Physics

Electric Potential Energy and Potential

Find potential energy (U) of a mass in earth's gravitational field or in electric field: F*d --> displacement in the direction opposite of mgh and d is measured from a zero point or U=q*E*d Find electrical potential energy of a charge depends on position of the charge in the field: U=k[(q.1*q.2)/r] --> represented at point of charge. but electric potential energy is zero when particles separated by infinite distance --dipole can be understood by a mountain on a plane --electric dipole can only be made by two opposite charges with equal magnitude -- a peak (like a mountain pointing up and out of a plane) represent positive charge while a valley (low surface that has a point underneath the plane) signifies negative charge --a path is typically drawn from the positive to the negative region --the marble path repels from positive area and attractive by the valley --electric dipole moment is p=q*d --altitudes is analogous to potential --potential of the field is mass multiplied by g*h which gives work done by the field in moving the mass/object Voltage: voltage (V) is potential for work by an electric field in moving any charge; V=E*d --voltage in units of volts (V) or J/C which is scalar --voltage at point charge or individual charge is V=k(q.1/r) --essentially voltage is a way to talk about energy (potential energy per unit charge) --but for electric field, it talks about force (force per unit charge) Force 1. Gravity of F=[g*m.1*m.2/r^2]=mg is force of two masses (m) separated by distance (r) and gravitational constant (G) 2. Gravity of g=F/m 3. Electricity of force F=[(k*q.1*q.2)/r^2]=q*E in units Newtons 4. Electricity of Field E=F/q in units N/C or V/m Energy 1. Gravity of PE=F*d=mgh 2. Gravity of gh=(PE/m) 3. Electricity of potential energy PE=F*d=q*E*d in units J 4. Electricity of voltage V=PE/q=E*d in units J/C or V Work: --work done by electrostatic field is independent of path since mechanical energy is conserved --so any path does not matter between two objects --W=mgh or W=q*E*d

Ideal Fluids

Lacks certain characteristics of real fluids: 1. ideal fluids have no viscosity --is the measure of fluid's resistance to forces that are not perpendicular to its surface or resist flow --ex. syrup has great viscosity than water --drag, a type of force that is similar to friction, is created by viscosity and pressure due to motion --drag opposes motion through fluid 2. ideal fluids are incompressible due to uniform density 3. ideal fluids lack turbulence --means it experience steady flow meaning all fluids flow through fixed points with the same velocity --but since velocity specifics magnitude and directions, velocity at any fixed point in the fluid may vary with time --turbulent flow generates sound waves which means changing pressure --for ideal fluid, flow rate (Q) is constant 4. ideal fluids experience irrotational flow --object moving with an ideal fluid will not rotate as it flows --the object will continue to point in one direction regardless of the direction of flow --essentially ideal fluid doesn't actually exist but it is used to make rough predictions about real fluids

Power

Power is scalar which means it does not have a direction Power formulas... 1. P=W/t --> work done by a force per unit time 2. Power (P) is the rate of energy transfer so.. P=DeltaE/t 3. units of power is watts (W-not in italics) which is defined as J/s **italics W represents work** 4. instantaneous power due to force --> P=F*v*cos@ and @ is the angle between F and v and cos@ indicates force (F) in the direction of the velocity **shorthand, cos180=-1 and cos90=0** --if there is heat or pressure-volume change, you have a thermodynamics problem

Graphs of Linear Motion [Velocity Vs. Time]

Velocity Vs Time Interpretations (represents acceleration): --upward slope indicated positive acceleration while downward is negative acceleration --negative acceleration could mean reverse direction --displacement and distance can be seen based on he area between or below zero velocity curve slope --more specifically, area beneath zero velocity that is labeled as negative represents displacement --area between curve and zero velocity labeled as positive is represented as total area distance --if the velocity is the positive direction, then the negative acceleration means slowing down --straight line indicates constant slope or constant acceleration --a curved line is a changing slope, meaning changing acceleration --lets say north is designated as positive...constant slope begins at 10 m/s velocity in the north --if the slope line goes down after 20 seconds, it went from 10 m/s to -10 m/s which means acceleration is -1 m/s^2. the negative sign shows particle is accelerating to the south --since it start at 10 m/s and ends at -10 m/s, displacement is zero meters but particle can still be travelling --keep in mind, the first 10 seconds, the line was above the X-axis but decreasing. this means particle is moving north since its in the positive hemisphere but slowing down since its going to 0 m/s --when the line pass X-Axis to negative hemisphere, velocity moving constant for the next 10 seconds to the south and speeding up --when you calculate the area under the line its (rise/run)/2 representing distance or how much it traveled --to another way to calculate distant, its the (consistent velocity)*(time) ex. for every 5 seconds, slope moves in speed of 5 m/s. so after 20 seconds multiple 5 m/s to get 100 meters particle travelled. --horizontal line indicates no acceleration and constant velocity of ex. 10 m/s and since its negative meaning moving to the south --when the curve to going down approaching 0 m/s, it is decelerating but still moving in the north (upper hemisphere) and slowing down. the negative acceleration is not constant when line is not straight line --when it reaches 0 m/s, there is no velocity or acceleration but there is a positive nonzero displacement (curve slope), area beneath x-axis is negative displacement --remember, displacement is calculated by subtracting the area (under the X-Axis and above the curve) from the area (above the X-Axis and below the curve). --or displacement is the average velocity multiplied by time and it is also the average velocity divided by acceleration --acceleration is the difference between the two ends of the slope lines divided by the rate of change in velocity --area above and beneath the curve are positive distance **overall, slope is acceleration and area is displacement** **acceleration is how fast velocity change** You can draw chart for every question: Q. what is the distance traveled by a particle that starts at 30 m/s and accelerate to 50 m/s in 4 seconds? What is the acceleration? 1. average velocity is 40 m/s which is at the middle 2. average velocity multiplied by time is a distance of 160 meters 3. acceleration is 50 m/s -30 m/s divided by rate of change in velocity so 4 seconds equals 5 m/s^2 **objects dropped straight down or vertical velocity for projectile change is usually 10 m/s per second.**

Nature of Force

—force is defined as what causes and changes motion —this is what create acceleration and causes object to move from rest and vice versa Four Types of Forces: 1. Strong nuclear force 2. Weak nuclear force —> nuclear found in nucleus of an atom 3. Gravitational force —> also type of contact force since act at a distance 4. Electromagnetic force/contact force—> ex. Person pushes a book with his finger and that force moves the book by the electro static repulsion between the atoms in the finger and atoms of the book. Unlike gravitational, it requires charged objects or magnetic. —contact forces occur perpendicular to a surface (also known as normal force) or parallel lines to the surface which requires friction

The Energy of Fluids in Motion

--Bernoulli's Equation: states conservation of energy in terms of density and pressure --it also written as P1+[(1/2)*p*v1^2]+p*g*h1 = P2+[(1/2)*p*v2^2]+p*g*h2 --P is the pressure of the fluid, v is the velocity and h is the height or distance above an arbitrary point --can also be rewritten as P+pgh+1/2pv^2=K --so h is not the same as y since y is the distance beneath the surface --P1 and P2 are typically the atmosphere pressure --other equations are p*g*h=1/2*p*v2^2 --h2=0 typically referring to water flowing out of tank --h1 is the high of volume of fluid in tank and v1=0 --keep in mind, lost pressure equals increased velocity --this makes sense since increase in kinetic energy corresponds to increase in velocity --for ideal fluid, energy is conserved so that means potential energy and pressure decreases as kinetic energy increase --pressure changes while height of fluid assumed to remain --usually pitot tube and venturi tube are used to obtain pressure measurement in order to calculate fluid velocities --pitot tube is a horizontal tube containing U-shaped tube and two openings facing the fluid flow. --first opening encounters zero velocity while the second opening has a pressure equal to the total pressure exerted by the moving fluid --the U tube calculate the difference in pressures based on Delta.P=p*g*delta.h --venturi tube is a horizontal tube with a constricted region with decreased cross-sectional area in the middle --this tube is used to determine velocity of a flowing fluid within it unlike pitot tube that measures velocity of flowing fluid past it --for this tube, constant flow rate Q is constant, meaning decrease in cross section area is associated with increase velocity (also decrease pressure) --venturi effect is when low pressure occurs when fluid flow into constricted region of the pipe Bernoulli's Equation Has Different Terms of Volume and Energy --Second term gives gravitation potential energy (mgh) per unit volume or mgh/V --third term gives kinetic energy per unit volume or (1/2mv^2)/V --first term is pressure is the energy per unit of volume from random motion of molecules --remember, energy is conserved or constant in ideal fluid flow --if there is a spigot attached to a tank of fluid making it an opening, h=0 or height of spigot --so the velocity of the fluid coming from spigot is written as v2=√2gh1 --another way of writing it is v2^2=2*g*h1 --if the density of the fluid is known, difference in pressure measured by the U-tube can be used to determine velocity V2=√[(2delta.P)/p.fluid] --remember, V1=0m/s and h1=h2 --simplified Bernoulli's equation is P2+1/2pv2^2=P1 or 1/2pv2^2=P1-P2=Delta.P --but with venturi tube, it focus on flow rate Q using equation Q=A*v as v in velocity

Representing Waves as Sine Functions

--Sine graphs can be used to depict displacement of medium (y-axis) as a function of time or direction of propagation (x-axis); known as displacement as a function of position --the longitudinal wave moves in the direction of propagation --the wave on the graph consists of crest (looks like upside down smile above x-axis) --trough is the side to side of a dip and the wave dip (looks like a smile) is located below the x-axis --wavelength is from one crest to the next crest --number of waves that pass a certain point in one second is (f) --Sine graph can also be depicted as displacement at a given position as a function of time --on this graph the position is on y-axis while time is on x-axis --amplitude (A) is a wave represented by sine function that measures distance between x-axis and either top of a crest or bottom of a trough --amplitude change as a wave moves from one medium to another --remember displacement of transverse waves refers to changing distance and movement of medium perpendicular to direction of propagation --but displacement of longitudinal wave means displacement of medium parallel to direction of propagation

Forces Experienced by Objects in Fluids at Rest

--a standing fluid exerts a force called buoyant force (F.b) --this force applied on an object that is floating, submerged or sunk in the fluid --pressure increases as a function of depth P=p*g*y --remember pressure is measured by force per unit area or P=F/A --this means pressure is proportional to force and both pressure and force increases with depth (or points father from the fluid's surface) --as a result, the object will experience an upward force or buoyant force which is a force that allows object to float --remember, buoyant force reaches its maximum value when object is fully submerged Formulas to Remember: --F.buoyancy=p.fluid*v.fluid*g --equation above can be rewritten as...F.b=(m.fluid/v.fluid)(v.fluid)(g)=m.fluid*g --V=A*h --F.b=p*g*A*h --F.b/A=p*g*h --P=p*g*h **remember p represents density of fluid and v is the volume of fluid displaced** --remember, magnitude of buoyancy (floating, submerged or sunk) is directly proportional to volume of fluid displaces F.b=p.fluid*v.fluid*g --another way to rewrite this equation is F.b=(m.fluid/v.fluid)*v.fluid*g=m.fluid*g and this equation represent the upward buoyant force is equal to magnitude to the weight of the displaced fluid --when paying attention to depth, see the difference between the distance of object closest to and farthest from the fluid surface (y1 and y2) --also, pay attention to the volume of the fluid displaced which is reflected by delta.y and this is proportional to delta.P --in other words, if depth is low, so is the volume fluid and so is the buoyant force --or V.displaced fluid=A*delta.y1(or y2) --as the object sinks deeper and deeper, the delta.y increases and buoyant force also reaches maximum --objects experience buoyant force because of the difference in pressure experienced by the upper and lower surfaces --so if depth increases so does pressure --the equation to keep in mind is P=F/A=p.fluid*g*delta.y

