent on the color of light that it reflects Object that appears red is one that absorbs all colors except for red (it reflects red) -So, a red object under green illumination will appear black because it absorbs green light and has no red light to reflect *We see colors that are NOT absorbed Blackbody: ideal absorber of all wavelengths, which would appear completely black (if at lower temp than surroundings) *Ultraviolet light is more likely to induce a current in a metal than visible light. This is because photons of ultraviolet light have a higher energy

Capacitors and Capacitance

Have ability to hold charge at particular voltage (stores amount of energy in the form of charge separation) Capacitance: The ratio of the magnitude of the charge on one plate to the potential difference (voltage) across the capacitor C= Q/V (Q= +Q on positive plate + -Q on negative plate) Capacitance measured in Farads (1F = 1 C/V), but that's a lot, so it is usually measured in microfarads (1X10^-6 F) or picofarads (1X10^-9 F) C = ε0 (A/d) where ε0 is the permittivity of free space (8.85X10^-12 F/m) A is area of overlap of 2 plates, d is separation of two plates (separation sets up uniform electric field with parallel field vectors)

Intensity

I = P/A P is power produced by the source and A is the area over which the power is spread Power = Intensity * Area Intensity is proportional to the square of the amplitude (doubling amplitude = 4 times the intensity) Sound waves spread sound over larger and larger areas the further they travel from the source *Intensity inversely proportional to square of distance When light of a high frequency (usually blue light or UV light) is incident (An incident ray is a ray of light that strikes a surface) on a metal in a vacuum, metal atoms emit electrons -> these liberated electrons produce current (net charge flow per unit time (I=Q/t) *Magnitude of current is proportional to intensity * If light beams frequency is above the threshold frequency of metal, light beams of greater intensity produce more photons per unit time that fall on electrode producing more electrons liberated *Greater intensity = more electrons liberated *When light frequency is above threshold frequency, magnitude of resulting current is directly proportional to intensity and amplitude of light beam The greater the intensity, the greater the number of incident photons and, therefore, the greater the number of photoelectrons that will be ejected from the metal surface (provided that the frequency of the light remains above the threshold). This means a larger current. Remember that the frequency of the light (assuming it is above the threshold frequency) will determine the kinetic energy of the ejected electrons; the intensity of the light determines the number of electrons ejected per time (the current).

Current (I) measured in Amps =

I = V/R V = Volts R = resistance (Ω) Magnitude of I = amount of charge (Q) passing through conductor per unit time Δt I = Q/Δt So, Q = V* Δt/ R Measured in ampere ( 1 A = 1 Coulomb / second) Current is direction of positive flow (from higher electrical potential to lower electrical potential -Direction of current is opposite of actual electron flow (Which is from low potential to high potential, reducing their potential energy) *regions around the positive charges are considered high potential, and regions around the negative charges, low potential. Since electrons are negative they should be repelled by the negative charge and attracted by the positive charge, move from regions of low potential to the regions with high potential (and because the negative charge of electron is then close to positive charge, there is less electrical potential energy, which is the energy of how far electron can "fall" (less space to fall = less energy, and there is less space to fall now because e- is right by +) Positive charge moves from points with high potential to points with lower potential. Negative charge moves to points with higher potential. Positive charge moves to a lower potential energy. Negative charge moves to a lower potential energy. ANYWAY: Current is opposite to the direction of electron flow (electrons go from low to high, current goes from high to low electrical potential) 2 patterns of currents: DC (charge flows in one direction)(house hold batteries) and AC (Charge flow changes directions periodically ) (Used for longer distances ) *Current only flows in conductive materials

Exponents

If the base is the same, for addition, b^n + b^n = 2b^n -If they have different bases, don't try and add Multiplication and division with same base: X^A * X^B = X^(A+B) X^A / X^B = X^(A-B) For a number that is raised to an exponent and then raised to another, the two exponents are multiplied (X^A)^B = X^(A*B) When a fraction is raised to an exponent, both are raised (X/Y)^A = X^A / Y^A Negative exponents are inverse functions: X^-A = 1/ X^A For fractional exponents, numerator can be treated like exponent and denominator represents root of the number: X^A/B = Bsqrrt (X^A) sqrrt of 4.9X10^7 -> sqr rt of 49X10^8 = 7X10^4

