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97 Cards in this Set
- Front
- Back
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zeroth law
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if a=b and b=c, then a=c temperature-wise
Objects in thermal equilibrium when they are at same temp. |
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absolute zero
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0 K
-273°C -460°F |
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freezing point of water
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273 K
0 °C 32 °F |
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boiling point of water
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373 K
100 °C 212 °F |
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Key Eq?
Have or want: v₀, v, a, t |
v = v₀ + at
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Key Eq?
Have or want: v₀, a, t, Δx |
∆x = v₀t + ½ at²
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Key Eq?
Have or want: v₀, v, a, Δx |
v² = v₀² + 2a∆x
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Key Eqs?
Have or want: v̄, v₀, v, Δx, t |
v̄ = ½(v₀ + v)
∆x = v̄·t |
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√(3)/2
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= 0.87
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√(2)/2
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= 0.71
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Use this equation to determine the change in length of an object subjected to temp change. (thermal expansion)
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ΔL = αLΔT
ΔL = change in length L = original length α = coeffecient of linear expansion - constant that characterizes specific material in units K⁻¹ (sometimes °C⁻¹) ΔT = change in temperature |
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Use this equation to determine change in volume of a fluid or object subjected to temp change. (thermal expansion)
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ΔV = β V ΔT
ΔV = change in volume β = 3α (3 times the coefficient of linear expansion) V = starting volume ΔT = change in temp |
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Terminal velocity concept
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air resistance = gravity
constant v ∴ a=0 |
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weight
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unit Newtons (kg * ms²)
mass * gravity |
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Newton's 2° Law
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ΣF = ma
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Newtons's 3° Law
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equal & opposite
F₁ = -F₂ |
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Key Eqn for gravitational force
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F = (Gm₁m₂) / r²
G = universal grav constant m₁ and m₂ = masses of 2 objects r = distance bw mass centers |
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Key Eqn for torque
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torque aka moment of force, force along a lever arm
𝜏 = rF sin𝛳 r = radius F = magnitude of force 𝛳 = ∠ bw F and lever arm, greatest at 90° |
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Key eqn for centripetal force
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Picture car driving in circle, pull towards center is c.F.
Eqn describes circular motion F = ma = m(v² / r) a = centripetal accel here = v²/r |
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Key eqn for friction
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range of possible values for static friction: 0 ≤ f ≤ μFⁿ
specific value for kinetic friction: f = μFⁿ f = static friction μ = coefficient of static friction or kinetic friction Fⁿ = normal force |
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translational equilibrium and rotational equilibrium concepts
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translational eq: constant speed ∴ ΣF = 0
rotational eq: constant angular freq ∴ Σ𝜏 = 0 constant speed/freq may be 0 (no mv't) |
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Key eqn for kinetic energy
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K = ½ mv²
energy unit = joules = kg⋅m²/s² |
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Key eqn for potential energy
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U = mgh
Potential E = mass * grav * height |
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Interaction bw kinetic and potential energies
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Total E = K + U = Constant (w/no friction)
Relates to first law of thermodynamics that E does not get created or destroyed. With no E lost to friction/other dissipative F, total E will stay the same. |
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Key eqn for work
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W = Fd cos𝛳
W = work (unit J = kg⋅m²/s² = N⋅m) d = displacement 𝛳 = ∠ bw force and displacement vectors |
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Key eqn for power
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P = W/t
P = power (in Watts) W = work t = time Watt = J/s |
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Key eqn for Work-Energy theorem
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shows relationship bw work and kinetic E
W = ΔK = Kf - Ki Net work is change in kinetic energy. |
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Key eqn for momentum
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Momentum (a vector quantity) has to do w/quality of objects in motion.
p = mv total p of multiple objects = m₁v₁ + m₂v₂ + etc. p = momentum m = mass v = velocity |
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Key eqn for relation bw impulse & momentum
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Impulse (a vector quantity) is change in momentum. Momentum changes when you change apply a force.
I = FΔt = Δp = mv₂ - mv₁ Units impulse = kg⋅m/s²⋅s = kg⋅m/s |
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Key eqn for conservation of momentum
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For elastic & inelastic collisions!
m₁v₁ⁱ + m₂v₂ⁱ = m₁v₁𝘧 + m₂v₂𝘧 total initial momentums = total final momentums For completely inelastic (sticky) collisions! ½m₁v₁ⁱ² + ½m₂v₂ⁱ² = ½m₁v₁𝘧² + ½m₂v₂𝘧² |
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Key eqn for conservation of Kinetic energy
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For completely elastic collisions!
m₁v₁ⁱ + m₂v₂ⁱ = (m₁ + m₂) v𝘧 |
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Key eqn for efficiency of a simple machine
(ramp, pulley, lever) |
Efficiency = W(in) / W(out)
Efficiency = Load*Load distance / Effort*Effort distance usually expressed as a percentage Load & Effort (unit N) |
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Key eqn for Center of mass
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Center of mass is point at which an entire object's mass could be represented as a single particle.