Motion and Force

--acceleration is required for any change in motion --change in motion is change in direction or speed --when viewing net force, think acceleration or vice versa. --on the MCAT will ask to apply physic concepts to biological system and questions/passages will involve physiological processes --ex. connections with circulatory system

Types of Images

--an image is a representation of an object derived from light reflected from the object --two kinds of images: real image and virtual --Real image is located on the same side of the mirror or lens as the observer, defining as positive and inverted --inverted stands for top of the object appears bottom of the image. located on the side of observer meaning positive --Virtual is located on the opposite side of the mirror or lens from the observer, defining as negative and upright --upright stands for top of the object is the top of the image --the negative and positive signs next to the distance between an image and the lens or mirror is necessary for thin lens equation --difference between virtual and image is that real image can be captured on a screen while virtual image cannot --diverging lenses and mirrors always form virtual images located opposite side of observer which is why its called negative --if the object is located beyond the focal point, real inverted image located on the side of the observer appear --if the object is within the focal length, the image formed is virtual and upright --but if the object is exactly placed at the focal point, no image is formed --for the MCAT, the mirrors and lenses are small so the focal distance is tiny --this means most objects are located beyond the focal point and convergers almost always create images that are real and positive

Moving Electricity, Conductivity and Current

--charges move from areas of higher potential to areas of lower potential --potential difference or voltage produces a flow of charge or current --conductive electricity is when charge moves along an object in the form of electrons --while conductive electricity occurs, the object also experience resistance of charge movement --substances include both to some extent or varying degree, but its usually either conduct charge very well or very poorly --good conductors are metals that allow electrons to flow freely --poor conductors or good resistors hold electrons tightly in place and are diamonds or glass --moving charge btw is current --current in units Amps (A) or C/s --current is scalar so the flow in direction of movement of positive charge or current move in the opposite direction of electron flow --overall, the current is defined as the flow of positive charge not the flow of electrons (which is from cathode to anode or opposite direction of electron flow). high to low potential --electrons move very fast in a random direction and freely through the conductor --excess charges found on object surface since they want to maximize the average distance from each other. so electric field inside a charged conductor is zero --ex. when you rub electron off a sock, you become positively charged and your finger pulls electrons from the doorknob --electric current (i) is equal to potential difference or voltage divided by resistance i=V/R --> this is Ohm's Law --Ohm's law is known to analyze circuits

The Thin Lens Equation

--object distance is represented by "p" or "d.o" --image distance is represented as "q" or "d.i" --thin lens equation applies to both lenses and mirrors --object and image distances can be calculated using thin lens equation... 1/f=(1/d.o)+(1/d.i) where d.o represent object distance, d.i represent image distance and f represent focal distance of mirror or lens --values in the equation often expressed in centimeters but converted to meters --recall that lens power equation is P=1/f which uses m^-1 which is why centimeters are converted to meters --depending on if the image is opposite or on the same side of the observer (negative or positive) --thin lens equation applies to both lenses and mirrors --ex. focal distance of a converging lens or mirror or real image is given as a positive sign while diverging mirror or lens or virtual image is a negative sign --single lens system is always a positive object distance

Shock Waves

--sonic boom is when the waves especially wave fronts get closer and bunch together until they overlap --remember for light, the wavelength shortens when the source and observer are approaching each other which is known as blue shift --but red shift is when the observer and source moves away --there is no doppler effect when the objects move move in the same direction at the same speed which means zero velocity and zero change in frequency --shock wave is a conical wave front --it is a shape of a cone or funnel where circular waves get closer and becomes smaller toward a point --it is produced when SOURCE sound velocity exceeds SOUND wave velocity. ex. train moving faster and getting closer to the honking sound wave --pressure variation within a shock wave is so great that observers perceive it as a boom --according to ratio V.source/V.wave, the Mach number increases as the velocity of the sound source increases

Wave Interference: Constructive and Destructive

--when two or more transverse waves are superimposed (occupying the same space), their displacements add at each point along a wave to form a new wave --this is called interference Two Types of Interference: 1. Constructive Interference --> sum of displacements results in greater displacement 2. Destructive Interference --> sum of displacements results in a smaller displacement **interference wave will revert to the original shape** **whether interference is constructive or destructive depends on phase of the wave relating to wavelength, frequency and place and time of origin --think of phase as horizontal shift of a wave on a Cartesian graph --half of the 360 degree wavelength is 180 degrees --two waves begin at the same point and time with the same wavelength this is known as phase --out of phase are two waves that have the same wavelength but travel different distances to arrive at the same point

Absorption vs. Polarization of Light

Absorption: --waves propagating through media will undergo absorption --this depends on medium and frequency of the wave --consider light waves of three different frequencies; one in the ultraviolet region, one in the visible light region, and third in the infrared region --when the ultraviolet light strike glass, much of it is absorbed and the electrons in the glass begin to vibrate --vibration dissipate through the glass as heat to prevent any more ultraviolet light from passing through --frequencies of the visible light does not cause the electrons of the glass to resonate and wave passes through unchanged --but the transfer of energy from visible light causes it to have a slight delay due to slower speed of light through the glass --low frequency of infrared light causes the entire glass atoms to vibrate, warming the glass and prevent infrared light from passing through --many instruments such as nuclear magnetic resonance (NMR), infrared spectroscopy (IR), and ultraviolet visible light spectroscopy (UV-Vis) all detect differential absorption of electromagnetic radiation or energy of light --remember, spectroscopy is the study of interaction between electromagnetic radiation/light and matter Polarization: --polarized subjects exhibits a particular alignment, separation or orientation --ex. polarized object experience a separation between positive and negative charge --ex. polarized light has electric and magnetic fields that are oriented in a random way --light is commonly described as horizontally, vertically, circularly or randomly polarized --vertically polarized light is when electric field oscillates parallel to y-axis and vice versa for x-axis and horizontal --nonpolarized light tends to vibrate in all direction but switched to polarization when it becomes "a cross" or perpendicular of vertical and horizontal overlap. --remember a source of light is a vibrating charge --there are two ways light is polarized; horizontally (lays flat like paper) and vertically (up and down) --light can also be circularly polarized which means light consists of electric fields of constant magnitude that change direction in a circular or rotating manner, either clockwise or counterclockwise --light source emitted commonly randomly polarized --random polarized light will have intersecting double headed arrows (one vertical and other horizontal) --unpolarized light can become polarized by reflection, scattering and polarizing filters --four things light is most likely to do on the MCAT; reflect, refract, diffract, or disperse --reflection is light that bounces off the boundary between media --refraction is light bending as it passes into new medium --dispersion is a type of refraction but light is split --diffraction is spreading of light when it encounters an edge

Circuit Elements

--circuit requires complete circle for current or charge to flow around or else there will not be a current flow --circuit is a cyclical pathway for moving charge and a battery is able to maintain this circuit due to the potential difference --but there is always substance resisting the flow of charge. --resistivity (p) is quantitative measure of substance resistance --resistance (R) is quantitative measure of an object's features that cause resisting flow such as shape and size --resistance in ohms (Ω) and equation to remember R=p(L/A); p as in resistivity, Le for length of object and A is current in Amps --so if length doubles or area is cut in half, resistance doubles --electrode with high potential is located in cathode while low potential is anode --battery only has a wire connecting electrodes because wire connecting cathode to anode cause discharges at the battery's energy --battery energy is calculated using equation DeltaG=-n*F*E where E is maximum potential difference of reduction-oxidation (redox), and Delta G is energy generated by redox --battery adds energy to a circuit by pumping fluid to a greater height --battery do include internal resistance and its rated by voltage level known as electromotive force (EMF) --remember, while cathode (positive charge) move from positive to anode (negative charge), electrons move from anode to cathode in a battery or electrolyte --essentially charge flows downhill which is another way of saying high to low potential --battery consists of one or more galvanic cells where oxidation occurs at anode while reduction at cathode --ionization energy is how easily an electron is removed from an atom by determining the potential or voltage --while circuit elements in series is like increasing length , putting circuit in parallel is increasing width or area

Converging and Diverging Lenses and Mirrors

--converging mirror reflects light rays such that they converge at a point in front of the mirror --the light rays from the source approaching the mirror begins as parallel --the point the reflected rays converge is the focal point --ex. is an observer standing where the light source and the light converges on the same side as the observer after hitting off the mirror --converging lens refracts light rays such that they converge at a point on the side of he lens which is opposite the light source --lens and mirrors have different shapes --while mirrors are concave or saved in, lens are convex with a thick center --on the MCAT, unless said otherwise, spherical mirrors behave like parabolic mirrors (its after the focal point, rays spread out in to different direction-not parallel toward the light source) Diverging vs. Converging: --for diverging, its opposite --parallel light rays encounter a diverging mirror or lens --mirror or lens will cause the light to spread out such that they will never intersect --although the lights do not converge at a focal point, divergers produce images --the brain traces back the path and perceive an image at the point they would have originated if they have been traveling in a straight line --diverging mirror reflects light rays and observer see them as converging at a point on opposite side of the mirror from the observer --diverging lens refract light rays and appear converge at a point on the same side of the lens or opposite from the side of observer --while diverging lens are concave, mirror is a convex mirror --need to remember difference of mirrors, lens, converging and diverging Tips & Tricks Mirrors --> FRONT --Concave mirrors: light rays head inwards, reflect & CONVERGE in the front --Convex mirror: light rays go off in all directions after reflection and never converge (DIVERGE) in the front Lens--> FOLLOW OPPOSITE PATTERN so BACK --Concave lens: diverge in the back --Convex lens: converge in the back of the lens