Thermodynamic Processes

Isothermal (ΔU =change in internal energy = 0): no temperature change/constant temp/no change in internal energy (First law of thermodynamics (ΔU = Q-W) reduces to Q=W) Isobaric: Constant pressure (First law of thermodynamics reduces to multiple possible forms) Isovolumetric/Isochoric: Constant volume = no change in work (W=0)(First law of thermodynamics reduces to ΔU= Q) *Work = PΔV Adiabatic (Q=0): no heat exchange (First law of thermodynamics reduces to ΔU= -W) Closed loop process graph: Work is area inside the loop

Kinetic Energy Equation

KE=1/2mv^2 m is mass in kilograms, v is speed in meters/second, k is kinetic energy in joules (J)(kg*m^2/s^2) *Faster speed = more kinetic energy (as speed doubles, kinetic energy quadruples)

Kirchoff's Rules

Kirchhoff's Junction Rule: At any point in a circuit, the use of currents directed into points = sum of currents directed away from point I into junction = I leaving junction -number of electrons entering and leaving point are the same Kirchhoff's Loop Rule: -Closed circuit loop: Sum of voltage sources = sum of voltage (potential) drops -Consequence of conservation of energy -Kirchhoff's loop rule states that the total potential difference around any closed loop of a circuit is 0 V. -No excess energy appears or disappears (but it can change forms) -terms of voltage (J/C) -V source = V drop -If all of the voltage was not "used up" in each loop, it would build up after each trip (which is impossible) -Only true for closed loop

Resistance

R (Ohms) = pL/A Where p (rho) is resistivity (measured in meters X ohms), L is length of resistor, and A is cross-sectional area (m^2) Resistivity is the number that characterizes the intrinsic resistance to current flow -Resistance is directly proportional to length and resistivity (longer resistor = more resistance) -Inverse relationship between resistance and area (more area = less resistance, because it increases the number of pathways through resistor (conduction pathways)) -Wider area, more current can flow Resistance of resistor is dependent on resistivity, length, cross-sectional area, and temp

Power (P) Measured in Watts (J/sec)

Rate at which energy is transferred from one system to another (how fast work happens) P = W/t = ΔE/t W is work, which equals change in energy (ΔE) t is time over which work is done Power is measured in Watts (W) = (J/second) In electrical power, we use P = IV where I is current and V is electrical potential difference) The rate at which energy is dissipated from resistor: P= IV = I^2R = V^2/R (All related to Ohm's Law V= IR *High voltage power lines carry smaller current, so less energy is lost from system (High current = high energy loss) P = 1/f Power (P) measured in diopters, f = focal length in meters P and f are positive for converging lens (convex) and negative for diverging lens (concave)

Reflection VS Refraction VS Diffraction

Reflection: angle of incoming light is same as angle of reflected light, allows us to see objects (mirrors) Refraction: the bending/change of speed when light encounters a different medium (lenses) Diffraction: light passes through slit and bends slightly around the edges Dispersion: Dispersion involves the breaking up of polychromatic light into its component wavelengths because the degree of refraction depends on the wavelength. We are told that the incident light is monochromatic or, in other words, of only one wavelength; therefore, light will not be dispersed Polarization: alignment of the electric field component of light waves.

Thermal Expansion

Rising temp = increasing length of solid , decrease = decrease The amount of length change is proportional to the original length of the solid and the increase in temp according to: ΔL=αLΔT Where ΔL = change in length, a (alpha) = coefficient of linear expansion (constant, usually with units of K^-1 or deg C^-1), L = original length, ΔT is change in temp *Negative answer = decrease in length *Expansion result of increase in dimension at all point. If object initially longer, it will experience greater expansion *THIS GIVES YOU CHANGE IN length, not final length For liquids: Formula for volumetric thermal expansion for liquids and solids: ΔV = B(beta)*VΔT where ΔV is change in volume, beta = coefficient of volumetric expansion, V is original volume (constant that characterizes specific materials volume changes as temp changes -> its value = 3X coefficient of linear expansion (alpha) so that B = 3a)