(at geometric center of object) X = (m₁x₁ + m₂x₂ + ...) / (m₁ + m₂ +...) X = center of mass on x axis x = center of individual mass along x axis |
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Key eqn for determining change in total energy of a system undergoing a thermodynamic process.
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ΔU = Q - W
ΔU = change in system's internal energy Q = E trxfr'd through heat to the system (in = +, out = -) W = work done (by = + ; on = -) the system |
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Concept of heat
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Process of energy txfer bw 2 objects at diff temps until thermal equilibrium reached.
unit Joules (SI) also calories and British thermal units (Btu) |
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3 ways of transferring energy
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Conduction (direct txfer through mol collisions - direct physical contact implied)
Convection (txfer by phys motion of heated material - liquids and gases only) Radiation (txfer by electromagnetic waves - can travel thru vacuum) |
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Specific heat
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abbrev. 𝒄
The amt of heat E required to raise 1 kg of a substance by 1°C or 1 K. 𝒄(H₂O) = 1000 cal / kg⋅K |
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Key eqn for determining the heat gained or lost by a substance subjected to temp change.
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Q = m𝒄ΔT = m𝒄(T₂-T₁)
Q = amt heat gained/lost by object m = mass 𝒄 = specific heat ΔT = change in temp (°C or K) |
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Phase changes
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solid to gas — sublimation
gas to solid — deposition solid to liquid — fusion liquid to solid — freezing gas to liquid — condensation liquid to gas — vaporization |
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Key eqn to determine heat gained or lost by a substance subjected to a change in phase.
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Q = mL
Q = amt heat gained/lost by object m = mass L = heat of transformation (given for spec substance) (units J/kg) Δ's potential E, not KE. |
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Units for pressure
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atmosphere (atm)
pascal (Pa) torr mmHg 1 atm = 1.013 E5 Pa = 760 torr = 760 mmHg |
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Key eqn to determine the work done on/by a system that undergoes volume change with constant pressure.
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W = PΔV
W = work in J P = pressure in pascals (1 atm = 1.013 E5 Pa) ΔV = change in volume graph: P on y-axis, V on x-axis Area under line formed / enclosed by curve = Work ∴ ∅ΔV = ∅W, but ∅ΔP (isobaric), follow equation |
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Three special cases for First Law where a condition in a gas system is held constant.
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isovolumetric = isochoric (constant volume ∴W = 0)
adiabatic (no heat exchange ∴ Q = 0) closed cycle (constant internal energy) = isothermal (constant temp) ∴ ΔU = 0 (*isobaric (constant pressure, ∅effect on ΔU = Q - W)) |
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Key eqn to determine the change in entropy of a system at a given temp.
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ΔS = Q/T = (for a reversible process) Lm / T
ΔS = change in entropy Q = heat gained/lost T = temperature (K) L = latent heat (either of fusion or vaporization) m = mass |
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Terms for describing processes
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natural
unnatural reversible (process must go so slowly that system is always in equilibrium) irreversible |
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First law of thermodynamics
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conservation of E
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Second law of thermodynamics
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E will spread spontaneously and irreversibly in a closed system.
(Entropy!) |
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Key eqn to determine attractive/repulsive force 2 charges exert on each other.
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Coulomb's Law
F = kq₁q₂ / r² k = permittivity of free space constant 9E9 q = charge r = distance bw charges |
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Key eqn to determine the electric field produced by a source charge at a chosen point. (Can also be used to determine force on charge in an electric field.)
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E = F / q₀ = (if no test charge) kq / r²
E = electric field magnitude F = force felt by test charge q₀ q = source charge magnitude k = electrostatic constant r = distance between charges |
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Key eqn to determine the electric potential energy bw 2 charges separated in space.
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U = kqQ / r
U = potential energy k = electrostatic constant q & Q = charges r = distance bw charges +U = repulsion -U = attraction |
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Electric potential energy vs. electric potential concepts
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PE: The work necessary to move a test charge from infinity to a point in an electric field surrounding a source charge.
F = kqQ / r² ∴ U = W = Fd = (kqQ / r²)(r) = kqQ / r P: Ratio of work to move a test charge from infinity to pt in electric field surrounding source charge divided by test charge magnitude. |
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Key eqn to determine electric potential due to known source charge at chosen point.
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V = W / q₀ = kQ / r
V = volts = 1 J/C W = work q₀ = test charge magnitude Q = source charge |
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Key eqn to determine potential difference bw 2 points in space.