Resonance: Pipes and Strings

--depending on the source, waves can have any frequency --a structure like strings and pipes will undergo a particular type of vibration (resonance) for certain frequencies and based on the length of the structure --it begins when the wave reaches an interface between two media --the energy will reflect back into the first medium and, depending on the media density, it influence the orientation of reflected wave --reflected wave off a dense medium cause it to be inverted due to a phase shift --for a less dense medium, the wave is shifted upright --ex. wave pulse through a thread which is a less dense medium will have energy reflected back into the string as an upright wave pulse --ex. wave pulse down a heavy rope the reflected wave could be turn-around and upside down (from smiley curve to upside down frowning curve) --when waves pass each other and experience interference, they can collide --point of collision is never displaced or doesn't move at all --at this point, known as node, the wave can plataeu or standing wave. string would hold perfectly still at nodes --while antinodes are points intersected by two vertical lines and experience maximum constructive interference --string would move violently up and down at the antinodes. looks like slope increase of decrease from one wave to the next --for standing wave, length of the string is equal to half a wavelength and standing wave cause string to resonate or vibrate at its natural frequency (resonant frequency) --resonant frequenct for any given wavelength that creates standing wave can be determined using V=f*wavelength since velocity is constant for a given medium --structure will experience maximum vibration if outside driving force is applied to resonant frequency --resonance stands for equal natural frequency and driving frequency --in non-ideal situation, energy is lost to damping at the resonant frequency and replaced by outside driving force --damping is known as attenuation which is the decrease in intensity of a wave propagating through a medium --one cause of damping is reflection which makes it difficult for the wave to create ultrasonic images of bone's interior --since bone exterior is so dense, waves tends to reflect so very few waves can reflect off of the interior --another cause of damping is spreading which means as waves spread to larger and larger areas, the intensity reduces --absorption is also another way attenuation occurs --when a wave attenuates, intensity decreases --also frequency stays constant or does not change for emitted wave --however, its perceived frequency can change when its source moves relative to an observer --intensity as a result depends on square of both frequency and amplitude --for the mcat, resonance will appear in pipes and strings in context of sound waves --for strings, one or both ends may be fixed to a point while for pipes one or both ends are open --open ends behaves like unfixed ends of a string while closed ends act like fixed ends of a string --if both ends are fixed, there is a node at each end --if there are both unfixed ends, then there is an antinode at each end

Newton's Laws of Motion

--describes how and to what extent forces cause objects to accelerate --Newton's First Law states that an object in a state of rest or motion will remain in that state unless it is acted upon by a net force --remember, any change in motion requires acceleration and where acceleration is means net force is present --Second Law states when a net force acts on an object, the change of state of motion will be inversely proportional to the mass and directly proportional to the net force (F) --it is written as.. F=m*a or motion change=F/mass --as it is shown on the equation, smaller the mass, the greater the acceleration and greater effect of a force --remember force and acceleration are proportional --Third law states that every action have an equal and opposite reaction --ex. system A applies a force on another system B. both experiences equal force magnitudes by each other but different directions

Translational Motion

--distance, displacement, speed, velocity and acceleration are all characteristics that describe motion --displacement is distance with added dimension of direction --velocity is speed with added dimension of direction --speed=distance/time --velocity=displacement/time Distance vs. Displacement: --ex. distance is someone's footsteps from point A and point B --ex. displacement is someone's various method of route from point A to point B. so distance, time and number of steps not all equal. if route Z took 100 seconds and speed of 0.1 m/s then multiply the values to solve displacement --Instantaneous speed and instantaneous velocity or someone's speed or velocity is unknown at any one moment during the entire trip --this is the case if the distance traveled and average speed is unknown --it is possible speed and velocity are constant throughout the trip --it is also possible that someone cover the first half of the trip in 99 seconds and the second half in 1 second meaning change in velocity or speed --change in velocity is acceleration x time --in other words, acceleration is change in velocity or speed over time. --unlike displacement and distance, speed and velocity will have the same magnitude --remember change in velocity is acceleration whether it is the change in magnitude, direction or both --acceleration encourage directional change of motion. ex one object may change from 10 m/s north to 10 m/s east even though the speed has not changed --particles moving at constant velocity has no acceleration or equal to zero --also keep in mind that acceleration and velocity do not have to be the same direction. ex. a particle can be moving to the left while accelerating to the right or moving up while accelerating down --if velocity and acceleration are in opposite direction, the object is slowing down. --ex. a ball thrown upwards is accelerating downwards due to the force of gravity even though it is moving upwards. this is why the ball slows down and eventually falls. when the ball reaches maximum height, the velocity is zero because its changing direction

Doppler Effect

--doppler effect refers to the change in perceived frequency --this refers to the time of a wave source and its observer moving towards or away from each other --essentially the observed frequency is higher than the source frequency when the two aspects move toward each other and vice versa --source frequency is the frequency of waves emitted and it does not change --only the observed frequency changes --the doppler effect is due to change in relative motion of a source and observer changes the distance traveled by each wave front --so when observer and source move toward each other, distance traveled is less than it would if both stationary. & vice versa --wave front emitted gets closer to the observer meaning higher frequency perceived --oppositely wave front emitted father from the observer will cause the observer to perceive a lower frequency Scenario: --speed of a wave is determined by medium --a sound wave omitted has a given speed that will continue to travel at that speed --because wave speed is constant since speed=distance/time --so a change in distance traveled will change the time interval --so as distance decrease, time interval between wave fronts also decrease --decrease time interval or period is perceived as increase in frequency --frequency changes which depends upon relative motion --for the mcat formula is given as f.o=f.s[(c +/- v.o)/(c +/- v.s)] --f.o is observed frequency --f.s is source frequency --c is the velocity of the wave in given medium which is not necessarily the speed of light --v.o is the observer velocity --v.s is the velocity of the source --Another Doppler Effect for all waves is... delta.f/f.s=v/c and delta.wavelength/source wavelength=v/c --v is the relative velocity of the source and observer --once you find the frequency or wavelength of change...can use second formulas.. f.o=f.s+/-delta.f or wavelength.o=wavelength.s+/-delta.wavelength --to calculate for speed such as a vehicle....use equation delta.f/f.s=(2v/c) or v=(c*delta.f)/2*f.s Three Steps of Doppler Effect Formula: 1. assume the observer is not moving 2. label the direction negative or use minus sign for v.s if source is moving toward the object 3. if the direction of the observer is the same as in move toward source, then use the same negative sign for v.o. but use positive sign for v.o if its away from the source 4. if you label a direction positive for one vector, it is usually so for all vectors since velocity is a vector 5. another way to choose signs, think that f.o is greater than f.s when source or observer is moving towards each other. this is vice versa for moving away Rules about Calculating Relative Speed: 1. same direction between source (5 to the left) and observer (6 to the left) --> 1 m/s 2. opposite direction between source (5 to the right) and observser (6 to the left) --> 11 m/s

Electricity

--electric force can be either attractive or repulsive --gravitational force is always attractive and exists between two masses and electric force between two opposite charges (inversely proportional to square of distance) --electric force is given force per unit charge --similarly gravitational force is given force per unit mass --the flow of charge continuing or not depends on potential difference and if it is present or not --in electric circuits, batteries maintain potential difference which causes electrons to flow through wires from areas of higher to lower potential areas --other circuits act as energy store --electric field (E) is general express of force (force per unit charge) and general expression of energy (voltage and energy per unit charge) --when there is increased with, there are more capacitance while less resistance --when there is increased length or distance, there are more resistance but less capacitance

Static electric charge

--electric force exists between charges --surrounding a charge or group of charges is a field --at a given position, the field has a particular strength called its potential --potential is known as potential energy per unit charge --main difference between gravitational and electric force are that gravitational is always attractive while electric can be either attractive or repulsive --charge is an entity that defies definition and is an intrinsic to nature of subatomic particles --currents run in the opposite direction of electrons between negative and positive charges --charge is represented as q and units of coulombs (C) --charges can attract as well as repel each other --formula for magnitude of force of repulsion and attraction between two charged objects is called Coulomb's law --coulomb's law is F=k[(q^1*q^2)/r^2] --k is Coulomb constant 8.988x10^9 N*m^2/C^2 while q represents charges and r is the distance between centers of charge

Wavelength, Frequency and Speed of Light

--electromagnetic radiation exists at all wavelengths ----remember, electromagnetic waves are produced by accelerating charges --for MCAT remember visible light includes all wavelengths from 390x10^9 m (violet since shorter wavelengths) to 700x10^-9 m (shown as red since low frequency and longer wavelength) --shorter wavelengths correspond to violet light and on the visible spectrum is ultraviolet side (beyond violet). --longer wavelengths are red light and on the visible spectrum is infrared side (beyond red) --beyond red or past infrared consists with microwaves, radio waves and long waves ( gets shorter frequencies in Hz but higher wavelengths in m) --past ultraviolet are x-rays, and gamma rays (unlike infrared, the wavelengths gets smaller and frequencies get larger so waves get closer or less spread out) --recall that ultraviolet and beyond are dangerous by thinking how the high energy can damage your DNA --3 primary colors of light from low to high frequencies are red, then green, then violet. Or recall ROY G BIV to memorize color spectrum --visibility stands for the photoreceptors in the human eyes capabilities --speed of light in a vacuum is measured in vacuo (c) which is a constant and equal to electric field magnitude (E) and not proportional to magnetic field (B) --c = E/B = 3x10^8 m/s --since c is constant, it can be used to find frequency or wavelength f=c/λ like how velocity is equal to f*λ

Emission of Light

--electrons are what makes up light produced from accelerating charges --electrons are found within atoms which gain speed as they transition from higher to lower energy states --so electrons emit light during transitions from high to low energy states --light emitted by electrons is in the form of photons --photon is a tupe of particle and measured as quantum of light or electromagnetic radiation --photons carry energy (E) that is proportional to radiation frequency --E = h*f where h is the Plank's constant --photon can be perceived as a color depending on where the frequency of photons fall within range of visible spectrum Three Ways Electrons Can Receive Energy Needed to Transition from Ground to Excited State: 1. atoms with orbiting electrons are bombarded by electrons high speed. --when bombardment by electrons is subject to alternating current voltage, mercury vapor emits light in the ultraviolet region 2. atom could absorb photon of light. when it absorbs photons of high frequency light like ultraviolet light, electrons jump over states to reach the higher level --when electrons lose energy, it falls into one of the intermediate states which emits fluorescent light with wavelengths in the visible light range. --visible light is a lower frequency than ultraviolet light made from bombarded high energy electrons --intermediate is opposite to transition state which looks like a smile curve/lowest point located between two hills or peaks 3. atoms could be subject to thermal agitation. --closely packed atoms tend to be influenced by high temperatures such as solids --dominant frequency among atoms is directly proportional to temperature --temperature can be measured by the color of incandescent light (continuous range of wavelengths due to infinite number of electron transitions)

