# MCAT Physics

∆U=Q-W change in internal energy is due to heat transfer and work done by system (+W=expansion, work done by system; -W=compression, work done on system; +Q=heat flow into system; -Q=heat flow out of system; +∆U=inc temp; -∆U=dec temp

1st law of thermodynamics

for any process, entropy of universe inc (for irreversible) or stays the same (for reversible); ∆Suniverse=∆Ssytem + ∆Ssurroundings > 0; objects exchange heat higher->lower temp until they reach equilibrium

2nd law of thermodynamics

Fbuoy=pfluid x Vfl displaced or object submerged x g = mass fl displaced x g SGobject=% of object volume submerged in water

Archimedes' principle and buoyant force

P₁ + (1/2)pv₁² + pgh₁=P₂ + (1/2)pv₂² + pgh₂

Bernoulli's equation: sum of static and dynamic pressures is consistent, relates to venturi effect

real (-m/+i), virtual (+m/-i)

For images with a single lens or mirror, inverted images are always _____ and upright images are always _____

V=IR

Ohm's law (voltage drop btw 2 points in a circuit)

V=A1d1=A2d2 P=F1/A1=F2/A2 W=F1d1=F2d2

Pascal's Principle/hydraulic systems equations

diverging, myopia

a concave lens is (converging/diverging) and is used to treat (myopia/hyperopia)

converging

a concave mirror is (converging/diverging)

virtual, upright (-i, +m)

a concave/diverging lens will always produce __, __ images

converging, hyperopia

a convex lens in (converging/diverging) and is used to treat (myopia/hyperopia)

diverging

a convex mirror is (converging/diverging)

chromatic aberration

a dispersive effect of a lens where white light splits significantly, resulting in a rainbow halo around images

perpendicular

a magnetic force acts on a moving charge in a direction that is ____ to the velocity of the charge and ____ to the direction of the magnetic field

Pabs=P₀ + pgz p=density in kg/m³ z=depth of object P₀=pressure at the surface/ambient pressure

absolute (hydrostatic) pressure

a = ∆V/∆t = ∆x/t²

acceleration

V=Ecell - iRint (Ecell=emf of cell, i=current, Rint=internal resistance) if cell not driving any current (switch is open) then Rint is zero so voltage of cell=emf. When i is not zero and there is internal resistance, voltage < emf.

actual voltage supplied by cell to a circuit

4,2α or 4,2He

alpha decay emits this

w=2πf=2π/T

angular frequency of a wave, given in radians

A=(1/2)bh

area of a triangle

dec, dec, dec, inc

as a ramp's angle increases, Normal force (inc/dec), kinetic friction (inc/dec), Work (inc/dec), and acceleration (inc/dec). Fk=µFₙ, W=Fdcosθ, W=-µFₙd

6E23

avogadro's number

0,-1β or β⁻

beta decay emits this

Fg=pVg=(m/V)Vg=mg

buoyant force=weight of a given volume of liquid (Archimedes' principle)

avg speed=distance/time

calculate avg speed

v=∆x/t (∆x=displacement, NOT distance)

calculate avg velocity

Cp=C1 + C2 + C3 (total capacitance increases as more capacitors in parallel are added; more charge is being added while voltage is the same for each) compare to resistors in series

calculate capacitance of the system for 3 capacitors in parallel

1/Cs=1/C1 + 1/C2 + 1/C3 (capacitors must share voltage drop in loop, so as more are added they can't store as much charge, decreasing the total capacitance) compare to resistors in parallel

calculate capacitance of the system for 3 capacitors in series

∆S=Qreversible process/Temp in kelvin

calculate entropy

r=(mv)/(qB) Fc=Fb (mv²)/r=qvBsinθ

calculate radius of a particle moving on a circular path due to a magnetic field B