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V₂ - V₁ = W₁₂ / q₀
V₁ & V₂ = potentials at pts 1 and 2 W₁₂ = Work needed to move test charge q₀ through electric field from point 1 to point 2 (independent of pathway) |
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Major(ly confusing) equations to know regarding electrostatics
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F = k q₁q₂ / r²
U = k q₁q₂ / r E = k q₁ / r² V = k q₁ / r |
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Key eqn to determine the electric potential at a point in space due to electric dipole.
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V = ( kp / r² ) cos𝛳
k = electrostatic constant p = qd = dipole moment (C⋅m) (phys draw towards +, chem opp w/⇸ ) 𝛳 = 0 along dipole axis 𝛳 = 1 along perpendicular bisector |
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Key eqn to determine electric field due to an electric dipole along ⟂ bisector of dipole.
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E = kp / r³
p = qd = dipole moment (C⋅m) |
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Key eqn to determine net torque experienced by an electric dipole about the center of the dipole axis due to an external electric field.
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𝜏 = pE sin𝛳
𝜏 = net torque experienced about center of dipole axis p = qd = dipole moment (C⋅m) E = electric field magnitude 𝛳 = angle the dipole makes with the electric field |
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Electric dipole concept
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2 charges of opposite sign separated by distance d generate an electric dipole of magnitude p = qd.
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Classifications of magnetic materials
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diamagnetic ("antimagnetic stuff")
paramagnetic (weakly magnetic in presence of external magnetic field (Al, Cu, Ag)) ferromagnetic (have unpaired electrons and permanent atomic magnetic dipoles; turn strongly magnetic when below Curie temp or exposed to mag field) |
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Key eqn to determine total electrice current passing through a conductor per unit time.
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i = Δq / Δt
i = current (unit A/amperes) (opposes direction of e⁻ flow) Δq = amt of charge Δt = time |
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Key eqn to determine the magnitude of magnetic field produced by a straight, current-carrying wire.
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B = μ₀i / 2πr
B = magnetic field (unit Tesla = 10⁴ gauss) µ₀ = permeability of free space constant i = current (amps) r = distance from wire |
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Key eqn to determine the magnitude of magnetic field produced by a current-carrying loop.
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B = μ₀i / 2r
B = magnetic field (unit Tesla = 10⁴ gauss) μ₀ = constant i = current (amps) r = distance to center of loop |
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Key eqn to determine the magnetic force on a moving charge in an external magnetic field.
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F = qvB sin𝛳
If sin𝛳 = 1, then F = qvB = mv² / r (centripetal F) F = magnetic F v = velocity B = magnetic field (Tesla = 10⁴ gauss) 𝛳 = ∠ bw direction of magnetic field and velocity vectors |
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Key eqn to determine the magnetic force on a current-carrying wire in a uniform external magnetic field.
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F = iLB sin𝛳
F = magnetic force i = current (amps) L = length of wire B = magnetic field magnitude (T = 10⁴ gauss) 𝛳 = ∠ bw current direction and magnetic field B direction same thing really as qvB sin𝛳 ∵ i = Δq/Δt & v = L /ΔT |
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Key eqn to determine the total electric current passing through a conductor per unit time.
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i = Δq / Δt
i = current (amp = C/s; opposite to the dxn of e⁻ flow) Δq = amt of charge Δt = amt of time |
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Kirchhoff's Rules
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Junction Rule: sum of currents directed in = sum of currents directed out of a pt
Loop Rule: ∑V sources = ∑V drops |
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Key eqn to determine resistance of a given resistor.
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R = ρL / A
R = resistance (unit ohms) ρ = resistivity constant for material L = length of resistor A = cross-sectional area (not in eqn - for most materials ↑T = ↑R) |
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Key eqn to determine drop in electric potential across a resistor.
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Ohm's Law
V = iR V = potential (volts) i = current (amps) R = resistance (ohms) |
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Key eqn to determine the actual voltage supplied by a cell to a circuit.
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V = ε - ir
V = voltage supplied to circuit ε = emf of cell (=V when internal resistance is 0) i = current (mvt of + charges) r = internal resistance of cell |
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Key eqn to determine the power of resistors.
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P = iV = i²R = V²/R
P = E / Δt P = power (watts = J/s) E = Energy supplied by cell Δt = amt time |
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Key eqns to determine total voltage drop & total resistance of resistors in series.
Key eqn to determine total resistance of resistors in parallel. Vs. capacitors? |
V = V₁ + V₂ + ...
R = R₁ + R₂ + ... 1/C = 1/C₁ + 1/C₂ + ... 1/R = 1/R₁ + 1/R₂ + ... C = C₁ + C₂ + ... |
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Key eqn to determine the capacitance of a reactor:
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C = Q/V
C = capacitance (Farads = Coulombs / Volt) Q = charge V = volts |
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Key eqn to determine the capacitance of a parallel plate capacitor.
