Equations Flashcards
static friction
fs (us)(Fn)
*if surfaces do not slide relative to each other; static friction
kinetic friction
fk = (uk)(Fn)
*if surfaces slide relative to each other
peak height of a projectile
v = sqrt(2gh)
vo must be zero; horizontal velocity is constant at vcos(theta)
universal law of gravitation equation for force
F = Gm1m2/r^2
G= 6.67 *10^-11 m^3/kgs^2
normal force on an incline
mgcos(theta)
net force due to gravity and normal force
mgsin(theta)
average speed
average speed = distance/time
average velocity
average velocity = displacement/time
linear motion equation involving velocity, time, and acceleration
v-vo=at
*acceleration must be constant
linear motion equation involving displacement, initial velocity, acceleration, time
x-xo = vot +1/2at^2
*acceleration must be constant
linear motion equation involving displacement, velocity, and acceleration
v^2 = Vo^2 + 2a(x-xo)
*acceleration must be constant
torque
torque = Frsin(theta)
F=force vector
r=distance from the point of rotation to the point of application of force
theta= angle between force and position vectors
torque (lever arm)
torque= Fl
F=force vector
l=position vector extends from the point of rotation to the point where the force acts at 90 degrees
kinetic energy
KE = 1/2mv^2
m=mass
v=velocity
gravitational potential energy
Ug = -Gm1m2/r
G= 6.67 * 10^-11 m^3 k^-1 s^-2
Ug = mgh
elastic potential energy
Ue = 1/2k(deltax)^2
k=
x=
power
P = delta E/t = W/t = Fvcos(theta)
- rate of energy transfer, work done by a force per unit time*
unit: Watt (W)
Work / First law of thermodynamics
W + q = delta E total = deltaK + U
W = Fdcos(theta) = delta K + U
*no work if perpendicular: cos(90) = 0
in absence of heat: W = deltaK
density
p = M/V
density of water
p water = 1000kg/m^3 = 1g/cm^3
pressure
*unit: Pascal (Pa)
P = F/A
P = pgy for a fluid at rest with uniform density in a sealed container
p=density
g=gravitational constant
y=depth of fluid
absolute pressure
P abs = P gauge + P atm
buoyant force
FB= (pfluid)(vfluid)(g)
p=density
v= volume of the fluid displaced
g=acceleration due to gravity
buoyant force for floating object
Fbuoyant = Fgobject
buoyant force for a submerged, floating object
Fbuoyant = Fgobject
buoyant force for a fully submerged, sunk object
Fg object = F normal + F buoyant
continuity equation (volume flow rate)
Q = Av
Q = volume flow rate
A =
v = velocity (distance/time)
mass flow rate
I = pQ = pAv
same as continuity equation, but multiply by density
Bernoulli’s equation
P1 + 1/2 pv1^2 + pgh1 = P2 + 1/2 pv2^2 + pgh2
P = pressure h = distance above an arbitrary point y = distance beneath the surface
velocity of a fluid from a spigot
v = sqrt(2gh)
volume flow rate for a real fluid in a horizontal pipe with constant cross-sectional area
Q = deltaP (pi) r^4 / 8 n L
Q = volume flow rate
r = pipe radius
L = pipe length
viscosity
coulomb’s law
equation for force of attraction/repulsion between two charged objects
F = k q1 q2 / r^2
k = Coulomb's constant 8.988 *10^9 Nm^2/C^2 r = distance between the centers of charge
electron charge: 1.6 *10^-19 C
voltage (due to a point charge)
V = k q1/r
- scalar
- units: volts (J/C) (V)
- electric potential*
electric field (due to a point charge)
electrostatic force per unit charge
force on a charge in an electric field
N/C or V/m
E = kq1/r^2
potential energy (U) (due to a point charge)
U = kq1q2/r
force multiplied by displacement, can also be derived from Coulomb’s law by multiplying by the distance (r)
electric force due to a constant electric field
F = qE
voltage due to a constant electric field
V = Ed
potential energy due to a constant electric field
U = qEd = W = qV
current
- moving charge*
units: Amps (A) or C/s
i = V/R
i = current V = voltage R = resistance
resistance
R = pL/A
p: resistivity (nature of substance to resist change)
L: length
A: area is inversely proportional to resistance
*measured in ohms
resistors in series
RT = R1 + R2 + ….
- have greater resistance
- highway lane analogy
resistors in parallel
1/RT = 1/R1 + 1/R2 +…..
*have less resistance (greater area)
capacitance for parallel plate capacitor
C = kAeo /d
k = dielectric constant; insulator, resists creation of electric field so capacitor can store more charge A= area of the plates d = distance between the plates
electric field that is constant everywhere on the plates:
E = Q/kAeo
capacitance
C = QV
capacitor in series
1/CT = 1/C1 + 1/C2 +1/C3
distance between the plates
capacitor in parallel
CT = C1 + C2 + C3
force (in a magnetic field)
F = qVBsin(theta)
wavelength, frequency, period
v = wavelength/T (analogous to v = d/t)
OR
v = f (wavelength)
intensity
I = 2 (pi) p (f^2) (A^2) (v)
p = density of media f = wave frequency A = amplitude v = velocity
doppler effect
delta f / fs = v/c
delta (wavelength) / wavelength s = v/c
fs/ws: frequency/wavelength of source
fo = fs + deltaf
wavelength o = fs + delta (wavelength)
- when the relative velocity brings the source and observer closer, the observed frequency goes up and the observed frequency goes down
- if they are approaching, add deltaf + fs; subtract ws -delta w
an emitted photon has a frequency f, that is proportional to the energy change of the electron
E = hf
h:
f:
refraction
n = c/v
*the greater n, the slower the light moves through the medium
nwater= 1.3 nglass= 1.5
Snell’s law
n1sin(theta1) = n2sin(theta2)
total internal reflection
theta critical = sin inverse (n2/n1)
thin film interference
constructive interference: delta x = m (wavelength)
destructive interference: delta x = (m+1/2) (wavelength)
Young’s double slit experiment
maxima occur: dsin(theta) = m(wavelength)
minima occur: dsin(theta) = (m+1/2) (wavelength)
thin lens focal length, radius of curvature
F = R/2
thin lens equation
1/f = 1/do + 1/di
do: object distance, also p
di: image distance, also q
thin lens magnification
m = -di/do = hi/ho
power of a thin lens
P = 1/f (measured in diopters, inverse meters)
lateral magnification of a multiple lens system
M = m1m2 Peff = P1 + P2