1/Rp=1/R1 + 1/R2 + 1/R3 (greater # of conduction paths reduces total resistance; Rp will dec as more resistors are added)

calculate resistance of the system for 3 resistors in parallel

Rs=R1+R2+R3 (I is the same at each point)

calculate resistance of the system for 3 resistors in series

β=10log (I/I₀) dB

calculate sound level (intensity) in decibels

Vp=V1=V2=V3 (V is the same at each point, same as resistors in parallel)

calculate voltage of the system for 3 capacitors in parallel

Vs=V1 + V2 + V3 (same as resistors in series)

calculate voltage of the system for 3 capacitors in series

Vp=V1=V2=V3 (V is the same at each point)

calculate voltage of the system for 3 resistors in parallel

Vs=V1+V2+V3 (I is the same at each point)

calculate voltage of the system for 3 resistors in series

C=Q/V

capacitance (units: farad 1 F=1 C/V)

C=ε₀(A/d) ε₀=8.85E-12 F/m A=area of overlap btw 2 plates

capacitance for parallel plate capacitors

C'=κC=κε₀(A/d) (κ≥1 because the dielectric material is insulating)

capacitance when a dielectric material is inserted btw the plates (inc capacitance)

x=(m₁x₁ + m₂x₂)/(m₁ + m₂) v=(m₁v₁ + m₂v₂)/(m₁ + m₂)

center of mass

ac=v²/r

centripetal acceleration

Fc=(mv²)/r

centripetal force of circular motion

nodes

closed boundaries correspond to (nodes/antinodes)

insulator (nonmetals, rubber, glass, wood, plastic)

conducts electric charge poorly; high resistance

conductor (metals, copper, gold, silver)

conducts electric charge readily; low resistance

Q=v1A1=v2A2 v=speed, A=cross-sectional area

continuity equation (fluids), flow rate (Q)

F=(9/5)C + 32 1∆C=1.8∆F

convert between celsius and fahrenheit

K=C + 273

convert between celsius and kelvin

confidence (1-α)

correctly fail to reject a null hypothesis when it is true

power (1-β)

correctly reject a null hypothesis when it is false

1/(4πε₀)=9E9 Nm²/C² (ε₀=8.85E-12 C²/Nm²)

coulomb's constant (k)

Fe=(kQq)/r² units: N (k=1/(4πε₀)=9E9 Nm²/C²)

coulomb's law: magnitude of electrostatic force

θc=sin⁻¹(n₂/n₁)

critical angle: the refracted light ray passes along the interface between the media (has a 90° with the normal line) if incident angle at a medium boundary is greater than the critical angle, total internal reflection will occur

Vc=(Nr x viscosity)/(p x diameter)

critical speed: point at which smooth laminar flow becomes turbulent flow

I=Q/∆t (ampere 1 A=1 C/s)

current (flow of positive charge between 2 points w/ diff electrical potentials connected by a conductor)

D=m/v=SG substance x SG water

density (D or p)

Cp-Cv=R

difference between heat capacities at a constant volume (Cv) and constant pressure (Cp)

p=q x d

dipole moment (p)

f'=f(v±vD)/(v-+vS) (use top/first sign when moving toward, and bottom/second sign when moving away) vD=detector speed, vS=source speed, f=speed of sound in medium

doppler effect

Wout/Win = (Fload x load distance)/(Feffort x effort distance)

efficiency

load distance x pulley strings (at least 2)

effort distance of pulleys

U=(1/2)kx²

elastic potential energy

E=kp/r³

electric field on perpendicular bisector of a dipole

V=kQ/r=EPE/q units: J/C or V

electrical potential

EPE=W=U=kQq/r units: J

electrical potential energy

V=((kqd)/r²)cosθ=((kp)/r²)cosθ

electrical potential near a dipole

nothing, the starting element "captures" an e- or 0,-1e⁻

electron capture emits this

E=hf (h=6.6E-34 Js) (note c=fλ)

energy of a photon

n=c/v (c=speed of light in vacuum=3E8, v=speed of light in medium)

equation for index of refraction (n)