Energy and Accounting

--energy is never destroyed but converted to one form to another or transferred as work or heat --it is a scalar --for mcat, think like an accountant and keep record of where the energy is coming from and where it is going EX: 1. energy of system + surroundings before = energy of system + surroundings after 2. energy leaving system = energy entering surroundings 3. energy entering system = energy leaving the surrounding 4. total energy of system = sum of all forms of energy in the system --energy in units is joules (J) --1 joules is 1 kg m^2/s^2 or 1 N m Types of Energy: 1. Mechanical energy (delta Em) and non mechanical --> energy of a macroscopic system which is a system that can be examined without a microscope. non-mechanical is energy of microscopic energy which is seen through microscope 2. Kinetic Energy (K) --> mechanical energy is divided into kinetic and potential. kinetic is the energy of motion and written in equation of K=1/2*m*v^2 3. Potential Energy (U) --> energy of position and it depends where the object is located. the most important types are gravitational potential energy and elastic potential energy --gravitational potential energy (Ug) which is created by the force of gravity --equation is Ug=-G*m2*m1/r where G is universal gravitational constant and r is the distance between two mass's centers of gravity --keep in mind, the negative represent as two objects increase in distance or get further away, energy decreases --when the gravitational potential energy of an object is near earth's surface, the formula is Ug=m*g*h where g is the free fall acceleration gravity and h is the heart of the object above a point --elastic potential energy (Ue) is when a restorative elastic force acts on it. the restorative force follows Hooke's Law F=-k*deltaX. so the deformed object that follows this law will have an elastic potential energy and the formula is Ue=1/2*k*deltaX^2 where k is Hooke's Law and deltaX is displacement from relaxed position --k measures the extent the object resists deformation and is expressed in newtons per meter (N/m) --magnitude k is equal to F/deltaX --kinetic can convert to potential energy and vice versa

Systems and Energy

--energy is transferred from system to surroundings --system is an area that we choose to consider separate from the rest of the universe --the rest of the universe is surroundings Types of Systems" 1. Open system --> exchange of energy and mass with the surrounding 2. Closed system --> exchange of energy with the surroundings but not exchange of mass 3. Isolated system --> no exchange of energy, mass or work with the surroundings. the energy may change its form but is mostly conserved. remember First Law of Thermodynamics is that energy remains constant in the universe, making the universe an isolated system

In the case of floating object

--floating object displaces a volume of fluid --its mass is also equal to its own mass --also when object experiences upward buoyant force which is equal to downward gravitational force --its equal upward and downward forces allow object to float --the object initially penetrates the surface pf the fluid but the displacement of fluid volume (its depth) is relatively small --therefore, F.b=p.fluid*v.fluid*g=m.fluid*g=F.G=m.object*g --basically implies that m.fluid=m.object --since masses are equal, there is a ratio of density of a floating object to density of fluid --meaning p.object/p.fluid which equals to (m.object/v.object) ÷ (m.fluid/v.fluid) --all masses cancels out in the equation to essentially make (p.object/p.fluid = v.fluid/v.object). this is known as fraction submerged. --remember the density ratio is always equal to or less than one, otherwise it doesn't make sense that a submerging or floating object is greater than 1.

Fluids at Rest

--fluid at rest experiences only forces perpendicular to its surface --fluid at rest with uniform density in a sealed container has a formula of P=p*g*y where p is density of the fluid, g is gravitational constant and y is the depth of the fluid --also at any given depth, pressure is equal to (mass*gravity)/A and this is equal to the equation of p*g*y. --air is also considered fluid which is spilled to the atmosphere pressure when the container is no longer sealed --so fluid in an open atmosphere has a formula of P=p*g*y+P.atm --P.atmospheric is equal to 101,000 Pa. --fluid pressure is associated to the depth and not affected by the shape of the container --Pascal's principle states that pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout --think about how you have trouble breathing when traveling up (less depth) meaning fewer molecules above you so lower weight and lack of air pressure to push air throughout the lungs

Multiple Lens Systems

--for a combination of lenses, objects are not where they belong and so the object distance is not positive --to solve questions consist of two lens system, focus one lens at a time --use the image of the first mirror or lens as the object of the second mirror of lens --sometimes that first image is located behind the second mirror or lens which means the object distance for the second part is negative --on the MCAT, multiple lens system will likely appear in the context of optical instruments --an example is a magnifying glass, compound microscopes and refracting telescopes since these instruments allow humans to view objects that cannot be viewed with the naked eye and enlarge the object --converging lens forms an enlarged image when the object is within the radius of curvature --this means objective creates an image to be located within the radius curvature --objective is the eyepiece that forms real, inverted image which is outside the focal length and acts as the object --the eyepiece is made up of two converging lenses in microscope or telescope --if a formed image by objective falls outside the focal length, an in Lateral Magnification for Two Lens: M=m1*m2 Power of Two lenses in Contact with Each Other: P.eff=P1*P2

Uniformly Accelerated Motion and Linear Motion

--for acceleration to be considered constant, both its direction and magnitude must remain constant --no change of velocity = speed is not constant (zero) and no acceleration --motion of a particle can be uniformly accelerated on a linear path --these four basic variables are.. 1. displacement (X) --> vector 2. velocity (v) --> vector 3. acceleration (a) --> vector 4. time (t) --> scalar These variables are included in linear motion equation: --can only be used for objects that are experiencing constant acceleration: 1. X-Xo = Vo*t + 1/2a*t^2 2. V-Vo = a*t 3. V^2 = Vo^2 + 2a(X - Xo) --remember X - Xo = Delta X meaning changing in displacement --velocities in these equation are instantaneous velocities --while average velocity in an accelerated motion is.... V(avg) = 1/2(V + Vo)

Friction and Air Resistance

--friction is unlikely to show up on mcat --it is defined as a force that does not oppose motion instead it oppose relative motion --ex. friction makes a car's movement possible by opposing relative motion between the tires and road --without friction, tires would slide easily on the surface of the road and the car would not move --the surface molecules are attracted the other surface molecules --with friction, those attracted molecules allow surfaces to past each other easily --when drawing it on a free diagram, the frictional force on the front tires will point in the direction of motion of the car that's accelerating --the direction of the frictional force prevents the tires from sliding backwards on the road Air Resistance: --common type of friction is drag or air resistance --it is resulted from an object's collisions with air molecules --ex. object in projectile motion moves through a fluid such as air or air moves past the object --the air molecules collide with and drag past the object which impede relative motion between air and object --in other words, drag slows down projectile and greater the number of molecule collisions, greater the drag --streamlined objects with smooth surfaces and small surface area will experience decreased collisions with fluid molecules or small drag ---but when velocity of an object increases, number of collisions with fluid molecules each second increases and drag increases --mass on the other hand does not affect the force of air resistance or force of resistance remains constant for mass --however, mass affects acceleration that results from air resistance --so acceleration must decrease as mass increase --if force is constant in F=m*a, acceleration and mass are inversely proportional to each other --ex. projectile motion of golf ball and ping pong ball experience similar forces of air resistance. but given their different mass, each experience different acceleration due to air resistance. --direction of air resistance is opposite to the direction of relative motion --ex. as projectile object traveling upward, the air resistance is a downward force like gravity --vice versa when object is moving downward or slowing down with acceleration becoming less than gravity --massive objects are less affected by air resistance than less massive objects since golf balls for instance will slow down less than ping pong ball

The Law of Universal Gravitation

--gravitational force is the attractive force that every mass in the universe exerts on every other mass --basically, each mass pulls on the other --gravitational force is directly proportional to both mass (m1 and m2) --it is also inversely proportional to the square of the distance (r) between two center of masses --Newton's Law of Universal Gravitation equation.... F=G(m1*m2)/r^2 --Do Not confuse big G (constant anywhere in the universe) with little g (constant only near surface of the earth) --G is equal to 6.67x10^-11 m^3 kg^-1 s^-2 --the formula only gives the magnitude of the force but not the direction --based on Newton's Third Law, the earth pulls a person toward its center with a force equal to the person's weight and the person pulls the earth toward his/her center of mass with a force also equal to the person's --in order to determine how quickly two objects with similar mass will accelerate toward each other... 1. apply Newton's Second Law to each mass F=m*a 2. add the magnitudes of their accelerations --ex. object A and object B are accelerating toward each other. One is moving at 10 m/s^2 while the other is moving at 20 m/s^2. --both objects have equal force values or magnitudes --the magnitudes of the objects' individual accelerations equals to 30 m/s^2 which is the rate the objects are accelerating toward each other

Work and Power

--heat (q) is a type of energy that is transferred between system and surroundings due to temperature differences --work (W) is the energy transferred for any reason besides temperature difference --remember, energy transfer out of a system is equal to energy transferred into the surrounding --also, energy transfer into a system is equal to energy transfer out of its surrounding --work is a scalar and measured in energy or joules --following First Law of Thermodynamics, the equation is W+q=Delta E.total or DeltaK+DeltaU+DeltaEinternal=Delta E.total --in other words, if you combine the two equations together W+q=DeltaK+DeltaU --remember change in energy is proportional to magnitude of work done --what else changes energy especially E.internal is frictional force --the expression of Work-Kinetic Energy Theorem is W=DeltaK which means heat is absent and all energy transfer changes only kinetic energy (on moving object) --work equation when force acts over a distance.. W=f*d*cos@=DeltaK+DeltaU where d is displacement and cos90=0 and use F*dcos@ when direction of force is in the parallel direction of surface --energy divided into mechanical or non mechanical and then further divided into potential or kinetic can be represented as the metaphor.. ex. a hundred dollar bill can be separated into two 50$ bills

Human Eye

--human eye acts an optical instrument as well like microscopes and telescopes --it receives incoming light that is refracted and focused on an area at the back of the eye known as retina --cornea (does most of the bending) and lens (most control to focus light to retina) are two structures that bend incoming light rays and have them converge on the retina --the muscles around the lens relaxes, causing filaments to tighten and flattens the lens --this help increase focal length or focus light from far objects --muscles that tighten help focuses light from near objects by causing lens to bulge and reduce focal length of the lengths --essentially lens of near-sighted person causes light to focus too near the front of eye --while far sighted people can see far objects clearly and the lens causes light to focus too far from the front of the eye --therefore, converging lens corrects the vision of far sighted person by bending light from nearby objects that the lens can focus closer to the general area of retina since it is too far --based on near point and far point, far-sighted person has a near point located farther than average which happens by age when the lens stiffens and resists bulging necessary to reduce focal length --for normal vision, far point is at any point or infinity --diverging lenses correct near-sightedness by spreading light rays out more as it moves toward the eye which makes far away objects appear closer

Mass and Weight

--inertia stands for the tendency of objects to remain in their present state of motion (whether they are moving or at rest) --mass is the measure of an object's inertia --mass tells us how much that object will resist change in its motion (typically measured in kg) --weight is gravitational force that an object experiences when it is close to a larger object like near Earth --weight is typically measured in newtons (N) --Weight on the surface of Earth is mass * gravity --essentially weight and mass are proportional --on earth you have weight but in space you are weightless but still have the same mass as on earth so it does not change --forces act at the center of mass which cause acceleration and it the point of concentrated mass where single force can be applied --if there is a system and it is not uniformly dense, its center mass that coincide with its geometric center will shift away toward denser side --ex. is a cube half made of steal and half made of Styrofoam, the center of mass is toward the steal side --ex. the center of mass can be located in the hole of a doughnut or located in the middle of surrounded planets since the point is where it is perfectly balanced in any orientation

