Physics: Equations (copy)

Equation: final velocity (2)

vf =

v_f= v₀+at

v_f² = v₀²+2ax

Equation: displacement (2)

x =

x = v₀t+1/2at²

x = vt (where v is average velocity)

What is the difference between vectors and scalars?

Give examples of each

Vectors have magnitude and direction

Scalars have only magnitude

Ex:

Vectors: Force, velocity, acceleration, displacement

Scalars: Energy, distance, speed, mass.

An object rests atop an incline. How can the force of static friction (Fs) be calculated?

What equation denotes the maximum static friction an object can experience?

F_g||=Fs = (mg)sinθ

Fs(max) = μₛ(N)

Torque (τ) equation

rFsinθ

Kinetic energy: (K) =

K = (1/2)mv²

Gravitational potential energy: (U) =

U = mgh

Elastic potential energy: (U) =

U = (1/2)kx²

Total mechanical energy: (E) =

E = U + K

Conservation of E in a system: (ΔE) =

ΔU + ΔK = 0

Work (W) done by NONconservative forces =

ΔE = ΔU + ΔK

Mechanical definition of work: (W) =

W = Fd or

W = Fdcosθ

Isobaric gas-piston system definition of work: (W) =

W = pΔV

Definition of power: (P) =

Watts (W) = J/s

P = W/Δt = ΔE/Δt

Work-energy theorem: (Wnet)

Wnet = ΔK = Kf-Ki

Mechanical advantage: MA =

(F)out/(F)in

Efficiency of a system:

(W)out/(W)in

(load)(load distance) / (effort)(effort distance)

Describe the type of system, and give an example:

Open

Closed

Isolated

Open: Exchange of both matter and energy. eg: boiling water

Closed: Exchange of energy only

Isolated: Exchange of neither matter nor energy

Describe and give examples of a state function.

A state function is one whose properties depend only on the CURRENT thermodynamic equilibrium state of a given system, such that they are path independent of their current state.

Temperature, density, pressure, volume, internal energy U, entropy S

Describe and give examples of non-state functions (process functions)

Process functions are path-dependent, meaning they describe the path taken to get to the current equilibrium state.

Heat and work.

Celsius to Fahrenheit conversion:

C (9/5) + 32 = F

Celsius to Kelvin conversion:

C + 273 = K

Thermal expansion: ΔL:

ΔL = αLΔT

where α is the coefficient of linear expansion

Volume expansion ΔV =

ΔV = βVΔT

adiabatic processes

no heat exchanged

Q = 0

First law of thermodynamics: ΔU =

ΔU = Q - W

where Q is the energy content transferred to the system in the form of heat, and W is the energy transferred from the system in the form of work.

Change in heat due to temperature change: q =

q = mcΔT

Change in heat due to phase change: q =

q = mL

where L is the heat of transformation coefficient.

Entropy and heat: S =

ΔS = Q_rev / T

Second Law of Thermodynamics: ΔS_universe =

ΔS_universe = S_system+ S_surroundings > 0

Density: (ρ) =

ρ = m/V

Pressure: (P) =

P = F/A

Force of a fluid: (F_g) =

If ρ = m/v and

F = ma, then

ρv = m, therefore

F = ρVg

Specific Gravity: (SG) =

ρ(substance) / 1g/cm^3

1 atm in Pa

1×10⁵ Pa

Absolute Pressure: (Pabs) =

P_abs = P_o + ρgz

where z is the depth of the fluid

Gauge pressure: (P_gauge) =

P_gauge = P_abs - P_atm

Just the difference between a given system’s pressure (absolute pressure) compared to normal atmospheric pressure.

when P_abs = P₀, P_gauge=ρgz

Pascal’s Principle: (P) =

P = F₁/A₁ = F₂/A₂

Allows for more work to be done over a larger area.

Archimedes’ Buoyant Force Principle: (Fb) =

F_b = ρ_fluid* V_{fluid displaced; submerged}*g

Poiseuille’s Law: (Q) =

Q = flow rate (m³/s); constant regardless of area

π(r⁴)(ΔP) / (8ηL)

where r = radius of pipe

ΔP = change in pressure

η = viscosity of fluid

L = length of pipe

Critical speed of a fluid: (Vc)

Vc = (Nr)η / (ρD)

where Nr is the Reynold’s constant

η = viscosity of fluid

ρ = density of fluid

D = Diameter of tube

linear speed of fluids

depends on area

fluids have higher speeds through narrow tubes

Bernoulli’s equation

P₁+½ρv₁²+ρgh₁=P₂+½ρv₂²+ρgh₂

_{At equal heights, speed and pressure are inversely related}

What is the Venturi effect?

Occurs in a Venturi tube as a result of differing tube radii, the speed and pressure of the fluid within the tube adjust to remain constant, and the tubes that come off the top have different heights of fluid to reflect that adjustment.