λ=4L/n f=nv/4L

equations for wavelength and frequency of a closed pipe (one closed boundary and one open boundary)

λ=2L/n f=nv/2L

equations for wavelength and frequency of a string (closed boundaries on both ends)

λ=2L/n f=nv/2L

equations for wavelength and frequency of an open pipe

Vf=Vo + at x=((Vf + Vo)/2)t x=Vot + (1/2)at² Vf²=Vo² + 2ax

equations of kinematics (linear motion), used when the acceleration is constant

n=n₀e^(-λt) (n₀=initial quantity, λ=decay constant)

exponential decay

hyperopia

farsightedness

1/f=1/f₁ + 1/f₂ + 1/f₃

focal length of a multiple lens system w/ 3 lenses

e=1.6E-19 C

fundamental unit of charge (+ charge of a proton, - charge of an e-)

γ and forms same element at lower energy level

gamma decay emits this and does this

Pgauge=Pabs - Patm=(P₀ + pgz) - Patm (when P₀=Patm, Pgague=pgz)

gauge pressure

f=v/λ

general equation for frequency of a string/pipe

U=mgh

gravitational potential energy

resistor

has an intermediate amount of resistance to electric charge R=p(L/A)=V/I

enthalpy (∆H)

heat (Q) at a constant pressure is called

Cp=(5/2)R

heat capacity (C) at constant pressure (isobaric)

Cv=(3/2)R

heat capacity (C) at constant volume (isochoric/isovolumetric)

q=mc∆T c=specific heat

heat lost/gained due to change in temp

q=mL (L=heat of transformation/latent heat of substance)

heat lost/gained during a phase change; enthalpy of an isothermal (const temp) process

radiation

heat transfer by electromagnetic waves; objects that are good absorbers are also good emitters

conduction

heat transfer through a material; bulk motion plays no role

convection

heat transfer via bulk movement of a fluid; the warmer, less dense part of fluid is pushed upward by buoyant force provided by the surrounding cooler and denser part

charge (Q) is increased to increase capacitance (C=Q/V)

how does a dielectric material impact charge in a capacitor in circuit?

charge (Q) is constant (not changed) because there is no additional source of charge. Voltage is decreased to increase capacitance (C=Q/V)

how does a dielectric material impact charge in an isolated capacitor?

Voltage is constant as it is dictated by the voltage source. Charge is increased to increase capacitance (C=Q/V)

how does a dielectric material impact voltage in a capacitor in circuit?

Voltage decreases to increase capacitance (C=Q/V)

how does a dielectric material impact voltage in an isolated capacitor?

volume is less than predicted due to intermolecular attraction (a)

how does a real gas deviate from an ideal gas as the temperature is reduced toward the condensation point?

volume is less than predicted due to intermolecular attraction (a)

how does a real gas deviate from an ideal gas at a moderately high pressure?

volume is greater than predicted due to the size of the particles (b)

how does a real gas deviate from an ideal gas at an extremely high pressure?

volume is greater than predicted

how does a real gas deviate from an ideal gas at an extremely low temperature?

amplitude²

how is intensity proportional to amplitude?

1/d²

how is intensity proportional to distance?

number of quarter wavelengths (distance from node to antinode)

how to find the harmonic of a closed pipe (n)

number of antinodes

how to find the harmonic of a string (n)

number of nodes

how to find the harmonic of an open pipe (n)

PV=nRT=Nkt (N=# of particles, k=R/Na=Boltzmann's constant=1.4E-23 J/k)

ideal gas law

J=F∆t=∆p=mvf-mvi

impulse

(∑F)∆t=mvf - mv0 (change in momentum p) when a net average force acts on an object, the impulse of this force is equal to the change in momentum

impulse-momentum theorem

-, virtual

in a convex/converging lens, if o < f, i is (+/-) and the image is (real/virtual)