Equilibrium

--is the state in which there is no net force and no net torque meaning no acceleration --objects in equilibrium may be moving but not accelerating --if it is moving and rotating at a constant velocity, a system is in equilibrium --remember that force is inversely proportional to lever arm since it keeps system in equilibrium --ex. place finger closer to the heavier end so that the increased downward force of gravity is balanced by the decreased lever arm. causing it to still move --static equilibrium is when objects and systems have constant zero velocities --ex. of static equilibrium is when force due to gravity and normal force cancel out --dynamic equilibrium is when objects and systems have nonzero velocities, meaning velocities are constant --ex. of dynamic equilibrium is when force due to gravity and force of air resistance cancel out. --in an equilibrium, the sums of all the forces and torques equals to zero --when viewing systems in equilibrium think of.. 1. F.upward=F.downward 2. F.rightward=F.leftward 3. T.clockwise=T.counterclockwise

Inclined Planes

--normal forces opposes the gravitational force that causes an object to accelerate down on an inclined plane --the normal forces are typically perpendicular to the surface --the force of friction opposes the component of gravity parallel to the surface --lets say there is no friction and no attachments to the object on an inclined plane, the only forces are gravity pulling it downward and force from the plane pushing back against the block known as normal force --normal force is always perpendicular to the surface which makes a right triangle with the gravitational force --the normal force and gravity added together (mg+Fn) becomes net force which can be plugged into Newton's Second Law to find acceleration --that net force is always equal to mg*sin@ which points in the direction parallel to the plane surface --mg*sin@ is the vector sum of the weight and normal force. remember its for only incline plane since S represents Sliding. --mg*cos@ is always for normal force --acceleration of object moving down an incline is 0<a<g while object moving parallel on a surface a=o

Capacitor

--is used to temporarily store energy in a circuit --a circuit is able to draw current from a battery by adding a resistor, capacitor, or inductor --resistor is like a light bulb and is attached to a wire connected to the positive and negative nodes --a capacitor is added to a circuit to have energy generated by the battery to be stored --the capacitor can then discharge the energy at a faster rate than battery supplied --between two plates (one plate with positive charge with the same amount of negative charge of another plate), electric field can be determined using formula... E=(1/k)*(Q/A*E.o) --k is not the Coulomb's constant, instead it is the dielectric. Q is the charge on either plate while E.o is derived from Coulomb's constant K --remember Coulomb's constant K is calculated by 1/(4πE.o) --as voltage or electric field increase, so does the stored charge since E or V and Q are proportional --high capacity can store a lot of charge at low voltage C=Q/V --if there is parallel plate capacitors and separated by a distance, use equation C=k[(A*E.o)/d] and A is the area of the plate --also, the amount of charge that is stored is proportional to the area of each plate --the farther the plates are separated, the greater the voltage and lower the capacitance --the energy in units U stored in the capacitor is determined by.. U=1/2(QV) U=1/2(C*V62) or U=1/2[(Q^2)/C] --remember Q=CV --capacitors are exactly opposite to resistors but there are capacitors in series and in parallel --capacitors in series: (1/Ceff)=(1/C.1)+(1/C.2)+.. --for series, it can be thought of as a single capacitor with a distance between plates which is equal to the distance between plates and two capacitors --increasing the distance between the plates of capacitors decrease its capacitance --Capacitors in parallel: Ceff=C.1+C.2+.. --for parallel, it can be viewed as a single capacitor with a plate area equal to the sum of capacitor areas --so increasing area of plates increases its capacitance --ammeter is an instrument to measure current or voltage flowing through a circuit --voltmeter is an instrument that measures potential difference between any two points on a circuit --voltmeter attaches to two separate points on a circuit specifically parallel areas so the instrument does not affect the voltage and not draw a current --it requires a circuit element that provides voltage

Hydraulic Lift

--it is a simple machine that works with Pascal's Principle (pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout) --the machine consists of two pistons and container that enclose an incompressible fluid --the piston 1 applied pressure on the fluid which transferred to piston 2 --piston 2 has a greater force than piston 1 --remember force and area are inversely proportional when pressure is constant --the machine does not influence or change work since force of piston 2 is applied through a smaller distance --however, if piston 2 moves the same distance as piston 1 while experiencing greater force, then work is greater by piston 2 --in other words, F1D1=D2D2 or F1/A1=F2/A2

Center of Buoyancy

--it is the buoyant force that acts at an object's center of buoyancy --this only occurs if the object has a uniform density --this means the center of mass and center of buoyancy is the same --if there isn't a uniform density, this can be caused by torque on the object that causes it to spin --remember upward buoyancy force (F.b) is equal to the force pointing straight down or downward force (mg) which cancels out

Torque

--it is the measure of a force's ability to cause rotational acceleration --remember force acts at the object's center of mass which starts acceleration --but if the force acts anywhere else besides center of mass, it cause accelerated rotation --torque is a vector and the magnitude is given by the equation.. Torque=F*r*sin@ --force represents force vector while r is the position vector --r or position vector is the distance from the point of rotation to the point of application of the force --if the object is not rotating, any fixed point can be the point of rotation --So, since sin90 is equal to 1, it is easier to make the position vector extend from the point of rotation to the point where force acts at 90 degrees --90 degree point is called lever arm (l) and equation used is Torque=F*l --so greater the torque, greater the force and distance between points (r) meaning greater rotational acceleration --but force and lever arm are inversely proportional. this inverse proportionality is important for equilibrium --in other words, lever arm decrease will help torque stay constant and increase force

Projectile Motion

--it is the movement of an object through the air along a curved path due to gravity --good example of accelerated motion --gravity acceleration is constant about 10 m/s^2 --remember, this is not a linear motion but you can apply the linear motion equations once you resolve its vertical and horizontal components --acceleration in the vertical direction is constant and equal to gravity --acceleration is zero in the horizontal direction --without air resistance and force of gravity, acceleration remains constant meaning no change in motion and projectile would travel indefinitely in horizontal direction Overview SOH CAH TOA Rule: --Vo for vertical velocity is always Vsin@ (negative if arrow points down) while for horizontal velocity is Vcos@ --gravity (Ay or vertical acceleration) is -10 m/s^2 --acceleration on X-Axis or horizontal (Ax) is 0 but initial speed is equal to final speed (remain the same) --peak height of projectile curve can be solved using equation... V = √2gh and substitute V with VoSin@ --if an object is dropped straight down, the height can be determined. but remember vertical velocity (Vo) is zero **mass does not affect projectile motion assuming air resistance is absent** **remember, even if the projectile is motionless, acceleration is still equal to gravity so its constant** **if two projectiles leave with the same vertical velocity (same distance away), they will land at the same time regardless of their horizontal velocities**

Lens Aberrations

--lens aberration is when images are blurred and lack theoretical images Two Types: 1. Chromatic Aberrations --> --when light of higher frequencies focuses closer to a lens than does light of lower frequencies --higher frequency light bends more than lower frequency lights which means violet light will focus closer to lens than red light --this aberration occurs when different frequencies of light pass through lens simultaneously 2. Spherical Aberrations --> --unlike chromatic, only monochromatic light (multiple rays of light from a single optic frequency) is used --this aberration arise when rays are farther from the center of a lens focus at different points --images produced by this lens are clear only when viewed through the center of the lens

Light Waves

--light is the transfer of energy through alternating electric and magnetic fields --a change in magnetic field and ultimately change in electric field, depends on the charge movement --electric and magnetic fields are perpendicular to one another and direction of propagation is perpendicular --this means on a graph, a wave for electric field is located above X-axis while wave of magnetic field is direction facing downward located below the X-axis --but keep in mind that electrical and magnetic fields regenerate one another and they emanates from vibrating charge --light becomes visible when electromagnetic radiation is bent by the lens of the eye and focused on the retina --the electrical impulses are triggered and traveled to the brain --remember, electromagnetic waves are produced by accelerating charges --essentially when charge oscillates (swings back and forth/side to side) with frequency, it radiates energy in the form of electromagnetic radiation --remember light acts as a wave and a particle --in some cases, light as a ray moving in a straight line represents as an arrow

Reflection and Refraction

--light reflects when it encounters a mirror --light refracts when it encounters a lens --the angle at which a wave strikes an interface is called angle of incidence --the angle at which light it reflects is called angle of reflection --angle of incidence is equal to angle of reflection after reflecting off a plane or flat surface --all waves refract. for example, sound waves bend as they move from air of one temperature to air of another temperature --recall that speed of light in a vacuum is a constant c=3x10^8 m/s --index of refraction (n) can be found by n=c/v --greater the index of refraction for a medium, slower light moves or smaller velocity --memorize that indices of refraction for water is 1.3 while for glass is 1.5 --calculating the extent to change light speed that will bend light ray is predicted by Snell's Law: n1*sin@1=n2*sin@2 --remember n1 and n2 are the indices of refraction which is extent of each media on either side of the interface --while @1 is the angle of incidence that is located in the first or top media (ex. air), @2 is the angle of refraction located second or bottom media (ex. glass) --Snell's law does not violate the conservation of energy or light will have the same energy per photon regardless of incident. So do not be fooled, light when it reflects and refracts (even at the same time), there isn't twice the energy or light energy is not half split --regardless of energy conserved, light still bends as it moves from one medium to another --think about how the light source is so far away that the circular wave appears as a straight line --higher the index of refraction, speed increase and wave fronts cluster closer together. but if it transition to to a lower index refraction, speed still increase but wave fronts spread out meaning bends away from normal --recall that wave front can be side to side (line splitting high and low media), so if light approaches at 90 degrees, it is penetrating that line from top to bottom --light bends at an angle other than 90 degrees cause one part of the wave to slow down until rest --light ray bends toward normal (like normal force is perpendicular to a surface) is perpendicular to wave fronts --in other words, at 90 degrees, light rays do not bend and the speed is uniformly slowed down making waves more closely to each other instead of spread out like how it is in top high media --v=f*wavelength where frequency is constant, so larger the wavelength the greater speed and the greater the distance between wave front, the greater the speed and wavelength of the light --remember when light crosses into a new medium, frequency remains the same while the velocity and wavelength change --medium index is not proportional to wavelength meaning wavelength becomes longer as index is lower --Snell's law can determine critical angle meaning all photons are reflected at the angle of reflection and none will be refracted --angle of refraction is 90 degrees meaning sin90 is equal to 1, using Snell's law @critical=(n2/n1)Sin^-1