Newton

SI unit of force = Kg* m /s^2

Watt

SI unit of power = J/ sec = Kg*m^2/s^2

Density

Scalar quantity (no direction) Density (p = rho) = mass (m) / volume (V) In units of kg/ m^3 or g/mL or g/cm^3 *millimeter = cubic centimeter 1 g/cm^3 = 1000 kg/m^3 (even though you would think it would be the other way around, but there are 1000 L in a cubic meter The weight of any volume with known density can be calculated by multiplying density (p) by volume and acceleration due to gravity Weight (Fg) = p(density)*V*g Density of fluid compared to that of pure water at 1 atm and 4 deg C (specific gravity) -> at 1 atm and 4 deg C, water has density = 1 g/cm^3 Specific gravity (SG) = p (density) / 1 g/cm^3 -Density of object / density of water -Unitless number / dimensionless -Can determine if object will sink or float A specific gravity = 1 would be completely submerged but not sink We have specific gravity of about 1.1

Sinusoidal Transverse and Longitudinal Waves

Sinusoidal waves have individual particles that oscillate back and froth with a displacement that follows a sinusoidal pattern Transverse waves: direction of particle oscillation is perpendicular to propagation (movement) of wave -Electromagnetic waves (x-rays, microwaves, visible light) -Energy is delivered in the direction of wave travel, so for transverse wave, the particles are oscillating perpendicular to the direction of energy transfer -Longitudinal waves have particle oscillation parallel to the direction of propagation and energy transfer -Sound waves -Oscillates through cycles of compression and rarefaction (decompression)

Solid to liquid: Fusion or melting (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to solid: freezing or solidification (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to gas: Evaporation or vaporization or boiling (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Gas to liquid: Condensation (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Solid to gas: sublimation Gas to solid: deposition

Solid to liquid: Fusion or melting (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to solid: freezing or solidification (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to gas: Evaporation or vaporization or boiling (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Gas to liquid: Condensation (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Solid to gas: sublimation Gas to solid: deposition

Right Hand Rule

Thumb: Velocity (indicates direction of movement) *Can also be current Fingers/index finger: Field lines Palm/middle finger: Force on positive charge (back of hand = negative charge) *Think "use the force" -The magnetic force must always point radially toward the center of the circle Negative Charge: If you use your right hand, thumb is left, back of hand is down (opposite of middle finger, because charge is negative, so back of hand represents force towards the center of the circle) -The magnetic force must always point radially toward the center of the circle. Index finger (magnetic field) pointing towards you now, out of page *If the current is to the top of the page, and the uniform magnetic field (B) is into page, then sin θ = sin 90 = 1, and the force (direction of palm/middle finger) is going to the left

What are the requirements to have a nonzero electric field? A nonzero magnetic field? A nonzero magnetic force?

To create an electric field, you need a charge To create a magnetic field, you need a moving charge To create a magnetic force, you need an external electric field acting on a charge moving any direction except for parallel or antiparallel to the external field

Potential Energy Stored in Capacitor

U = 1/2 CV^2

Equation for potential energy of spring system Elastic Potential Energy

U = 1/2 kx^2 where k is spring constant (measure of stiffness) and x is magnitude of displacement from equilibrium

Gravitational Potential Energy

U = mgh where U is potential energy in joules, m is mass in kilograms, g is the acceleration due to gravity, h is height above datum (usually sea level)

If two objects are traveling toward each other, how does the apparent frequency differ from the original frequency? Traveling away from each other? One following the other?

Use Doppler equation Travling toward = top sign used Apparent frequency is higher than actual frequency f' = f (V+VD/ V-VS) Away = bottom sign used Apparent frequency lower than original frequency f' = f (V-VD/ V+VS) Following: Either f' = f (V+VD/ V+VS) or f' = f (V-VD/ V-VS)

Velocity (V)

V=Δx / Δt V= displacement / change in time

Electric Potential Energy

Voltage (V) = k(constant) * Q (point charge)/r (distance from point charge) Electrical potential energy is U = k*Qq/r or U = V(voltage)*q(charge) Voltage (ΔV) is equal to the quotient of the amount of work done (W) divided by the charge of the particle on which the work is done (q), according to the equation V = delta U /q = W /q

Work

W (work, in joules) = F*d = Fdcos(theta) where F is magnitude of applied force, d is magnitude of displacement, and theta is angle between the applied force vector and displacement vector *First, solve for F using F = mg, then plug into equation *If there is no displacement, there is no work *During uniform circular motion, no work is done Work can be calculated using: W = PΔV (Pressure * change in volume) So, 3 methods of calculating work: W = Fd cos theta (dot product of force and displacement vectors) W = P Δ V (area under a pressure-volume curve) *If gas is neither expanded nor compressed (no change in volume, isovolumetric = isochoric) then no work is done W net = ΔK (Work-energy theorem)