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C = k ε₀ (A/d)
C = capacitance (Farads = Coulombs / Volt) k = dielectric constant of medium bw plates ε₀ = constant A = area of overlap of 2 plates d = separation |
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Key eqn to determine the electric field at a pt in space bw the plates of a parallel plate capacitor.
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E = V/d
E = electric field magnitude V = volts d = distance bw plates |
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Key eqn to determine the potential energy stored in a capacitor.
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U = ½ CV²
U = potential energy stored C = capacitance (Farads = coulomb/volt) V = volts |
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Concept of dielectric materials
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"insulation"
Shields opposite charges from each other, decreasing voltage across a capacitor. Intro of dielectric by itself has ∅ effect on charge. |
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Key eqn to determine the increase in capacitance due to a dielectric material.
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C' = KC
C' = new capacitance with dielectric K = dielectric constant C = original capacitance |
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Key eqn to estimate the avg magnitude of alternating current over one period.
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I (rms) = I (max) / √(2)
I (rms) = root-mean-square current I (max) = maximum current |
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Key eqn to estimate the avg magnitude of AC voltage over one period.
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V(rms) = V(max) / √√(2)
V(rms) = root-mean-square voltage V(max) = maximum voltage |
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Key eqn to determine the restoring force of a spring.
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Hooke's Law
F = -kx F = restoring force k = spring constant (higher k, stiffer spring) x = displacement from natural equilibrium |
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Key eqn to determine angular frequency, the rate of cycles of oscillation, for a spring.
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ω = 2πf = 2π/T = √(k/m)
T = period ω = angular frequency (units radians/sec) k = spring constant m = mass independent of x! |
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Eqn to determine displacement x of spring at a specific time.
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x = X cos(ωt)
x = displacement from equilibrium X = max displacement from equilibrium ω = angular freq (rad/sec) |
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Key eqn to determine potential energy of a spring.
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U = ½ kx²
U = potential E k = spring constant x = displacement from equilibrium |
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Key eqn to determine angular frequency for a pendulum.
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ω = 2πf = 2π/T = √(g/L)
ω = angular freq g = gravity L = length of pendulum (independent of mass!) |
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Eqn to determine displacement y of a particle in a wave at a specific time.
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y = Y sin(kx - ωt)
y = displacement from equilibrium along y axis Y = max displacement (amplitude) k = wavenumber (∅ spring constant!) ω = angular freq t = time With constant velocity, freq & λ are inverses! |
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Key eqn to determine speed of a wave.
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v = fλ = ω/k
v = velocity f = freq λ = wavelength |
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Principle of Superposition
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constructive interference (amplitudes add together)
destructive interference (amplitudes cancel out each other; 180° out of phase) |
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Key eqn to determine sound intensity.
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I = P/A
I = intensity P = power (Watts or J/s) A = area |
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Eqn to determine the sound level in decibels.
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β = 10 log (I / I₀)
β = sound level (unit decibels = dB) I = intensity I₀ = a reference intensity set at the threshold of hearing |
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Key eqn to determine the sign conventions that best define the relationship bw objects in motion.
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Doppler effect eqn
f' = f [ (v±v(𝖣)) / (v∓v(s)) ] f' = perceived freq f = actual freq v = speed of sound in medium v(𝖣) = speed of detector relative to medium v(s) = speed of source relative to medium towards observer, use - away from observer, use + |
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Key eqn to relate wavelength of a standing wave and L an open pipe or string.
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λ = 2L / n
λ = wavelength L = length of pipe or string n = positive nonzero integer |
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Key eqn to relate wavelength and length of a closed pipe.
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λ = 4L / n
L = length of closed pipe n = odd integer |
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Ideal gas law equation
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PV = nRT
n = number of moles of gas |
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Eqn to determine internal energy of an ideal gas
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ΔU = (3/2) nRΔT
ΔU = change in internal energy of ideal gas n = number of moles of ideal gas R = constant |
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Prob: Mass suspended from spring. When displaced, oscillates with freq x. Find spring constant.
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Remember that ω = 2πf to relate angular freq to regular freq f
2πf = √(k/m) |
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Oscillating properties dependent on...
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length of pendulum
mass of weight attached to spring gravity (envision equation) NOT dependent on amplitude |
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Prob: Given # of maxima, how many cycles have occurred?
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Only (# - 1) complete cycles have occurred!
e.g. 6 maxima pass a certain point along the direction of travel of the wave every 2.5 sec. Going to only have 5 complete cycles divided by 2.5 sec to determine freq! |