Magnetism

--magnets create magnetic field and any/all current (flow of charges) induces magnetic field --magnetic field strength can be measures in unit Tesla (T) --only moving charges produce magnetic field while electric field can include static or moving charges --magnetic comes with a north and south pole like how electric consists of positive and negative charges --also magnetic poles usually does not exist in isolation --the lines of force typically point from the north pole to the south pole of the magnetic creating the field --earth it self is a magnet, ironically, north pole is the south pole of Earth's magnetic dipole --ex. our magnetic compass is attracted to Earth's magnetic south pole which was named our geographic north pole --so the line of force moves from the south to the north pole --when electric field (stationary charge) is changed, it induces magnetic field and vice versa --a charge moving through magnetic field experiences a force perpendicular to velocity and magnetic field --magnitude of the force on a charge moving with velocity through a magnetic field can be found using.. F=q*v*Bsin@ --q as charge, v as velocity, B as magnetic field and @ is the angle between magnetic field and velocity --remember is @=90, then sin@ is 1 --magnetic force is always applied at 90 to the velocity of the particle --equation can be rewritten as qvB=m(v^2/r) --unlike electric field, magnetic field is non-conservative --so changing magnetic field that creates electric field is not conserved but is dissipated as heat in the charged object or current develops in the wire --the current generated in the wire or object as it moves out of external magnetic field creates its own magnetic field --thermal energy in the loop is developed since work is done on a force that is used to remove the loop at a constant velocity --recall W=F*dcos@, since magnetic field is applied at 90, cos90=0 meaning no work can be done by this force --without work, energy is not transferred to the particle so cannot change the speed or velocity

Magnification

--magnifying (m) light means making it larger --it is essentially the measure of the image's size and orientation relative to size --m = -(d.i/d.o) = h.i/h.o --image height is positive when the image is upright --when image is inverted it is negative --image smaller than the object has a magnification smaller than one while image larger than the object has magnification greater than one --positive magnification indicate image and object has the same orientation --negative magnification represent image has opposite orientation of the object --this means magnification tells the size between the image and object as well as its orientation --plane mirror questions tend to be too easy so it is not usually tested --but plane mirror is when the image is the same size as the object or h.i/h.o and m=1 -- -d.1/d.o means the image formed by plane mirror is the same distance from the object --also know that looking in a flat mirror it creates an upright image or virtual and located on the opposite side of the mirror from the eye and negative

Pressure

--molecules are moving in random directions and at random speeds --without single direction and collisions happen between fluid molecules and submerged object --force on one side of the object will be exactly countered by the force on its other side --so we will ignore gravity for the moment and assume fluid is moving while object is moving with the same fluid velocity --fluid pressure is the pressure experienced by the object as a result of the impulse of molecular collisions --Formula.. Pressure=Force/Area --SI unit pressure is Pascal (Pa) and pressure is a scalar --fluid pressure can be thought of as a type of 'stored' energy per unit volume --unit of pressure is equivalent to energy per unit volume --essentially pressure is a measure of energy of random velocities molecules within a fluid that's distributed over the volume --it's not possible to have negative pressure because that means there's fewer than zero collisions --so the negative pressure means gauge pressure which is the measure of pressured in comparison to local atmospheric pressure (assigned as zero) meaning chest pressure is lower than atmospheric pressure --the higher pressure in the chest allow air to be pushed into the lungs --another type of pressure is absolute pressure and it can be found from gauge pressure by P.abs=P.gauge+P.atm

Non-Ideal Fluids (Real Fluids)

--non ideal fluids are real fluids --remember drag and viscosity are like friction or what impede flow --this means viscosity and drag are proportional --drag occurs at the fluid-object interface where force is working against flow --so if you move away from this interface, the effect of drag decrease --the center of the pipe is where the highest velocity occurs and where it is furthest from fluid object interface --the resistance to flow increases as the length of a pipe increase --this is because the amount of fluid object interface increase with length --drag also increase when the pipe becomes more narrow since fluid volume and surface area reduces: Area or Volume=π*r^2*d. --ex. if the pipe radius decreases by factor of 2, the surface area is cut in half while fluid volume is reduced by a factor of 4 --since pressure is a scalar with no direction, fluid does not necessarily move from high pressure to low (unless its normal conditions) --if it does, equation to recall is Delta.P=Q*R where R is resistance to flow --instead, fluid flow direction depends on the tendency to increase entropy --the flow rate for a horizontal pipe with constant cross-sectional area can be determined by using Q=Delta.P[(π*r^4)/(8*n*L)] --its pressure, n for viscosity and L for pipe length and r for pipe radius --this equation is known as Poiseuille's Law which is used to determine blood flow rate in circulatory system --based on the equation you notice that viscosity increase causes the flow rate to decrease

Wave Features: Wavelength, Frequency & Period

--production of sound occurs by the vibration of a source such as vocal cords --vocal cords vibrate and create sound waves that travel as oscillation (point to point) or between high and low pressures --waves are said to be transfers of energy --wave is the result of vibration from one point to another --energy is transferred from the source such as vocal cords and to the ear through the air --the energy causes the ear to vibrate and create sensation of sound Types of Waves.. 1. Mechanical Wave: require a medium or substance. ex is sound waves or waves on a strong since it displace the media through which they travel -->transverse wave is a wave on a string in which the medium is displaced (displacement of medium) is up and down or perpendicular to the direction of wave propagation or side to side -->longitudinal wave is a sound wave in which the medium is displaced parallel to the direction of wave propagation 2. Electromagnetic Wave: does not require a medium through which to travel since it can propagate in vacuo. ex is light --on the MCAT assume all waves are ideal unless told otherwise --ideal waves are waves that travel through non-dispersive media --nondispersive is when the medium is elastic and wave is momentarily displaced but goes back to original position or maintain its shape. so it can't disperse as it travel --velocity of a wave is the distance the wave travels per unit time and it is determined by the medium through which waves travel --wave velocity is expressed as v=frequency*wavelength which is a similar equation to the velocity in translational motion v=d/t --keep in mind wavelength is the measurement of distance (meters or nanometers) or wave distance from any point in the wave to the point where the wave begins to repeat itself --frequency is inverse of time expressed in s^-1 or hertz (Hz) or it is the number of wavelengths that pass a fixed point in one second --frequency does not change as a wave moves from one medium to another --period (T) is the time it takes a wave to travel the distance of one wavelength and is the reciprocal of frequency (1/f) --it is the length of time the wave requires to complete one vibratory cycle --frequency and period both do not change when wave moves from one medium to another so period T can be determines by T=1/f or v=wavelength/T

The Pulley

--pulley acts by the same principle as the ramp and lever --it allows force to act over a greater distance --it also allows same amount of work to be done with less force --the force acts on the rope that is pulling and increasing the distance --this magnitude of force is known as tension which is a scalar quantity and is usually constant T=T1=T2+T3 --without the pulley, the force that lifts the mass would be equal to mg --with the pulley, the tension force is what lifts the mass --when tackling Tension or Pulley systems... 1. find regions of pulleys (looks like wheel) 2. add/sum up all the ropes pulling up the mass T1+T2=2T 3. ropes pulling down is T3=mg 4. follow T1=T2=T3 meaning 2T=mg or T=1/2mg 5. Tension force is halved so the force must be applied over twice the distance EX. lets say a mass is raised one meter by one rope on a pulley wheel system. this means one meter must come off of both side of the same rope (pull up as one side of the rope goes down) making a total of 2 meters. So reduced force (mg) by a factor of 2 leads to increasing the distance over by a factor of 2. **overall, force and distance inversely proportional** 6. work required to lift the mass is not changed or held constant

Hooke's Law

--remember its about compressing and stretching an object which creates another type of force --this law describes the force that most objects apply against a deforming force --object's force is directly proportional to the amount of deformation or change in position (delta X). --Hooke's Law equation is F=-k*deltaX --k is constant unique to a given object and negative sign in the formula can usually be ignored if its not compressed but rather stretched or thickens --on mcat it is often referred as spring constant, k=mg/deltaX --any object deformed beyond yield point or displacement. will loose ability to regain original shape which means the object reached fracture point --this type of law often applied to springs where force is the tension on the spring and delta X is change from spring's position at rest

Resistors & Dielectric Constant (k)

--resistance in parallel are like one wider resistor, meaning may have less resistance Symbols in Circuits and in Parallel: 1. Resistors --> appear like up and down waves 2. Capacitor --> parallel equal lines facing each other with a gap 3. Battery --> parallel unequal lines facing each other with a gap --side to side (in a row) resistors is called resistors in series and there shouldn't be two resistors separated by a node (i) --total effective resistance is the sum of individual resistances Reff=R.1+R.2+... --resistors in series can be thought of as a single resistor with a length equal to sum of the lengths of individual resistors --in other words length of resistor (L) is proportional to its resistance (R) --a resistor facing or located across another resistor (regardless of orientation) is known as resistors in parallel and there is a node (i) in between the components --so (1/Reff)=(1/R.1)+(1/R.2)+... --resistance is inversely proportional to cross sectional area of a single resistor R = 1/A --so decrease R means increase area. ex by having a bridge with parallel roads, it helps improve traffic flow or better current which is the opposite of resistor purpose --dielectric constant k is not the same as Coulomb constant K --dielectric contains dipole in external electric field --refers to the substance between the plate of a capacitor --the substance between the plates must be an insulator to prevent electrons to conduct from one plate to the other hindering charge built up --so dielectric help resist creation of electric field which allows capacitor to store more charge --when energy stored builds up, electric field increase between the plates of capacitor promoting dipole rotation to point in the direction of electric field --the energy is a form of work done on dielectric and the work is conversed in the field --basically work is done on dielectric while energy is stored by dielectric --in other words, the more charge added to build electric field made by dielectric, lower the energy stored or electric field within the capacitor --dielectric constant of a vacuum is a unity of one. ex air is very close to one --think of a right triangle on a graph in which voltage is the X-axis, and charge (Q) is Y-axis --so from a right triangle 1/2QV to find slope --you can use this idea to calculate potential energy in Joules U=Q*V --no charge means voltage across a capacitor is zero --or increase charge also increase voltage. To find Coulombs Q=C*V or V=J/C --dielectric is also in charge of limiting the value of the possible voltage across the plates --in fact maximum voltage can break down dielectric and conduct electricity which is known as dielectric strength

Center of Charge

--similar to center of mass, center of charge is the point from which the charge generated by an object or system of objects can be considered to originate --ex the center of charge exists in the center of a sphere since there is no actual charge at the center. --all the positive charges spread and surround outer sphere as a way of repelling each other and create distance --electrostatic force on a charged object placed outside the sphere can be found using Coulomb's Law --r in the law equation is the distance between one object and the center of a different sphere/object --a field is a type of distortion or condition in space creating force on a charge or mass (if its gravitational field) or magnet (if its magnetic field) --magnetic and electric field are essentially the same field --with fields, forces are created and act as a distance Lines of Force: a way a field can be represented --the line of force points in the direction of the field --for electric fields, the force points from positive to negative --or the towards the mass creating the field for gravitational fields --the distance between lines indicates strength of the field (closer the lines, stronger the field and vice versa) --lines of force do not interact and if it does cross, this represent a field pointing in two opposite directions from the same location --lets say a sphere covered of positive charges outside, there won't be electric field inside --this also happens for negative charged sphere and the reason is because line of force begin on a positive charge and end on a negative charge --another reason is that lines for not enter the sphere. for electric field, lines face out of the sphere Electric field: --is an electrostatic force per unit charge and the symbol is E --E is a vector pointing in the direction of the field --E is a unit of N/C or V/m --using Coulomb's law, electric field is E=k(q1/r^2) --force on a charge in an electric field is known as F=q*E