Wave Speed (V)

frequency x wavelength ( v = f λ ) The distance from one maximum (crest) to the next is called the wavelength (λ) f= frequency = number of wavelengths passing a fixed point per second (measured in hertz (Hz) or cycles per second (cps) *20-20000 Hz are generally audible to humans, high frequency hearing declines with age The inverse of frequency (cycles per second) is period (T) (seconds per cycle) T = 1/f Also: Period (T) = λ/v Angular frequency (w) is measured in radians per second (often used with simple harmonic motion in springs and strings (pendula) w = 2pi*f = 2 pi / T *The magnitude of the angular frequency is larger than the magnitude of the frequency. Waves oscillate about central point called equilibrium position Displacement (x) describes how far point is from equilibrium position (expressed as vector quantity) Amplitude (A): Maximum magnitude of displacement from equilibrium in a wave (Not the total height (which would be 2X amplitude), just from central point up or down) Pitch: Our perception of frequency lower frequency = lower pitch higher frequency = higher pitch

1 amu

mass of a proton 1.66 x 10^-27 g 1/12 the mass of 12 carbon atom

Refraction (Snell's Law)

n = c/v where c= speed of light in vacuum v is speed of light in medium n is dimensionless quantity called index of refraction Snell's Law: n₁sinθ₁=n₂sinθ₂, where n is index of refraction, c is speed of light, and v is speed of light in vacuum, and n1 and θ₁ refer to medium from which light is coming and n2 and θ2 refer to medium light is going in to. θ measured with respect to normal When light enters a medium with a higher index of refraction, it bends towards the normal (sinθ2 < sinθ₁, so θ2<θ₁) (going from air into water bends towards normal) When light enters medium with lower index of refraction, it bends away from normal Light will bend toward normal when going from low n to high n Light will bend _away from normal when going from high n to low n If incident angle is large than critical angle, total internal reflection will occur *When changing mediums, frequency stays the same, but wavelength changes. Going into higher index of refraction, wavelength slows * Frequency, Amplitude, Period do not change between mediums *from a low index of refraction to a higher one. According to Snell's law, the angle of refraction will be smaller than the incident angle (closer to the normal)

Buoyant Force Archimede's Principle

the upward force exerted by a fluid on a submerged object Archimede's Principle: A body that is fully or partially immersed in a liquid will be buoyed up by a force that is equal to the weight of the liquid displaced by the body.

First Law of Thermodynamics ΔU =

ΔU = Q -W W= work, measured in joules Work done BY the system is positive, work done ON the system is negative Heat (Q) positive = heat flows into system, negative = heat flows out of system The 1st law says that increase in total internal energy of system is caused by transferring heat into the system or performing work on the system (compression, W is negative, overall answer is positive). Decrease in total IE caused by when heat is lost from system and work is done by the system (expansion, W is positive so overall answer is negative)

Frictional Force Equation Static Friction Equation (same thing)

μs = Coefficient of static friction N = Normal Force (always perpendicular to surface) N = mg*cos(θ) F= mg mg = μs*N

Newton's 3 Laws

(1) Fnet = ma = 0 where fnet is net force: An object at rest will stay at rest unless acted upon by an unbalanced force and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced outside force; also known as Law of Inertia. (2) Fnet = ma: Acceleration is produced when a force acts on mass and the greater the mass of the object being accelerated, the greater amount of force is needed to accelerate that object. -An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector (No acceleration will occur when vector sum of forces results in cancellation of forces -Net force and acceleration vector point in same direction (3) Fab = -Fab: For every action there is an equal and opposite reaction. Car driven at constant velocity crashes into wall: First law: Prior to collision, vehicle has constant velocity so there is no acceleration or net force Second Law: Collision with wall = sudden deceleration -Acceleration means there is net force (massXacceleration) Third law: car exerts force on wall, and wall exerts = force back in opposite direction

Sin(30) Sin (45) Sin (60) Cos (0) Cos (30) Cos(60) Cos (90) tan30° tan^-1 (1) Degrees to radians Radians to degrees

1/2 √2/2 = 0.71 0.866 1 0.866 0.5 0 √3/3 45 degrees (pi/4) multiply by pi/180 *90 degrees X pi/180 = pi/2 multiply by 180/pi pi/2 X 180/pi = 90

