物理1

Equivalent capacitance (capacitors in series)

Ceq =/ (( /C₁)+( /C₂)+( /C₃))

Equivalent capacitance (capacitors in parallel)

Ceq = C₁ + C₂ + C₃ 

Total charge for capacitors in parallel

Qtotal = Q₁ + Q₂ + Q₃ 

Magnification of an image

m = -Di/Do = Hi/Ho

Mass Energy Equivalence

E = mc²

Momentum of a photon

p = E/c = hf/c = h/λ

Work Function of cutoff wavelength is known

Φ = hf₀ 

Photoelectric effect including stopping potential

E = Φ + qVs

Photoelectric effect including Kmax

E = Φ + Kmax

Energy of a photon

E = hf = hc/λ

EMF generated for a moving bar through a magnetic field

ε = Bl(this is L, not I)v

Faraday's Law of electromagnetic induction

ε = -(NBA)/(∆t) = -Φ/∆t

Magnetic Flux

Φ = NBA = NBAcosθ

Thin lens equation

( /f) = ( /Di) + ( /Do)

Snell's Law

n₁sinθi = n₂sinθr

Index of Refraction

n = c/v

Critical Angle

sinθc = n₁/n₂ (n₂>n₁)

Thin membrane interference

nt = ___λ (Constructive slit & Destructive slits: ___ = m + ½)(Destructive slit & Constructive slits: ___ = m)

Total resistance for resistors in series

 Rtotal = R₁ + R₂ + R₃

Total resistance for resistors in parallel

 Rtotal =/ (( /R₁)+( /R₂)+( /R₃))

Charge including time

 Q = It

Resistance in a wire of length L and area A

 Rwire = (pL)/A

 Pressure exerted on an area A

 P = F/A

 Absolute pressure

 Pabs = Patm + Pgauge = Patm + pgh

 Gauge pressure

 Pgauge = pgh

 Volume flow rate

 I = Av or A₁v₁ = A₂v₂

 Buoyant force

 Fb = p(fluid)V(fluid)g

 Density

 p = M/V

 Bernoulli's Equation

 P₁ + ½pv² + pg∆y = P₂ + ½pv² + pg∆y

 Force on a charge q moving parallel to a magnetic field (B)

 Newtons (PARALLEL!!)

Force on a current carrying wire perpendicular to a magnetic field

Fb = BIxl ( B i ⊥ L )

Force between two parallel current carrying wires of length L

F = (µ₀/( π))((I₁I₂ (as in i) l (as in L))/r

Limits of human sight

nm -nm

The wave equation

v = fλ

Magnetic field a distance r from a current carrying wire

Bwire = (µ₀/( π))(I (as in i) / r)

New wavelength if the original wavelength and n's are known

λ₂ = (n₁λ₁)/n₂ -> (n₁λ₁ = n₂λ₂)

Capacitance if area of plates is known

C = kε₀A/d

Electric Potential around a point charge q

V = K(Q/r)

K in electrostatics

K =/( πε₀) =E-Nm²/C²

Force on a charge (q) in an Electric field (E)

Fe = qE

Coulomb's Law

Fe = K(|q₁Q₂|/r²)

Charge on a capacitor

Q = CV

Energy stored in a capacitor

Ucap = ½QV = ½CV² = ½Q²/C

Formula definition of work

W = Fd = Fdcosθ

Electric Potential Energy

Ue = qV

Electric-field a distance r from a point charge (q)

E= K(|q|/r²)

Ohm's Law

V = IR

Total charge for capacitors in series

Q₁ = Q₂ = Q₃

Terminal Voltage (Vab) if external resistance (Rext) is known

Vab = IRext

Terminal Voltage (Vab) if EMF (ε) is known

Vab = ε - Irint

Voltage across the plates of a capacitor if the E-field is known

Ed = V

Electric Energy

E = VIt = I²Rt = (V²/R)t

Electric Power

P =IV = I²R = V²/R

Force on a charge (q) moving perpendiculary through a magnetic field (B)

Fb = qvxB

Work to move a point charge (q) a distance r away from another charge (Q)

Fe = K(q₁Q₂/r)

Change in Heat during an isovolumetric process

Q = nCv∆T

Frequency of a spring mass

f =/( π√(m/k)) =/T

Period of a pendulum

T =π√(l/g)

Frictional Force

Ff = Fnµ

Frictional Force on an incline

Ff = mgcosθµ

Acceleration

a = ∆v/t = (v-v₀)/t

Average Speed

S = dtotal/ttotal

Velocity

v = ∆x/t

Average Velocity of a molecule of gas

vrms = √(( kT)/m)

Change in internal energy during a cyclic process

∆U =J (JAIL!)