+, real

in a convex/converging lens, if o > f, i is (+/-) and the image is (real/virtual)

more

in single-slit diffraction, when the slit is narrowed, the light spreads out (more/less)

type II error (β)

incorrectly fail to reject the null hypothesis when it is false

type I error (α)

incorrectly reject the null hypothesis when it is true

I = E/t Intensity=energy emitted per unit time. Intensity is directly proportional to # of photons emitted

intensity of electromagnetic radiation

I=P/A = P/4πr² (Power per unit Area) W/m²

intensity of sound

∆U=(3/2)PV=(3/2)NkT=(3/2)RT

internal energy of a monatomic ideal gas

K=(1/2)mv²

kinetic energy

fk=µkN

kinetic friction

KE=(1/2)mv²(rms) = (3/2)kT (v=root mean square speed=√(3RT/M)

kinetic theory of gases

Iin=Iout

kirchhoff's junction rule

Vsource=Vdrop

kirchhoff's loop rule

θi=θf

law of reflection

image on opposite side of light source (real)

lens: +i indicates what

object on same side as light source

lens: +o indicates what

lens in converging/convex

lens: +r/+f/+p indicates what

image on same side as light source (virtual)

lens: -i indicates what

object on opposite side of light source (rare)

lens: -o indicates what

lens is diverging/concave

lens: -r/-f/-p indicates what

∆L=αL∆T (∆L=change in length, α=coefficient of linear expansion (K⁻¹), L=original length, ∆T=change in temp in Kelvin)

linear thermal expansion

d x sinθ=(n + ½)λ (d=distance btw 2 slits, θ=btw center line of the 2 slits to the dark fringe and the normal, n=assigned fringe number/integer)

location of dark fringes (minima due to destructive interference) in a multiple-slit system

a x sinθ=nλ (a=slit width, θ=btw center line and dark fringe/lens axis, n=assigned fringe number/integer)

location of dark fringes (minima due to destructive interference) in a slit-lens system

B=(µ₀I)/(2r)

magnetic field produced by a circular loop

B=(µ₀I)/(2πr)

magnetic field produced by a long, straight wire

Fb=ILBsinθ

magnetic force on a current-carrying wire

Fb=qvBsinθ

magnetic force on a moving charge (charge must have a velocity component perpendicular to the magnetic field in order to experience a magnetic force)

m=-i/o (+m=upright image, -m=inverted image, |m|>1=image enlarged/bigger than object, |m|<1=image reduced/smaller than object, |m|=1=image same size as object)

magnification of a mirror/lens and what its different values mean

m=m₁ x m₂ x m₃

magnification of a multiple lens system w/ 3 lenses

E= Fe/q = V/r = kQ/r² units: N/C

magnitude of electric field

ferromagnetic

material with unpaired e- and random permanent magnetic dipoles oriented so material has no net magnetic dipole; become strongly magnetized when exposed to magnetic field, retain magnetism when external magnetic field is removed

diamagnetic

materials with no unpaired e- and no net magnetic field, are weakly antimagnetic (slightly repelled by magnet)

paramagnetic

materials with unpaired e- and a net magnetic dipole moment but no net magnetic field; become weakly magnetized in presence of an external magnetic field, aligning magnetic dipoles w/ field, but magnetism disappears when external magnet is removed

ohmmeter

measures current though a point in a circuit while producing a known voltage via its own battery, so resistance can be calculated (R=V/I); circuit must be off; is placed in series with the element of interest; ideal resistance=0

voltmeter

measures potential difference (voltage drop) between two points; is placed in parallel w/ the two points (element) of interest; ideal resistance=infinity; circuit must be on

ammeter

measures the current through a point in the circuit; is placed in series w/ the point of interest; ideal resistance=zero; circuit must be on so current flows