A circuit is set up with 3 resistors. One branch through R1 = 3 ohms, then splits into two branches (parallel) through R2 = 2 Ohms and R3 = 6 Ohms. What proportion of total current will pass through each, and what is total resistance

100% of current goes through 1st resistor. Ratio of resistance for R2 and R3 = 1:3, so 3X more current will go through R2 than R1 (3/4 current through R2, 1/4 through R1) Total resistance = 3 + 1.5 = 4.5 Ohms

Electron Volt (eV)

1eV = 1.6X10^-19 J = amount of energy gained by electron accelerating through a potential difference of one volt

Relevant points in the three major temperature scales

Absolute 0: -460 deg F, -273 deg C, 0K Freezing point of water: 32 deg F, 0 deg C, 273 K Boiling point of water: 212 deg F, 100 deg C, 373 K A change of 10 K is equal to a change of 10°C. One degree Celsius is equal to 1.8 degrees Fahrenheit; therefore, 10°C = 18°F. Although the scale for Celsius and Kelvin have different 0 reference points, the size of their units are the same (1 deg C = 1 K) *But, there are 180 degrees difference from freezing to boiling in Fahrenheit, so the size of Fahrenheit unit is smaller! F = 9/5 C + 32 C= 5/9 (F - 32) K = C + 273 Body temp is 98.6 F or 37 degC *Length, volume, solubility, conductivity all change as function of temp *At what temperature do the Fahrenheit and Celsius scales give equal values? 233K

Absolute Pressure

Absolute pressure = Patm + pgz (gauge pressure) (where p = rho = density) The absolute and gauge pressures depend only on the density of the fluid, not that of the object. When the pressure at the surface is equal to atmospheric pressure, the gauge pressure is given by Pgauge = ρgz, where ρ represents the density of the fluid, not the object. If 2 objects are at the same depth, they must have the same gauge pressure.

Bernoulli's Equation

Bernoulli's equation says if more energy dedicated toward fluid movement then less energy dedicated toward static pressure Static pressure is the pressure associated with position; static pressure is sacrificed for dynamic pressure during flow. (measured by pitot tube) The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight. Venturi flow meter (image shown) and Pitot tube At equal heights, speed and pressure of a fluid are inversely related (the Venturi effect). Decreasing the speed of the water (increasing area) will therefore increase its pressure. An increase in pressure over a given area will result in increased force being transmitted to the piston.

Ohm's Law

Calculates voltage drop between 2 points in a circuit V = IR V= voltage drop I= current R = Magnitude of resistance (Ohms) -Current proportional to emf (voltage)

3 Mirror Types

Case 1: Converging (concave) mirror Distance of object >focal length (object outside of focal length) f is positive real and inverted di positive (image on same side of mirror as object) Magnification: Negative (inverted) *For lenses, only case 1 has real image too, and do>f and it has positive di and negative magnification, but it is a converging CONVEX lens *Inverted images are always Real Case 2 (converging mirror)(concave) F-positive di<f Image inside focal length Virtual rays don't actually go behind the mirror di negative (behind mirror) Magnification: Positive, m>1 (not inverted)(not negative) Like a make up mirror *Object between F and mirror -> image is virtual, upright, and magnified (rays appear to converge behind mirror, but they don't) Case 3 Diverging mirror (convex mirror) F=negative (behind the mirror) virtual Di negative (behind mirror) Magnification: Positive (not inverted), but, m<1 means smaller than object *Single diverging mirror only forms virtual, upright and smaller image -The further away the object, the smaller the image will be

3 Types of Lenses (Retract light)

Case 1: distance to image was positive (di>o so object on opposite side), m negative means its inverted (real image, rays actually do converge on other side)(Object outside of focal length = negative m) Case 2 is a magnifying glass (di<0, same side as object) (virtual image)(not inverted, larger image)(image on same side as object)(light rays appear to come from behind, negative distance)(Positive magnification because image is larger) Both case 1 and 2 have positive focal lengths, are for convex/converging lenses For converging lens, you can have object inside focal length (real image that is inverted) or outside focal length (virtual, inverted) Case 3: Diverging (Concave) lens: object and image on same side Doesn't matter if object is inside or outside focal length Virtual image, di is negative (same side as object) Positive m = not inverted, m<1 means its smaller Concave = NEGATIVE FOCAL LENGTHS Virtual images are typically on same side and not inverted Note: If object = focal distance (o = 2f because lenses have 2 focal points), you have a real inverted image that is the same size, but for mirrors, if o = f you have no image