First Law of Thermodynamics

∆U = ∆Q + ∆W

Acceleration of a mass sliding up an incline (with friction)

a = gsinθ + gcosθµ

Acceleration of a mass sliding down an incline (with friction)

a = gsinθ - gcosθµ or a = gcosθµ - gsinθ

Heat required to raise the temperature of a substance

∆Q = mc∆T

Heat required to vaporize a substance

∆Q = mL((sub)v)

Heat required to melt a substance

∆Q = mL((sub)f)

Forgotten Power Equation

P = Fv

Energy of a spring-mass when spring is neither at max displacement nor equilibrium

½kA² = ½kA₂ + ½mv²

Ideal Efficiency

εideal = εcarnot = (Th-Tl)/Th

Newton's Second Law of motion

∑F = ma

Torque

J = rxF = rFsinθ

Ideal Gas Law

PV = nRT = NkT

Boyle's Law

P₁V₁ = P₂V₂

Heat of an isobaric process

∆Q = nCp∆T

Work (thermo)

W = -P∆V

Internal Energy of an ideal gas

U = ( / )nRT

Actual efficiency

εactual = |Wnet|/Qin

Kinetic Energy

K = ½mv²

Hooke's Law

Fspring = -kx (A?)

Gravitational Potential Energy

Ug = mg∆y

Newton's Law of Universal Gravitation

Fg = G (m₁m₂)/r²

Centripetal Acceleration

ac = v²/r

Acceleration due to gravity

g = G m/(d/ )²

Momentum

p = mv

Impulse

J = Ft = mv - mv₀

Weight

w =mg

First Kinematic

v = v₀ + at

Second Kinematic

∆x = v₀t + ½at²

Third Kinematic

v² = v₀² +a∆x

Beat frequency

fbeat = |f₁-f₂|

Length L of a string producing the fundamental frequency (f)

L = vstring/( f) = (√(T/(m/l))(/( f)

Natural frequency of a closed tube of length lL

f = v/( L)

Wavelength in an open tube of length L

λ =L

Frequency of a pendulum

f =/( π√(l/g))

Velocity of waves on a string if tension is known

vstring = √(T/(m/l))

Period of a spring mass

T =π√(m/k)

Charle's Law

V₁/T₁ = V₂/T₂

Gay-Lussac's Law

P₁/T₁ = P₂/T₂

Work done during an isovolumetric process

∆W =J (no ∆V = no area on the curve = no work)

Change in internal energy during an isothermal process

∆U =J (no change in temp = no change in U)

Spring Potential Energy

Us = ½kA²

Heat due to friction on an incline

Q = mgcosθµd

Heat due to friction on level surface

Q = Fnµd

Speed

S = d/t (this is not velocity because it is not a vector)

First Angular Kinematic

ω = ω₀ + αt

Second Angular Kinematic

∆θ = ω₀t + ½αt²

Third Angular Kinematic

ω² = ω₀² +α∆θ

Centripetal Acceleration with angular (we've already done linear) quantaties

ac = ω²/r

Moment of Inertia of a point

I = mr²

Center of mass

Xcm = (X₁m₁ + X₂m₂ + X₃m₃)/ mtotal

Centripetal Acceleration in radians of the second hand of a clock

ac =π²r/sec

Rotational Kinetic Energy

Krot = ½Iω²

Net Torque when the moment of inertia is known

∑J = Iα

Angular momentum for aD object rotating

L = Iω

Position as a function of time using angular quantities

ω = θ/t

Conservation of Angular Momentum when the ball strikes the bar and causes rotation

rxp = Iω = (mr² + ( / )ml² (as in L))ω (where I = Iball +Irod; Iball = mr² and Irod = ( / )ml²)

Energy of a spring mass when the string is at maximum displacement

Us = ½kA²

Height of the block in terms of θ and l

∆y = l-lcosθ

Units of Power (not watts)

Watt = J/sec

Units of Current (nat amps)

Amp = C/sec

Three Power formulas

P = Fv = E/t = VI (as in i)

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂

Limits of human hearing

-Hz

Diameter of a Hydrogen Atom

 E- m

Units of Electric Field (capacitors)

V/m

Units of Electric Field (point charges)

N/C

Units of Momentum

kgm/s

Units of Energy

Joules or eV

Units of the spring constant k

N/m

R. A. Milliken

Oil drop experiment, elemental charge (e)

Thomas Young

Double slit experiment, light as a wave

Davisson and Germer

Electrons are waves

J.J. Thompson

Cathode ray tubes, charge to mass ratio (q/m) for an electron

Ernest Rutherford

Gold foil experiment, nucleus is a small and positively charged

Neils Bohr

Quantized energy levels and explained the bright line spectra