Section 1
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first law of thermodynamics
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Mar 1, 2020
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Section 1
(50 cards)
first law of thermodynamics
dU = q - W potential energy = heat gained - work done by system no heat transfer: dU = -W no change in volume: dU = q no change in energy: q = W
simple harmonic motion
spring: F = -kx U = 1/2 k x^2 KE = 1/2 m v^2 angular frequency (w) = sqrt(k/m) frequency (f) = 1/T = w/2pi pendulum: F = -mgsin(theta) U = mgh KE = 1/2 m v^2 angular frequency (w) = sqrt(g/L) frequency (f) = 1/T = w/2pi max U at ends of swing max KE at middle of swing
decibels
every 10 is a factor of 10
doppler effect
4 variables: frequency of sound, source frequency of sound, observed speed of sound speed of source if source is moving towards you, frequency observed is higher if source is moving away from you, frequency observed is lower used in Doppler ultrasound to calculate speed of blood or fetus, better than standard ultrasound linear relationship between speed and frequency stars have red shift (decreased frequency) since they're moving away from us
acceleration
a = v/t, vector area under curve is velocity g = 10 m/s^2
uniform circular motion
turning F = mv^2/r a = v^2/r force diagram on the object moving involves centripetal force, usually normal force (someone running will need to contact ground at an angle to turn) at the top of a loop, the absolute minimum velocity would involve no normal force, so centripetal force equals gravitational force
bernoulli's equation
bernoulli's equation P + ρgh + 1/2 ρv^2 = constant continuity equation (volume flow is constant) vA = constant pascal's principle (pressure is transmitted to every surface) V = Ad = constant P = F/A = constant W = Fd = constant venturi effect (constriction in pipe causes increased velocity because of continuity equation, thus causes decreased pressure because of bernoulli's equation) P + 1/2 ρv^2 = constant
circuit properties
current: I = Q/t units: amp (A) = C/s voltage: V = IR units: V = A*ohm resistance is a property of the wire, so only V and I can realistically be changed resistance: R = pL/A R is directly proportional to T units: ohm capacitance: Q = VC C = keA/d U = 1/2 C V^2 (potential energy stored by capacitor) units: farad (F) = C/V power: P = IV units: watt (W) = AV
elastic solids
shear modulus: S = (F/A) / (x/h) young's modulus: Y = (F/A) / (dL/L)
work
constant force acting on object over a distance W = F d cos(theta) units: J = N*m force perpendicular to displacement does no work area under a PV curve is work done by the system when volume expands, work is done by the system when volume compresses, work is done on the system
displacement
d, vector slope is velocity
timbre
tone or character of the sound
momentum
vector quantity p = mv units: kg*m/s elastic collision- conservation of momentum, conservation of kinetic energy inelastic collision- conservation of momentum, but kinetic energy is lost impulse = change in momentum (dp) = Ft
pitot tube
determine velocity of air by measuring pressure differential, one side has stagnant air so cross out KE P1 = P2 + 1/2 ρv^2
trig circle
sin(0) = 0, sin(30) = .5, sin(45) = .7, sin(60) = .86, sin(90) = 1 90 = (0, 1) 60 = (1/2, sqrt(3)/2) 45 = (sqrt(2)/2, sqrt(2)/2) 30 = (sqrt(3)/2, 1/2) 0 = (1,0)
hydrostatic pressure
P_s = ρgy y = distance belows the surface shape and surface area of water does not matter
torque
torque = rFsin(theta) units are N*m the greater the distance from the pivot point, the greater the torque
poiseuille's law
flow rate = ΔP(πr^4 / 8Lη) Q = dP/R flow rate depends on pressure difference, and radius, length, and viscosity of liquid increased resistance can be caused by increased length, increased viscosity, or decreased radius
frictional force
kinetic friction- F = u_kN, while moving/slipping static friction- F < u_sN, either rolling or not moving
index of refraction
n = speed of light/speed in new medium light slows down in a medium with greater index of refraction (light is slower in glass than air) sound is faster in glass than air glass
gravitational force
F = Gm_1m_2/r^2 mass is scalar (measures inertia) weight is vector (measures gravitational force)
magnification
m = -i/o m < 1 means image is reduced m > 1 means image is enlarged negative m means inverted image positive m means upright image
human range of hearing
20 Hz to 20 kHz ultrasound is greater than 20 kHz
doppler approximation
df = frequency*relative velocity/speed of light if wave reflects off object (police radar thing), double the doppler effect
speed of sound
343 m/s v = sqrt(K/p) depends on: 1. K = bulk modulus of medium (why sound is faster in solids) 2. p = density (why sound is faster in a dense solid) 3. temperature of medium (why sound is faster in hot air)
pressure difference
dP = pg dh from bernoulli's equation
vector addition
place the vectors tip to tip, addition of the vectors is the new shortcut vector break into component x and y then add up separately vector magnitude = sqrt(x^2 + y^2)
projectile motion
constant a, constant v_x, v_y = 0 at top break into component v_x and v_y
Newton's laws
1. no force means no acceleration, concept of inertia 2. F_net = ma, concerned with 1 object 3. objects exert the same force on each other in opposite directions, concerned with 2 objects units: N = kg*m/s^2 solving force problems: 1. draw force diagram on the object 2. break into x and y components, F_net = ma for both 3. solve equations
energy
KE = (1/2) m v^2 PE = m g h energy is conserved, unless outside forces act on the system W = dK E
internal resistance
R = internal resistance V_actual = V - IR
velocity
v = d/t, vector slope is accel, area under curve is displacement
circuits
voltage in series: V = V1 + V2 voltage in parallel V = V1 = V2 current in series: I = I1 = I2 current in parallel: I = I1 + I2 resistors in series: R = R1 + R2 resistors in parallel: 1/R = 1/R1 + 1/R2 capacitors in series: 1/C = 1/C1 +1/C2 capacitors in parallel: C = C1 + C2
power
power: P = IV units: watt (W) = AV power delivered = V^2/R power lost (as heat) = I^2 R high voltage, low current maximized power transmission!