Fout/Fin force exerted on object by simple machine (Fout)/force actually applied to simple machine (Fin)

mechanical advantage

image is upright

mirror/lens: +m indicates what

image is inverted

mirror/lens: -m indicates what

image is in front of mirror (real)

mirror: +i indicates what

object is in front of mirror

mirror: +o indicates what

mirror is converging/concave

mirror: +r/+f indicates what

image is behind mirror (virtual)

mirror: -i indicates what

object is behind mirror (rare)

mirror: -o indicates what

mirror is diverging/convex

mirror: -r/-f indicates what

p=mv

momentum

diffraction gratings

multiple slits arranged in patterns causes reflecting wave of external surface of medium to interfere w/ reflecting wave of internal surface of medium

myopia

nearsightedness

an object at rest stays and rest and an object in motion stays in motion w/ same speed and direction unless acted upon by an unbalanced force (if no net force acts on an object, its net force is constant)

newton's 1st law of motion (law of inertia)

F=ma an object will accelerate in proportion to the net force acting on it

newton's 2nd law of motion

if 1 object exerts a force on another, the other object exerts a force on the 1st that is equal in magnitude and opposite in direction

newton's 3rd law of motion (law of action-reaction)

Fg=(Gm₁m₂)/r²

newton's law of universal gravitation (gravitational force between 2 objects)

E=mc² (m=mass defect)

nuclear binding energy

conduction pathways

number of pathways through a resistor, inc w/ inc area

dispersion

occurs when a light ray of multiple wavelengths traveling at different speeds refract differently through a medium, causing the different wavelengths to separate from each other (like a rainbow out of a prism)

spherical aberration

occurs when inadequate refraction causes blurring at the periphery of an image of a lens

antinodes

open boundaries correspond to (nodes/antinodes)

Pa=Xa x Pt Xa = mol gas a/total mol

partial pressure of a gas

T=1/f

period of a wave (T)

Kmax = hf-W = hf-hfT = (1/2)mv² - W

photoelectric effect: kinetic energy of ejected e- ("extra energy" past the energy needed for e- to be ejected is converted to KE)

wavelength

pick all that apply: what changes when light is refracted? (freq, amplitude, wavelength)

Q=(πr⁴∆P)/(8ηL)=AV

poiseuille's law/flow rate

0,+1β or β⁺

positron emission emits this

∆V=Vb-Va=(kq/r₁)-(kq/r₂)=Wab/q

potential difference (voltage)

electromotive force (emf or E) volts 1V=1 J/C

potential difference (voltage) that results in current

U=(1/2)CV²=(1/2)qV=q²/(2C)

potential energy stored by a capacitor

P= W/t = ∆E/t = FV (work/energy expenditure per unit time; rate at which E is dissipated by a resistor)

power

P= W/t = ∆E/t = FV rate at which energy is transferred from 1 system to another (unit: Watt=J/s)

power

P=1/f (same sign as freq)

power of a lens (unit: diopters)

P=P₁ + P₂ + P₃

power of a multiple lens system w/ 3 lenses

P=F/A (units:Pa=N/m²)

pressure

20-20,000 Hz

range of sound wave freq that can be perceived by humans

λ=.7/T½

relate decay constant w/ half-life

1/f=1/o + 1/i = 2/r

relate focal length, object distance, image distance, and radius of curvature for a mirror/lens (thin lens equation)

P=IV=I²R=V²/R

relate power (P), current (I), voltage (V), and resistance (R)

R=(pL/A)

resistance equation (opposition to flow of charge), unit is Ohms

R=(8ηL)/(πr⁴) or R is proportional to 1/r⁴

resistance in a tube, poiseuille's law

∆f/f = v/c (∆f=freq shift, f=original freq, v=relative velocity btw source & observer, c=speed of wave in medium)

simplified doppler effect

n₁sinθ₁=n₂sinθ₂

snell's law, how light refracts when it enters a different medium

βf=βi + 10log(If/Ii) dB

sound level in decibels when intensity is changed

ultrasound

sound waves with a freq > 20,000 Hz

SG=p/(1 g/cm³)=p/(1000 kg/m³)

specific gravity

v=(2πr)/T

speed of an object in uniform circular motion, related to period T (time required for object to travel once around circle)

v=√(B/p) (B=bulk modulus=medium's resistance to compression, B solid>B liquid>B gas; p=density of medium)

speed of sound in a medium

Pascal's principle (V=Ad=Ad, P=F/A=F/A, W=fd=fd)

states that any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls

Archimedes' principle (Fb=pVg=mg)

states that the magnitude of the buoyant force equals the weight of the fluid that the object displaces

