physics mcat Flashcards
universal gravitation equation
F=(Gm1m2)/(r^2)
static friction
Fs ≤ μs η , and Fsmax = μs η
kinetic friction
F= μkN
force of gravity
F=mg
Newton’s first law
F=ma=0
Newton’s 2nd law
F=ma
Newton’s 3rd law
F(AB)=-F(BA)
Kinematics equation (no displacement)
v = v₀ + at
Kinematics equation (no final velocity)
x = x₀ + v₀t + ½at²
Kinematics equations (no time)
v² = v₀² + 2ax
Kinematics (no acceleration)
x=vt
perpendicular component of gravity on an inclined plane
F=mgcos θ
parallel component of gravity on an inclined plane
F=mgsin θ
Centripetal force
F=(mv^2)/r
Torque
t=r x F= rFsin θ
kinetic energy
K=(1/2)mv^2
gravitational potential energy
U=mgh
elastic potential energy
U=(1/2)kx^2
total mechanical energy
E=U+K
conservation of mechanical energy
ΔE=ΔU+ΔK
work done by nonconservative forces
W(nonconservative)=ΔE=ΔU+ΔK
definition of work (mechanical)
W=F dot d = Fdcosθ
Definition of work (isobaric gas-piston system)
W=PΔV
Definition of power
P=(W/t)=ΔE/t
Work-energy theorem
W(net)=ΔK
Mechanical advantage
F(out)/F(in)
Efficiency
W(out)/W(in) = ((load)(load distance))/((effort)(effort distance))
temperature conversions
F=(9/5)C+32
K=C+273
thermal expansion equation
ΔL=alphaLΔT
volume expansion equation
ΔV=betaVΔT
first law of thermodynamics
U=Q-W
heat gained or lost with temp change
q=mcΔT
heat gained or lost with phase change
q=mL
entropy and heat
ΔS=(Qrev)/T
second law of thermodynamics
ΔSuniv=ΔSsys+ΔSsurr > 0
density
ρ=m/V
weight of a volume of fluid
F= ρVg
specific gravity
SG= ρ/(1 g per cm^3)
pressure
P=F/A
Absolute pressure
P=P0+ ρgz
Gauge pressure
Pgauge=P-Patm= (P0+ ρgz) - Patm
Pascal’s principle
P=F1/A1=F2/A2
F2=F1(A2/A1)
Buoyant force
Fbuoy=ρfluidVfluiddisplacedg=ρfluidVsubmergedg
Poiseuille’s law
Q=ΔPπr^4/8ηl
Critical speed
V=nN/ρd
Continuity equation
Q=v1A1=v2A2
Bernoulli’s equation
P1+1/2ρv1^2+ρgh1=P2+1/2ρv2^2+ρgh2
Doppler’s from qpack
Δf/f=(-v/c)
fixed voltage between cathode and anode
E=(V-IR)/L
Coulomb’s law
F(e)=k|q1||q2| / d2
Electric field
E=F(e)/q=kQ/(r^2)=V/r
Electric potential energy
U=kQq/r
Electric potential (from electric potential energy)
V=U/q
Electric potential (from source charge)
V=kQ/r
Voltage
ΔV=V(a)-V(b)=W(ab)/q
Electric potential near dipole
V=(kqd)(cosθ)/(r^2)
Dipole moment
p=qd
electric field on the perpendicular bisector of a dipole
E=(1/4piepsilonnaught) x (p/r^3)
torque on a dipole in an electric field
torque=pEsinθ
magnetic field from a straight wire
B=u0I/(2pir)
magnetic force from a loop of wire
B=u0I/2r
magnetic force on a moving point charge
F=qvBsinθ
magnetic force on a current-carrying wire
F=ILBsinθ
current
I=Q/Δt
Kirchoff’s junction rule
I(into junction)=I(out of junction)
Kirchoff’s loop rule
V(source)=V(drop)
Resistance
R=ρL/A
Ohm’s law
V=IR
voltage and cell emf
V=E(cell)-ir(internal)
definition of power
P=W/t=ΔE/t
electric power
P=IV=(I^2)R=(V^2)/r
voltage drop across circuit elements (series)
Vtot=V1+V2+V3…
equivalent resistance (series)
Rtot=R1+R2+R3…
voltage drop across circuit elements (parallel)
Vp=V1=V2=V3…
equivalent resistance (parallel)
(1/R)=(1/R1)+(1/R2)+(1/R3)…
definition of capacitance
C=Q/V
capacitance based on parallel plate geometry
C=epsilonnaught (A/d)
electric field in a capacitor
E=V/d
potential energy of a capacitor
U=(1/2)CV^2
capacitance of a dielectric material
C’=kC
dielectrics in isolated capacitor
decrease in voltage
dielectrics in circuit capacitor
increase in charge
equivalent capacitance (series)
(1/C)=(1/C1)+(1/C2)+(1/C3)…
equivalent capacitance (parallel)
C=C1+C2+C3…
Wave speed
v=fλ
period
T=1/f
angular frequency
ω=(2pi)f=(2pi)/t
speed of sound
v=sqrt(B/ρ) B increases gas -> liquid -> solid
doppler effect
f’=f(v±vD)/(v∓vS)
intensity
I=P/A
sound level
beta=10log(I/I0) I0= 10^-12
change in sound level
betaf = betai +10log(If/Ii)
beat frequency
fbeat=f1-f2
wavelength of a standing wave (strings and open pipes)
λ=(2L)/n
frequency of a standing wave (strings and open pipes)
f=nv/(2L)
wavelength of a standing wave (closed pipes)
λ=(4L)/n where n can only be odd integers
frequency of a standing wave (closed pipes)
f=(nv)/4L
speed of light
c=λf
law of reflection
θ1=θ2
optics equation
(1/f)=(1/o)+(1/i)=(2/r)
magnification
m=-i/o
index of refraction
n=c/v
snell’s law
n1sinθ1=n2sinθ2
critical angle
θc=inversersin (n2/n1) for n2
lensmaker’s equation
1/f=(n-1)((1/r1)-(1/r2))
power
P=1/f
focal length of multiple lens systems
1/f=1/f1+1/f2+1/f3…
power of multiple lens systems
P=P1+P2+P3…
magnification of multiple lens systems
m=m1xm2xm3…
positions of dark fringes in slit-lens setup
asinθ=nλ
positions of dark fringes in double-slit setip
dsinθ=(n+1/2)λ
farsighted people need
converging lens
nearsighted people need
diverging lens
i is +/-
image is real/virtual
r is +/-
mirror is converging/diverging
f is +/-
mirror is converging/diverging
m is +/-
image is upright/inverted
energy of a photon of light
E=hf
maximum kinetic energy of an electron
Kmax=hf-W
work function
W=hf f=threshold frequency
mass defect and energy
E=mc^2
alpha decay
atomic number loses 2, mass number loses 4, alpha particle emitted
beta negative decay
atomic number gains one, electron emitted
beta positive decay/electron capture
atomic nimber loses one
gamma decay
gamma radiation emitted
rate of nuclear decay
Δn/Δt=-λn
exponential decay
n=n0e^-λt
decay constant
λ=ln2/T(1/2)=0.693/T(1/2)
log(n x 10^m)
approx. m+0.n
log to ln
logx==ln(x)/2.303