heat transfer
conduction- direct transfer of energy via molecular collisions convection- transfer of energy via physical motion of heated gas or liquid radiation- transfer of energy via EM waves specific heat: q = m c dT q is heat gained, does not apply during phase change units of q: J or calories units of c: J/g*C heat of transformation: q = m L units of L: J/g
frequency does not change between mediums helium is a lie
gatorade bottle thing
KE of water coming out = PE of water at surface due to bernoulli's equation
kinematics
d = (1/2)(vo + vf)/t, missing a v = vo + at, missing d d = vot + (1/2)at^2, missing vf d = vft - (1/2)at^2, missing vo vf^2 = vo^2 + 2ad, missing t
lens
f > 0 means converging lens object beyond f means image is real, inverted object inside f means image is virtual, upright, enlarged f < 0 means diverging lens all images are virtual, upright, smaller
thermal expansion
linear expansion: dL = a L dT volume expansion: dV = b V dT
index of refraction
w
refraction
n = c/v n1sin(theta1) = n2sin(theta2) always measure angles from the normal lines when light enters higher index medium, refracts towards normal line when light enters a lower index medium, refracts away from normal line total internal reflection- enters lower index medium and refracts a full 90 degrees away from normal, how fiber optics work
electrostatics
electrostatic force between two charges (coulomb's law) F = (k q1 q2) / r^2 units of F = N units of k: (N m^2) / C^2 electric field (field points from positive to negative charges) E = F/q = kq/r^2 E = V/d units of E: N/C, V/m electric potential energy (work required to move from infinity to this point in the field) U = q dV = qEd = k q1 q2 / r electric potential (work required to move positive test charge to this point in the field) V = U/q = kq/r V = Ed (potential difference between two plates) units of V: volt = J/C
mirrors
f > 0 means concave mirror object beyond f means image is real (in front of mirror), inverted object inside f means image is virtual (behind mirror), upright, enlarged f < 0 means convex mirror all images are virtual (behind mirror), upright, smaller
fluid properties
density: p = m/v units: kg/m^3 weight of fluid: F_g = pVg units: N buoyant force (equals weight of displaced fluid) F_b = p_fluid V_displaced g units: N archimedes principle: object weight in water = object weight in air - weight of water displaced weight of water displaced = p_fluid V_displaced g object weight in air = p_object V_displaced g pressure: P = F/A gauge pressure: P = pgh absolute pressure: P = P_atm + pgh units: pascal (P) = N/m^2
specific gravity
density of object/density of water used in archimedes principle, where volume of object equals volume of water displaced
thin lens equations
1/do + 1/di = 1/f do/di = ho/hi height of image/object is proportional to distance of image/object use to calculate magnification factor
magnetism
magnetic field (due to straight wire) B= u I / 2 pi r units: Tesla (T) = N s / m C magnetic field (due to wire loop) B = u I / 2 r field strength is related to current over radius of loop RHR magnetic force (experienced by moving charge) F = qvBsin(theta) magnetic force (experienced by current) F = ILBsin(theta) force is 0 when charges move parallel/antiparallel to magnetic field RHR
power
P = work/time = dKE/time units: watts = J/t, J = ft*lb
positive negative
do (object distance) is always positive di (image distance) is positive for real images, negative for virtual images f (focal length) is positive for concave mirrors, converging lens m (magnification) is positive for upright image
Section 2
(8 cards)