Dalton's law (Pt=Pa + Pb + Pc...)

states that when there is more than one gas in a container, each gas contributes to the total pressure as if it is the only gas present

0≤fs≤µsN

static friction

0

the electrical potential along the perpendicular bisector of a dipole or an equipotential line is

resistivity (p) Ωm

the intrinsic resistance to a current flow and its unit (note it is a function of temperature)

fundamental frequency/1st harmonic

the lowest frequency (and longest wavelength) of a standing wave that can be supported by a string/pipe

inertia

the natural tendency of an object to remain at rest or in motion at a constant velocity. Is the basis for newton's 1st law of motion

harmonic (n)

the number of half wavelengths supported by a string/pipe

conductivity (siemens or s)

the reciprocal of resistance; measure of permissiveness to current flow

buoyancy (Fb=pVg)

the upward force a fluid applies to an object immersed in it

∆A=2αA₀∆T

thermal expansion of an area (2D)

isobaric

thermodynamic process w/ a constant pressure, work done W=P∆V, ∆U=Q-W

isothermal

thermodynamic process w/ a constant temp so no change in internal energy ∆U=0, Q=W, Q=mL

isochoric/isovolumetric

thermodynamic process w/ a constant volume so no work done W=0, ∆U=Q

adiabatic

thermodynamic process w/ no heat exchange Q=0, ∆U=-W

Henry's law [A]=kh x Pa, or kh=[A]₁/P₁=[A]₂/P₂ kh=henry's constant, depends on gas

this law relates the solubility (concentration) and pressure of a gas

I₀=0 dB=1E-12 W/m²

threshold of hearing (softest sound that can be heard) in decibels (dB) and Watts/m^2

T=rFsinθ

torque

T=pEsinθ

torque on a dipole in an electric field

E=V/d (direction is + to - plate)

uniform electric field btw capacitor plates

1 tesla (T)=1E4 gauss

units of magnetism

temperature

vapor pressure depends only on

∆V=βV∆T (coefficient of volumetric expansion β=3α)

volumetric thermal expansion of liquids

<1E-11

wavelength of gamma rays in m (note c=fλ)

1E-2

wavelength of microwaves in m (note c=fλ)

>1

wavelength of radio waves in m (note c=fλ)

1E-8

wavelength of ultraviolet (UV) light in m (note c=fλ)

1E-7 m/400-700 nm

wavelength of visible spectrum in m and its range in its common unit (note c=fλ)

1E-10

wavelength of x-rays in m (note c=fλ)

1E-4 - 1E-6

wavelength range of infrared (IR) in m (note c=fλ)

medium's resistance to compression; B solid>B liquid>B gas

what is bulk modulus (B in v=sq rt(B/p))? and how does B of solids, gases, and liquids compare?

V

what is the same at each point for resistors and capacitors in parallel? P, I, V, or R?

I (there is only 1 path for current to take)

what is the same at each point for resistors and capacitors in series? P, I, V, or R?

towards

when light enters a medium w/ a higher index of refraction, it bends (towards/away) from normal

away

when light enters a medium w/ a lower index of refraction, it bends (towards/away) from normal

W=Fdcosθ

work due to applied force

W=P∆V

work for isobaric (constant pressure) process

W=hfT (fT=threshold freq)

work function: minimum energy required to eject e-

Wnet=∆K=Kf - Ki

work-energy theorem

objects in thermal contact w/ same temp are in thermal equilibrium

zeroth law of thermodyanmics