Magnitude of Electric Field (E) Magnitude of Electrostatic Force (Fe)

E = V/d (use this equation for magnitude of parallel field vectors) = Fe/q = kQ/r^2 where E is electric field magnitude (N/C), Fe is magnitude of force felt by q, k is electrostatic constant, Q is source charge magnitude, r is distance between charges Magnitude of Electrostatic Force (Fe): Fe = kq1q2/r^2

Energy of a photon

E=hf=h(c/λ) E = energy of photon f = frequency

6 simple machines designed to provide mechanical advantage: -Inclined plane -Wedge (2 merged incline planes) -Wheel and axle -Lever -Pulley -Screw (rotating inclined plane)

Efficiency = Work output / Work input = (load*load distance)/(effort*effort distance)

Coulomb's law:

Fe = kq1q2/r^2 r is distance between charges k = Coulumb's constant (electrostatic constant) = 8.99X10^9 N*m^2/C^2 = 1/4pi*E0 where E0 = permittivity of free space = 8.85 X10^-12 C^2/N*m^2 The force is inversely proportional to r2. Cutting the distance in half will therefore multiply the force by 2^2, making it four times its original value: direction at a given point is defined as the direction of the force that would be exerted on a positive test charge in that position. Because electrons are negatively charged particles, they will therefore feel a force in the opposite direction of the electric field's vector. In this case, because the force points to the left (toward R), an electron will feel a force pointing to the right (toward S) if E is in the same direction as F.

Flow rate would__________ with increasing radius of tube or pressure gradient, and would ________- with increasing viscosity or length of tube

Flow rate would increase with increasing radius of tube or pressure gradient, and would decrease with increasing viscosity or length of tube

Force on a current-carrying wire in a magnetic field

For a straight wire, the magnitude of the force (FB) = ILB sin θ where I = current, L = length of wire in field, B is magnitude of magnetic field, θ is angle between L and B CURRENT IS THE FLOW OF POSITIVE CHARGE (even though only negative charges are actually moving

Fusion and Fission

Fusion: Nuclear fission and fusion both release energy Size or reactant particles: Small (hydrogen, helium) Increase in nuclear mass Small nuclei combine to form larger nucleus -How many stars power themselves (including sun) -> 4 hydrogen nuclei to make 1 helium nucleus produces 3.85 X 10^26 joules / second (385 yottawatts) Fusion power plants (less common) generate energy from deuterium (2 over 1 H) and lithium nuclei Fission: large nucleus into smaller nuclei (size of reactant particles: Large (Lanthanides, actinides) (decrease in nuclear mass) -spontaneous fission rarely occurs -Absorption of low energy neutron can be induced in certain nuclei -Releasing neutrons causes chain reaction that causes nearby atoms to undergo fission (induced fusion: powers most commercial nuclear power plants)

Magnitude of gravitational force

Magnitude of gravitational force (Fg) = (G*m1*m2)/ r^2 where G is universal gravitational constant (6.67X10^-11 N*m^2/kg^2) m1 and m2 are masses of 2 objects r is distance between their centers of mass *magnitude of force inversely related to square of distance (if r is halved, Fg will quadruple) *If m1 is tripled, Fg will triple

Kinetic energy of ejected electrons

If frequency of photon on metal is at threshold frequency for metal, electron barely escapes If it is above threshold for metal, excess energy converted to kinetic energy in ejected electron Calculate max kinetic energy of ejected electron: K max = hf - W where W is work function of metal h is Planck's constant (6.626X10^-34 J*s) the work function is the minimum required to eject electron: W = h*fT -Think of it like activation energy: Must be matched or exceeded for escape of electron So K max = hf - h*fT) *fT is threshold frequency These formulas solve for maximum kinetic energy of electron rather than exact kinetic energy because actual energy can be anywhere from 0 to K max depending on subatomic interactions. K max is only achieved when all possible energy from photon is transferred to ejected electrons

If there is no net force acting on an object, the ___________ is constant and the acceleration is _

If there is no net force acting on an object, the velocity is constant and the acceleration is 0