The Continuity Equation

--since fluid is incompressible, the volume remains constant --fluid moving through a section of a pipe equals Area of pipe*distance of the pipe section --if the fluid moves completely through the pipe section in a given time, rate Q is equal to area*(distance/time) --velocity is d/t --by combining these equations, the continuity equation is Q=A*Velocity --remember Q is the volume flow rate --flow can be expressed in terms of mass --mass of flow rate (I) is equal to p*Q which is proportional to p*A*V --this formula shows that area is inversely proportional to velocity --for an ideal fluid, flow rate is constant --in other words, the narrower the pipe, the greater velocity

Sound and Intensity

--sound is the transfer of energy through oscillations between high and low pressures --sound becomes audible when oscillations in pressure within a certain frequency range within a certain frequency range --this sound cause sensory elements of the ear to vibrate and trigger transmission of electrical impulses to the brain --sound waves are characterized by its pitch and intensity --pitch is the measure of how high or low note sounds which correlates with frequency --higher the note, high the pitch and high frequency --intensity is the measure of rate at which a wave transfers energy from point to point P=Delta.E/f --intensity (I) or average rate of energy transfer per unit area is in units of W/m^2 --intensity of sound wave is given by I=2π^2*p*f^2*A^2*v --p is the density of the medium, f is the wave frequency while A is the amplitude and v is the wave velocity --recall frequency depends upon wave source while density is a property of the medium which can change amplitude and velocity --ex. when snapping your fingers in the air, some of the energy is transferred away from your fingers in the form of sound wave moving in all directions --total energy of wave is constant but spread over a surface area for an enlarging sphere --increase in area is associated with decrease in intensity --intensity can be used to describe any type of wave --intensity level is the measure of loudness or how intense a sound seems --ex. rustling of leaves are 10x more intense than created by normal breathing although we do not experience them as 10x louder --artificial scale for intensity level has been created based on logarithmic scale (B). --scale is in units of decibels (dB) --remember relationship between intensity and logarithmic scale or intensity level... B=10log(I/Io) where Io is the threshold intensity of human hearing (lowest intensity) --if intensity increase by a factor of 10, decibels increase by addition of 10 decibels --in other words, increase from 30 to 3000 W/m^2 is equal to increase of 20 decibels since you are adding 2 decibels (10+10) --ear vibrates in response to waves with frequencies between 20-20,000 Hz and waves with this frequency range are known as audible waves --waves above this range are called ultrasonic wave which is used in medical imaging technology such as sonography or ultrasonic imaging --ultrasounds start by having the probes containing crystal to vibrate and produce high frequency sound wave --then, the high frequency sound wave is received and processed as echoes --the high frequency of ultrasound sound waves are reflected off boundaries within the body which returns to ultrasound probe --the crystals will vibrate from the returning waves which generates a current that is analyzed by ultrasound machine --the machine evaluates the distance of the boundary from the probe as well as determine the relative densities of the media on either side of the boundary --remember, greater the difference in density, the greater the intensity of reflected sound --all these information help produce sonographic image

Fluids

--standing (non moving) fluids contain a pressure gradient that results in an upward force called buoyant force --buoyant force acts counter to the downward force of gravity --remember energy is never lost but converted or transferred as work or heat --similarly, sum of kinetic energy per unit volume and potential energy per unit volume remains constant --standing fluids means forces in equilibrium while moving fluids think energy --essentially, when receiving problems involved with moving fluids, think about energy --fluid is also described by density, p. formula uses.. m=p*v --when an object is floating, masses are equal (mass object = mass fluid) --when an object fully submerged, volumes equal (volume object = volume of fluid) --fluids are liquid or gas --the molecular bonds are constantly breaking and reforming due to high kinetic energy --the molecules are not arranged with any order or structure --they also move in random directions which is what causes fluids to have temporary resistance to forces of the surface --but fluids can create permanent force directed outward since it is what allows it to move within a large volume and withstand forces perpendicular to the surface --fluid pushes and mold until its surface matches the shape of the container --when fluid comes to rest, it experiences only normal force and force gravity --the way fluids withstand the weight of a motionless battleship by conforming its surface to that of a the battleship so that all forces are normal to its surface --the net force from the moving ship is not perpendicular to the water surface and the water provides temporal resistance --these qualities allow the ship to propel through the water with smaller force than its own weight

Visualizing an Ideal Fluid

--streamline helps visualize ideal fluid --it consists of multiple lines flowing through pipes and certain directions --velocity of the particle at any point along a streamline is tangent to the curve made by the streamline --ex. low velocity is when lines are more far apart from each other and existing an opening --high velocity is when streamlines get closer and sort of pinched to enter an opening

Surface Tension and Capillary Action

--surface tension is the intensity of the intermolecular forces of a fluid per unit length --ex. a needle is able to float on the surface of water even though it is more dense --what is supporting the needle is the force created by surface tension and not buoyant force since water is not displaced --essentially, the intermolecular bonds of the water are stretched and pull upward --surface tension is also responsible for the formation of water droplets --the intermolecular forces pull inward for water in order to minimize surface area and create a more spherical shape --remember a sphere has the least surface area per volume --surface tension is affected by temperature; higher temp leads to weaker surface tension --recall the capillary action where fluid is pulled up a thin tube --for this to occur, two types of forces are needed; intermolecular forces (cohesive forces) responsible for surface tension and forces between molecules of the tube and fluid molecules (adhesive forces) --think of how surface tension is crucial for lung function --the alveoli in our lungs are under constant pressure and surface tension of the alveolar wall makes it possible to collapse --to prevent the walls to collapse, the body produce surfactant that reduces intermolecular/cohesive forces and allow gas exchange Cohesive Greater Than Adhesive: --convex surface is formed as fluid is pulled downward by vertical component of surface tension Adhesive Greater Than Cohesive: --concave surface is formed as fluid pulled upward by vertical component of surface tension

System Not in Equilibrium

--systems not in equilibrium must have only translational acceleration --meaning center of mass is accelerating translationally or its parts are accelerating rotationally --also sums of forces or force of gravity is ΣF = m*a --for non-equilibrium, remember to ignore the acceleration and lay out the problem as if it is in equilibrium by writing out equations such as.. F.upward=F.downward --since its not equilibrium, those forces are not equal and decide which Force is greater --then predict the direction of acceleration and check if one of the axes is parallel to the direction of acceleration --ex. if it is accelerating downward, the downward force is greater and add 'ma' to the weak force which is F. upward... F.upward+ma=F.downward --then choose the system and find the formula to use for plugging. --when reaching terminal velocity, gravitational force downward is equal to force of air resistance upward --at terminal velocity he is in equilibrium and acceleration is zero

Conservation of Charge

--the universe has no net charge --net charge is created by separating electrons from protons --basically positive and negative charges cancel each other out --smallest unit of charge is one electron unit e=1.6x10^-19C --coulomb force is far greater magnitude than gravitational force since force due to gravity is ignored --especially if two or more masses are very large, gravitational forces are negligible/unimportant --when drawing a diagram of two objects, there are forces from each facing toward each other. it is because of attractive electric forces --also each have distinct charges (qA and qB) and masses (M.A and M.B) --like the forces, the accelerations from each object is moving toward each other (a.A and a.B) --since one object is larger than the other; q.A=2q.B M.A=2M.B |F.A|=|F.B| |2a.A|=|a.B| --> with object A to be bigger in size --in summary, |F.A|=|F.B|=M.A|a.A|=k(q.A*q.B)/r^2

Graphs of Linear Motion [Displacement Vs Time Interpretations]

--to examine changes in displacement (e.g., in meters), velocity and acceleration of an object in linear motion, graph them as Y-axis over function of time on X-axis --ex. linear motion graph describes a particle's north or south and east or west position and movement would not indicate this Displacement Vs Time Interpretations (represents velocity): --upward slope indicates positive velocity while downward is negative or in the reverse direction. --straight line slopes are constant velocity (constant decline or increase of displacement over time) while straight horizontal line has a zero slope meaning the particle isn't moving. --you see a changing velocity and acceleration (rate of change in velocity) when there is a curves line --the area under the curve has no meaning in this type of graph --for respect to north and south positions, lets say north is designated to be positive. so if a slope had a constant increase of 20 meters over 20 seconds, that velocity constantly 1 m/s. (position and direction of up and down cannot be determined by this) --stationary particles represented by horizontal slope can depict movement along north-south axis (positive and negative hemisphere) but no information of whether or not its moving east or west --slope of the entire line is total distance in meters over time. from the start, particle moved up by 20 meters (north) and from the start to the hemisphere under the X-axis, particle moved down by 20 meters (south which means total displacement is zero (not moving east or west) **overall, slope is velocity and area is meaningless**

Energy and Equilibrium Introduction

--torque is a rotational motion that is produced by forces acting at points other than an object's center of mass --torque measures the ability of a force to produce rotational motion --while translational motion is produced by forces acting at an object's center of mass --in equilibrium, there isn't a net force, no torque and no translational/rotational acceleration --energy is not destroyed, it either converts from one form to another or transferred between a system --in other words, energy is conserved so energy in or before equals energy after or out --energy's surrounding is heat or work --keep in mind, work is total change in energy or force*displacement --energy equation purpose is to keep track of where energy came from and where it is going Energy Equations: 1. energy of system + surroundings before = energy of system + surroundings after 2. energy leaving system = energy entering the surrounding 3. energy entering a system = energy leavening the surroundings 4. total energy = sum of all energy in that system

Vectors and Scalars

--translational motion includes displacement, velocity, and acceleration --change in the direction of motion is a change in velocity which requires acceleration --net force create acceleration and ultimately cause/change motion such as from rest to motion --vectors and scalars solve problems about motion and force Scalar: --a physical quantity that has magnitude but no direction. --distance and speed are scalars to describe motion. --changing the magnitude or direction of a vector creates a new vector Vector: --physical quantity with both magnitude and direction. --represented by an arrow which indicates the direction of the vector. --ex. is the length of the arrow, velocity, displacement, force and acceleration. Adding & Subtracting Vectors: --this helps produce new vectors such as adding forces to calculate net force --to add vectors geometrically, place the first vector above the second vector but their head arrows facing opposite from each other --notice for example, sum of two arrow velocity vectors with magnitude of 10 and 7 m/s is... 1. greater than or equal to the DIFFERENCE of the magnitudes of velocity vector (3 m/s) 2. smaller than or equal to the SUM of the velocity vectors magnitude (17 m/s) --to substract vectors geometrically, place the heads of the two vectors together and draw an arrow from the tail of the first to the tail of the second creating a triangle --add the negative vector with the other vector or substract the two positive vectors

