MCAT_Physics Concepts and Equations

taken from Quizlet

component vectors (Chapter 1)

component vectors (Chapter 1)

X=Vcosθ Y=Vsinθ

determination of direction from component vectors

θ = tan

Dot product

A*B = |A| |B| cosx

cross product

A*B = |A| |B| sinx

instantaneous velocity

v=lim (Δx/Δt) Δt

average velocity

v=(Δx/Δt)

Universal gravitation equation

Fg = G m1 m2 / r^2

static friction

0 < fs < usN

kinetic friction

fk=ukN

Force of gravity equation

Fg=mg

center of mass

x= m1x1 + m2x2 + m3x3...../m1 + m2 + m3 + ....

average acceleration

a=Δv/Δt

instantaneous acceleration

a= lim (Δv/Δt) Δt

Newton's First Law

Fnet =ma = 0

Newton's Second Law

F=ma

Newton's Third Law

Fab =

Kinematics (no displacement)

v = v0 + at

Kinematics (no final velocity)

x= v(o)t + (at^2)/2

kinetic energy (chapter 2)

KE = 1/2mv^2

gravitational potential energy

U = mgh

elastic potential energy

U = 1/2kx^2

Total Mechanical Energy

E = U + K

Conversion of Mechanical Energy

ΔE = ΔU + ΔK = 0

Work done by nonconservative forces

Wnonconservative = ΔE = ΔU + ΔK

Definition of work (mechanical)

W = Fd = Fdcosθ

Definition of work (isobaric gas

piston system)

Definition of power

P = W/t = ΔE/t

work

energy theorem

mechanical advantage

Mechanical advantage = (Fout)/(Fin)

Efficiency

Efficiency = Wout/Win = (load)(load Distance)/(effort)(effort distance)

Temperature Conversions (Chapter 3)

F = 9/5C + 32 K = C + 273

Thermal expansion equation

ΔL=αLΔT

Volume expansion equation

ΔV=βVΔT

first law of thermodynamics

ΔU = Q

Heat gained or lost (phase change)

Q = mL

Entropy and heat

ΔS = Qrev/T

second law of thermodynamics

ΔSuniverse = ΔSsystem + ΔSsurroundings > 0

Heat gained or lost (with temperature change)

q = mcΔT

Density (Chapter 4)

p = m(mass)/ v (volume)

Weight of a volume of fluid

Fg = pVg

specfic gravity

sg = p/ (1 (g/cm3))

pressure

p = f (force)/ a (area)

Absolute Pressure

P = Po + pgz

Gauge Pressure

Pgauge = P

Pascal's Principle

P = F1/A1 = F2/A2 F2 = f1( A2/A1)

buoyant force

Fbuoy = Pfluid Vfluiddisplaced * g = Pfluid Vsubmerged *g

Poiseuille's Law

Q= (πr^4 ∆P)/8ηL

η: viscosity of the fluid Q: flow rate (volume flowing per time) ΔP: pressure gradient r: radius of tube L: length of tube

Critical Speed

Vc=(Nrn)/(pD)

continuity equation

Q=v1A1=v2A2

Bernoulli's Equation

P1 +1/2 ρv_1^2+ρgh_1= P_2+1/2 ρv_2^2+ρgh_2

P : absolute pressure of the fluid v: linear speed h: height of the fluid

Coulomb's Law (chapter 5)

F=K q₁*q₂/r², magnitude of force between two charges

electric field

E = (Fe/ q )= (Kq/r²)

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 = Vb

Electric potential near a dipole

V = (kqd/r^2)cosθ

dipole moment

p = qd

Electric field on the perpendicular bisector of a dipole

E = (1 / 4πe0) *(p/r^3)

Torque on a dipole in an electric field

T= pEsin(ϴ)

Magnetic field from a straight wire

B = μ0I/2πr

Magnetic field from a loop of a wire

B=µ0I/2r

Magnetic force on a moving point charge

Fb = qvBsinθ

magnetic force on a current carrying wire

Fb=ILBsinθ

current (chapter 6)

I=Q/Δt

Kirchoff's Junction Rule

I into junction = I leaving junction

Kirchoff's Loop Rule

V source = V drop

Definition of resistance

R = pL/A

Ohm's Law

V=IR

Voltage and cell emf

V = Ecell

Definition of power

P = W/t = ΔE/t

electric power

P = IV = I^2R = V^2/R

Voltage drop across circuit elements (series)

Vs=V1+V2+V3+...+Vn

Equivalent resistance in series

Rs=R1+R2+R3+...+Rn

Voltage drop across circuit elements (parallel)

Vp=V1=V2=V3=...=Vn

Equivalent resistance in parallel

1/Rp = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Definition of Capacitance

C= Q/V

Capacitance based on parallel plate geometry

C=e0(A/d)

Electric field in a capacitor

E = V/d

Potential energy of a capacitor

U = 1/2CV^2

Capacitance with a dielectric material

C' = kC

Equivalent capacitance (series)

1/Cs = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

Equivalent capacitance (parallel)

Cp = C1 + C2 + C3 + ... + Cn

Wave speed (chapter 7)

v=fλ

period

T = 1/f

angular frequency

ω = 2πf = 2π/T

speed of sound

v = √B/p

Doppler effect

f=f₀(v±Vd)/(v±Vs), Vd is speed of detector, Vs is speed of source. + top

Intensity

I = P /A

sound level

B = 10 log (I/Io)

Change in sound level

Bf = Bi + 10 log (If/Ii)

beat frequency

f=|f₁

wave length of standing wave (strings and open pipes)

lambda = 2L /n

Frequency of a standing wave (strings and open pipes)

f = (nv) / (2L)

Wave length of a standing wave (closed pipes)

lambda = 4L/n

Frequency of a standing wave (closed pipes)

f = nv/4L

Speed of light from frequency and wave length (chapter 8)

c =f*lambda

law of reflection

θ1 = θ2