Magnetic Field Equation

Measured in Tesla (T)) 1T = 1 N*s/m*C -Sometimes measured in gauss (1T = 10^4 gauss) because teslas are really large B= Mu0 (meow 0) * I / 2 pi r where B = magnetic field at distance (r) from wire Mu0 = Permeability of free space (4piX10^-7 T*m/A) I = current Inverse relationship between the magnitude of the magnetic field and the distance from current -Straight wires create magnetic field in concentric (same center) rings, with direction of field vectors determined with right hand rule (thumb in direction of current, wrap fingers around invisible wire, fingers mimic circular field lines

Pascal's Principle

P = F1/A1 = F2/A2 F2 = F1 (A2/A1) *THE LARGER THE AREA, THE LARGER THE FORCE (although the force will be exerted through a smaller distance) Volume (V) = A1d1 = A2d2 where A is area and d is distance / displacement Combining equations for pressure and volume, we get equation for work as the product of constant pressure and volume change (isobaric process because no pressure change) W = PΔV = F1/A1 (A1d1) = F2/A2 (A2d2) W = F1d1 = F2d2 Change in pressure applied to enclosed fluid is transmitted undiminished to every part of fluid and to walls. If pressure is added, pressure will travel undiminished through pipe -Pressure stays the same, but force will vary in direct proportion with the area

Resistors in Parallel and Series

Parallel 1/Rp=1/R₁+1/R₂+1/R₃+... Overall reduction in equivalent resistance (total resistance will be less than smallest resistance in circuit) Rp decreases as more resistors are added Series: Rs increases as more resistors are added (in series) As electrons flow through each resistor, energy is dissipated, and there is voltage drop associated with each resistor (voltage drops are additive ) Rs =R₁+R₂+R₃+... Voltage drops: Vs = V₁+V₂+V₃=V... *resistor with smaller resistance has bigger current *Series and parallel opposite for capacitors

Pressure Volume Curves

Pressure-Volume (P-V) curves: Work done determined by area enclosed on graph (Straight line up) *If volume stays constant, delta V = 0, then no work is done because there is no change in area (shown in image A): this is called Isovolumetric / isochoric process *If volume changes but pressure remains constant (Delta P = 0), then the area under curve is rectangle (Rectangle graph because P is flat line but V (x-axis) changes): Isobaric processes Work can be calculated using: W = PΔV Neither pressure or volume held constant, so find area by saying area 1 (triangle) = 1/2 ΔVΔP and area 2 (rectangle) = PΔV, then add them up *Area of triangle + area of rectangle = Work Image shown Closed cycle where system returns to initial state (don't need to know how to calculate area)

Continuity equation:

Q = v₁A₁ = v₂A₂ A₂ = A₁v₁/v₂ = πr₁²v₁/v₂ V = volume A = Area *NOTE: if you are given diamter of a tube (as opposed to area), convert to area A = pi*r^2 OR use Vb = Va (dA / dB)^2 Flow rate = linear speed * cross-sectional area *Linear speed of fluid will increase with decreasing cross-sectional area fluids flow quicker through narrow spaces -Arises from the conservation of mass of fluids (because liquids are incompressible) -With constant flow rate, there is inverse relationship between linear speed and cross-sectional area

Acceleration

Rate of change of velocity that an object experiences as a result of some applied force Vector quantity Measured in SI units of m/s^2 a = (Δv/Δt) limit as Δt-->0 ΔV = aΔt a = f/m Δ V = fΔt/ m

Capacitors in Series and Parallel

Series: 1/Cs = 1/C1 +1/C2 +1/C3...... *Total voltage is the sum of individual voltages (like resistors in series) Parallel: C=C₁+C₂+C₃+... Produce resultant capacitance = to sum of individual capacitors Cp increases as more capacitors are added Voltage across each parallel same and equal as voltage across the source (same as resistors in parallel)

Cohesion and Adhesion

Surface tension: Causes liquid to form thin, strong layer at liquid surface -results from cohesion (occurs between molecules with the same properties) (the attractive force that a molecule of liquid feels towards molecules of the same liquid) -At the surface, molecules only have strong attractive forces pulling from below (instead of from all sides which balance out) -Pulls the surface of the liquid towards center -> establishes tension , so when small indentation is made on surface, the cohesion leads to net upward force Adhesion: another force liquids experience -the attractive force that a molecule of liquid feels towards molecules of some other substance -Cause water droplets to form on windshield even though gravity pulling down -In containers, this causes meniscus (Concave meniscus occurs when liquid crawls up the sides of the tube a tiny bit because adhesive forces are bigger than cohesive)(A convex/backwards meniscus is less common, tiny mountain, occurs when cohesive forces are greater than adhesive, like mercury)

Vector Addition If V = 10m/s and theta = 30°, what are X and Y? What is the magnitude of the vector with X= 3 m/s and Y = 4 m/s?