Sign Conventions for Work

--understand if there are transferred heat or work (overall energy) --ex. if the system has the same temperature as its surrounding, then there isn't any heat --energy change is accomplished through work done on the system --sign conventions for work provide a standardized way to show where energy is coming from and where it is going --if energy is entering the system when work are done on it, assign it as positive value and vice versa --the force acts in the direction of displacement, assign it to positive value and vice versa --force of gravity is positive for work on a skydiver falling toward the earth --force of air resistance does negative work on that same skydiver --remember, at maximum potential energy, there is minimum kinetic energy (ex. when a ball is tossed up at maximum height) --at maximum kinetic energy, there is minimal potential energy (ex. when ball coming down back to the hand)

Density

--understanding the exact amount of fluid or substance can be known from knowing mass and energy and vice versa --in other words mass and energy (extensive properties) change with quantity of a substance --other two properties that are analogous to mass and energy are density (p) and pressure --density is the heaviness of a fluid. formula is.... p=m/volume -- SI units of density is kg/m^3 --density is not easily changed like gas meaning usually constant --when there is a change in volume leading to change in density.. equation of ideal gas law is PV=nRT Rules: 1. changing amount of fluid/substance does not change density 2. compressing fluid changes volume and density but not mass 3. to understand density more, specific gravity (S.G.) is created. it is a substance's density (p.substance) compared to the density of the water (p.water). equation.. SG=(p.substance)/(p.water) --> SG less than one indicated substance lighter than water while SG of 1 means substance equally as heavy as water. --> also SG greater than 1 indicated substance heavier than water --> for the mcat, memorize density of water in two forms: p.water=1000kg/m^3 or 1g/cm^3

Waves: Sound & Light

--waves are disturbances that transfer energy from one point to another such as through vibrations or pressure variations --as waves propagate through media, reflection, refraction, diffraction and dispersion may occur --Doppler Effect is when a wave source and observer moves toward one another creating higher frequency and vice versa --sound is the transfer of energy as oscillations between high and low pressure through medium such as air --light is the transfer of energy through alternating electric and magnetic fields which does not require a medium

Waves: Within and Between Media

--when waves travel from one medium to another, velocity changes --ex. a fish may hear the tapping on the wall as a different version of the wave due to change in wavelength, velocity and loudness affected by glass and water --glass and water on the other side is a different medium --but the knock once per second stays constant for both human and fish Two Characteristics of Given Medium Determine the Velocity of Waves: 1. medium's elasticity or resistance to change in shape. **essentially it measures how quickly disrupted molecules will spring back into original shape which is due to increase intermolecular forces like stretched rubber band** **greater elasticity of the medium will allow object to snap back to its position faster and moving the wave along** 2. medium's inertia or resistance to change in motion **assuming temperature of the medium is constant** **recall how mass is a measure of inertia and the weight tends to slow the wave down** 3. when temperature was told that it does change, it affects the velocity of the sound wave v=√YRT/M where Y is a specific gas constant when temperature changes during contraction, R is the universal gas constant and M is molecular mass **greater the temperature, greater the random velocity and greater the sound wave velocity --velocity of a sound wave is v=√B/p where B is bulk modulus of a medium as a measure of elasticity and p is the density of medium as measure of inertia --this equation does not include wavelength of frequency because the velocity of a wave within a medium depends on characteristics of medium and not traits of wave --also it is possible that two different waves like sound waves have distinct wavelength so it will have the same velocity within a given medium --it is usually assumed that temperature of a medium is constant unless told otherwise --temperature affect velocity of a sound wave v=square root of (R*T*constant of specific gas/M) --R is the universe gas constant while constant specific gas (Y) is what compensates for temperature change --greater the temperature, greater the random velocity and greater sound wave velocity --ex. think of how waves move more quickly through hot gases than cold --remember, frequency of a wave that moves from one medium to another does not change --but the velocity does change according to the characteristics of medium --ex. increase in elasticity (promote intermolecular attraction between molecules) will increase wave velocity. increase in inertia (promote mass and density) will decrease velocity of a wave --people may think waves move faster in air than water because of its density difference --in fact, water has greater bulk modulus so waves move faster in water than air... V.wave in solid greater than V.wave in liquid which is greater than V.wave in gas

Component Vectors

--whose vector sum (ex. P and Q perpendicular) is equal to the original vector --it is by separating vectors into X and Y component vectors before adding and subtracting --vectors like X and Y are perpendicular to each other so they have limited to no fashion of affecting one another --this creates three different kinds of triangles or component vectors such as 3-4-5 triangle or less common 5-12-13 triangle --each component have different possible meeting of the head of one partner (ex. P) and the tail of another (ex. Q) --to find the lengths of the component vectors, use Pythagorean Theorem (SOH, CAH, TOA) or Sin@=O/A, Cos@=A/H and Tan@=O/A --O=HSin@ or A=HCos@ --keep in mind, opposite is the height, adjacent is the length and hypotenuse is the long ramp --component vectors are always right angles to each other and their sum is equal to the vector being replaced or original

Salty's Five Step Never-Fail Method for Solving Physics Problems

1. Breathe: remember that MCAT only tests basic physics 2. Diagram: draw a well labeled diagram to help provide you new insight into the problem and puts the question into your own terms 3. Isolate: only concentrate on the body or bodies that are relevant to the question and ignore extraneous information 4. Variable: identify variables that describe the body or system of bodies of interest such as values given and asked to find 5. Equation: write down equations that includes the variables you know and the one for which you must solve

Wave Characteristics

1. Frequency --> f, unit Hz which is defined as number of wavelengths to pass a fixed point in one second. determined by wave source 2. Period --> T, units seconds which is number of seconds required for one wavelength to pass a fixed point. determined by wave source 3. Velocity --> V, units m/s which is the distance a wave travels per unit time. influenced by medium and based on V=f*λ, increase velocity mans increase in wavelength 4. Wavelength --> λ, unit meter which is the distance from any point on a wave to the point where the wave begins to repeat. influenced by medium

Conservative and Non-Conservative Forces

Law of Conservation of Mechanical Energy: the sum of mechanical energies remain constant K1+U1=K2+U2 (no heat and only conservative forces) written another way is 0=DeltaK+DeltaU --when a conservative force does work on a system, the system experiences no change in mechanical energy --basically work by a conservative force is equal to zero since the mechanical energy before equal the mechanical energy after --the conservative force of gravity depends on the function of positions especially within a gravitational field --it is associated with potential energy which makes sense since potential energy is the energy of position --ex. conservative Hooke's law force depends on positions of springs or objects creating it --overall, total mechanical energy (sum of potential and kinetic energy) remains constant for conservative forces --conservative force can convert ofne form of mechanical energy to another but the total mechanical energy remains unchanged Law of Non-Conservative Force: if this does occur on a system, the mechanical energy will change, meaning mechanical energy before is not equal to mechanical energy after. --examples of non-conservative forces are kinetic frictional forces and pushing/pulling forces applied by animals --work done by non-conservative forces equals the change in mechanical energy of the system. essentially non-conservative forces do the work formula is....W=DeltaK+DeltaU

Fluids in Motion

Molecules of Moving Fluid Have Two Types of Motion: 1. random translational motion --> contributes to fluid pressure as in a fluid at rest 2. uniform translational motion --> shared equally by all the molecules at a given location in a fluid --object moving along with the fluid will not experience additional collisions or contribute to fluid pressure --this is because of uniform translational motion --the energy from two types of motion (ex. random translational motion vs. uniform translational motion) can be converted back and forth --lets say there is an openning in a container, the fluids and molecules will move through the opening without colliding with anything in that same direction meaning the random motion change to uniform motion --fewer collisions indicate less pressure --this is why water acts as an excellent buffer for chemical reactions

In the cause of submerged and sunk object

Submerged --submerged and sunk objects displace volume of fluid which is equal to its own volume --but only submerged object experiences an upward buoyant force that is equal in magnitude to the downward gravitational force --upward and downward force are equal when delta.y is at its maximum values --the object is entirely submerged within the fluid, so F.b=F.G meaning m.fluid=m.object and v.fluid=v.object --also density equals mass divided by volume and density sp p.object/p.fluid equaling to one --density reaches its maximum value the moment the object is submerged --then buoyant force depends on density --if the object moved from depth y1 and y2 to depth y3 and y4 --> object remain there and would not experience upward or downward force Sunk --object experiences as upward buoyant force of lesser magnitude than the downward gravitational force --the upward buoyant force never becomes as great as the downward gravitational force, so it is the reason why the object sings --until the object reaches the surface, the downward force no longer accelerates it downward and the upward normal force is just as much as the downward force --the density is greater than the density of the surrounding fluid --equation to keep in mind, F.b+F.N=F.G=m.object*g --apparent weight of the object (F.N) is less than m*g --essentially, weight is equal to the difference between the downward force and upward force --apparent weight loss of the object is (p.fluid/p.object)x100% --v.fluid=v.object*[(p/fluid)/(p.object)] --also equals to (m.fluid)/(m.object)=(m.fluid*g)/(m.object*g)

A System for Mirrors and Lenses

System of how to find positives and negatives: 1. remember an observer must stand on the same side of the mirror as the object (ex. both on the left side) 2. but to view an image formed by lens, an observer or object must stand on the opposite side of the lens **when rules 1 and 2 are true, object distances (d.o) are positive because the object is where it should be** 3. Converging lenses only produce positive focal points 4. Diverging lenses have negative focal points 5. Diverging mirrors and lenses also make negative, virtual, and upright images 6. Converging mirrors also make positive real, and inverted images **a way to remember it is "I (eye) am positive that the real is inverted" which is the image on the side of the eye. (unless if the object is within the focal point, then it is negative virtual and upright** **diverging is the opposite of that phrase so not eye side, negative, not real and not inverted** 7. Memorize the 3 formulas.. **P=1/f=(1/d.o + 1/d.i); M=h.i/h.o=(-d.i/d.o); tan@=(h.o/d.o)=(h.i/d.i) so h.i/h.o = d.i/d.o Summary: --Focal Rule --> positive focus (F) for converging while negative for diverging --Object Rule --> if object where it should be d.o is positive but if not it is negative --Image Rule --> eye side is positive (converge) while image on opposite of eye is negative (diverge)

Free Body Diagrams

—consists of all types of forces and vectors —the vectors demonstrate the direction and magnitude of each force —diagram is helpful in providing visual indication of whether or not a net force is acting on the system How to Draw: 1. Place a point at the center of mass of a simple shape 2. If Earth's gravitational force is acting on the body, draw a vector pointing downward from that center point 3. If normal force/contact perpendicular force is present, draw a vector pointing upward from the center point 4. The forces with greater magnitude, draw the vectors to be longer lines 5. Take note of which force vectors cancel out and which do not 6. Determine if there is a net force on the body, if there is then there will be acceleration 7. Typically there is a parallel force or friction resisting slide or falling which is a vector pointing toward center of point (Fk) 8. If the object is getting pulled up by a string, that is another type of frictional contact force (Ft) —net force is the sum of all forces acting on an object —forces of opposite directions with equal magnitude will be zero or cancel out —if there is gravitational force, it's written in mg **all these contact forces acting on the object should only be considered**