Charge of an electron

1.6x10^-19 C

Electric field lines

+ charges move in direction of field lines

- charges move in opposite direction

Coulomb’s Law: (Electrical force between charges) (Fe) =

F_e = kq₁q₂ / r²

Electrical potential energy: (U) =

U = kq₁q₂ / r

Electrical field (2): (E) =

E = Fe / q = kQ / r²

Electrical potential: (V) =

V = U / q = kq / r

Electric potential

+ charges move down hill

- charges move up hill

Relate electrical potential (V) to work:

V = V_b-V_a = W_ab / q

What are equipotential lines?

Equipotential lines are 3d spheres surrounding a source charge at which the electrical potential at any given point on one is the same; this is to say that the potential difference between any two points on an equipotential line is zero.

What is a dipole moment? p =

The product of charge and separation distance p = qd

Formula for electrical potential at a point in space distant from the dipole

V =

V = ( kqd / r² ) cosθ

What is the Perpendicular Bisector of the Dipole?

An equipotential line that lies exactly halfway between two charges where the potential along this plane is zero.

Formula for electrical field along the PBD

E = kp / r³

Net torque on a dipole: (τ) =

τ = pE sinθ

Magnetic field from straight wire

B = (μ₀ * I) / (2π * r)

Magnetic field from loop of wire

For loop of wire: B = (μ₀ * I) / (2r)

Magnetic force on moving point charge

F_B = qvBsinθ

Magnetic force on current-carrying wire

F_B = ILBsinθ

Kirchoff’s current law

(I)in = (I)out for any junction in a circuit

Resistance of a resistor (R) =

R = ρL / A

Ohm’s Law

V = IR

Cell emf

E - ir

E = emf

i = current

r = internal resistance

if cell off —> r = 0

Power (P) in circuits =

P = IV = I²R = V²/R

Total resistance in parallel vs series.

In parallel, take the inverse of the sum of the inverses.

In series, add directly.

capacitance equation (C) (2)

C=Q/V=ɛ_o(A/d)

electric field in capacitor (uniform electric field)

E = V/d

Potential energy of a capacitor

U = ½CV²=½QV=½(Q²/C)

capacitance with dialectric

C’=κC

Doppler effect equation

f' = f (v ± v_o) / (v ∓ v_s)

change in sound level equation

B_f-B_i = 10 log (I_f/I_i)

wavelength of standing waves

strings and open pipes:

λ = 2L/n

closed pipes

λ = 4L/n

intensity equation

I = P/A

Relate focal length, radius, image distance, object distance.

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

wave speed

v = fλ

angular frequency

ω = 2πf = 2π/T

speed of sound equation

v = √(B/ρ)

What parameters indicate a real vs. virtual image in a mirror?

What about a lens?

What parameters indicate an inverted vs. upright image?

A real image has an i (image distance) > 0.

If image distance is negative, it is a virtual image.

With lenses, real images still have a positive i, but the image is on the opposite side of the lens. The opposite is true for virtual images.

An inverted image will have a magnification (m) value < 0.

An upright image will have a magnification value > 0

Magnification of an image equation.

m = -i/o

Refraction index (n) =

n = c/v

c: speed of light in a vacuum

v: actual velocity of light

Snell’s law of refraction when passing through mediums.

n1(sinθ1) = n2(sinθ2)

Critical angle θc =

Also describe what that even is

θc = sin^-1(n2/n1)

This occurs when the angle of incident light θ1 increases such that the angle of refraction θ2 becomes 90 degrees. In practice, this is when light starts reflecting inwards within the same medium.

Relative focal length with refraction of a real lens. 1/f =

1/f = (n-1) ((1/r1) - (1/r2))

Power of a lens (diopters) P =

P = 1/f

Total power of multiple lens system Ptot =

Total focal length 1/f =

Ptot = P1+P2+P3. . .Pn

P = 1/f

Therefore 1/f = 1/f1 + 1/f2 + 1/f3. . . 1/fn

Total magnification of a multiple lens system m =

mtot = m1***m2*m3. *. .*mn

for a single-slit lens system, how to find θ, used to find d distance of slits later?

asinθ = nλ

a = width of slit

for a double-slit lens system, how to find the distance between slits?

dsinθ=(n+1/2)λ

when you find θ, you also have distance D between walls, so y can be found. which is distance between slits.

Energy of a photon: (E) =

E = hf

h is planck’s constant (6.626E-24)

f is frequency of the light

Kinetic energy of an electron being ejected from a metal: (K) =

K = hf-W

where W is the work function, hf_T

therefore, K = hf-hf_T

f_T=threshold frequency (min. freq. of light that causes ejection of electrons)

rate of nuclear decay

Δn/Δt = -λn

λ = decay constant

exponential decay equation

n = n_oe^-λt

decay constant

λ = 0.693/half-time