The sum or difference is called the resultant of the vectors Add tip to tail (length of arrows must be proportional to the magnitudes of the vectors -The sum is the line going from tail of A to tip of B (or tip of last letter, may be C or D) Another method for finding resultant = breaking vectors into perpendicular components (x and y components) -Image shown X= V cos theta Y = V sin theta If V = 10m/s and theta = 30°, X = 10 * √3/2 = 5√3 m/s Y= 10* 1/2 = 5 m/s V = √x^2 + y^2 or V^2 = X^2 + Y^2 Angle of resultant vector can be found by theta = tan^-1 (Y/X) What is the magnitude of the vector with X= 3 m/s and Y = 4 m/s? = √3^2 + 4^2 = √25 = 5 m/s

Threshold Frequency

Threshold Frequency (fT): The minimum frequency of light that causes ejection of electrons -Depends on chemical composition / type of metal exposed to radiation -"All or nothing response": If frequency of photon less than fT (f<fT) then no electron is ejected, but if f> fT, then an electron will be ejected and maximum kinetic energy of ejected electron will be equal to work function (hfT - hf) *Einstein: Light beams consists of integral number of light quanta called photons. The energy of each photon is proportional to frequency of light: E = hf where E is energy of photon of light, h is Planck's constant (6.626 X10^-34 J*s), and f is frequency of light *We can use frequency to find wavelength using c = f*wavelength Waves with higher frequency have higher energy and shorter wavelengths (toward blue to violet end and UV end of spectrum) *Lower frequency = longer wavelengths and lower energy ( red to infrared end of spectrum) *ENERGY OF PHOTON INCREASES WITH INCREASING FREQUENCY *Higher frequency = more electrons ejected

Half-life (t1/2)

Time it takes for half of the sample to decay Each half life: 1/2 of remaining sample decays so that remaining amount asymptomatically approaches 0 N(t) = N0 (1/2)^ (t/(T 1/2) N(t)= quantity of the substance remaining N0= initial quantity of the substance t= time elapsed T 1/2 = half life of the substance Portion remaining will never actually reach 0, but its usually considered decayed after 7 or 8 half lives

Force on a moving charge

When a charge moves in a magnetic field, a magnetic force may be exerted on it, with the magnitude = FB = qvB sinθ where q = charge, v = magnitude of velocity, B is magnitude of magnetic field, θ= smallest angle between velocity vector (v) and magnetic field vector (B) -Sin means charge must have perpendicular component of velocity (If charge is parallel or antiparallel to magnetic field (B), sine (0) or sin (180) = 0, so there would be no force) *Magnetic fields only exert magnetic forces on other moving charges (assume presence of fixed and uniform external magnetic field *Charges can have both electrostatic and magnetic forces acting on them at the same time (the sum of these forces is called Lorentz force)

Heat of Transformation

When a substance is undergoing phase change, like solid to liquid, the heat added/removed doesn't cause change in temp (phase change occurs at constant temperature) *During a phase change, heat energy causes changes in particles potential energy and energy distribution (entropy) but not kinetic energy = no change in temperature *Temp won't change into all of the substance has been converted from one phase to another (No matter how much heat you add to ice, it won't raise temp from 0 deg C until all ice has melted) Adding heat raises temp by increasing average kinetic energy = more freedom to move But, phase change related to potential energy, no kinetic -Breaking hydrogen bonds = greater degrees of freedom of movement = greater number of MICROSTATES = increases potential energy (average kinetic energy is same as solid water at same temp) When heat energy is added or removed from system in phase change, use: q = mL where q = amount of heat gained or lost, m is mass, L is heat of transformation or latent heat of substance because you cant calculate temp change (there is none)

When light enters a medium with higher index of refraction it bends:

When light enters a medium with higher index of refraction it bends towards normal so that theta 2 < theta 1 Air: 1 and glass: 1.5, so light bends towards normal when entering glass If index of refraction were smaller, light will bend away from normal as light exits glass