P = delta E/t = W/t = Fvcos(theta) rate of energy transfer, work done by a force per unit time unit: Watt (W)

Equations Flashcards by Marina R

static friction

fs (us)(Fn)

*if surfaces do not slide relative to each other; static friction

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kinetic friction

fk = (uk)(Fn)

*if surfaces slide relative to each other

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peak height of a projectile

v = sqrt(2gh)

vo must be zero; horizontal velocity is constant at vcos(theta)

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universal law of gravitation equation for force

F = Gm1m2/r^2

G= 6.67 *10^-11 m^3/kgs^2

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normal force on an incline

mgcos(theta)

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net force due to gravity and normal force

mgsin(theta)

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average speed

average speed = distance/time

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average velocity

average velocity = displacement/time

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linear motion equation involving velocity, time, and acceleration

v-vo=at

*acceleration must be constant

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linear motion equation involving displacement, initial velocity, acceleration, time

x-xo = vot +1/2at^2

*acceleration must be constant

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linear motion equation involving displacement, velocity, and acceleration

v^2 = Vo^2 + 2a(x-xo)

*acceleration must be constant

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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

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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

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kinetic energy

KE = 1/2mv^2
m=mass
v=velocity

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gravitational potential energy

Ug = -Gm1m2/r

G= 6.67 * 10^-11 m^3 k^-1 s^-2

Ug = mgh

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elastic potential energy

Ue = 1/2k(deltax)^2

k=
x=

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power

P = delta E/t = W/t = Fvcos(theta)

rate of energy transfer, work done by a force per unit time*
unit: Watt (W)

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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

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density

p = M/V

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density of water

p water = 1000kg/m^3 = 1g/cm^3

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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

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absolute pressure

P abs = P gauge + P atm

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buoyant force

FB= (pfluid)(vfluid)(g)
p=density
v= volume of the fluid displaced
g=acceleration due to gravity

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buoyant force for floating object

Fbuoyant = Fgobject

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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 ```

Equations Flashcards

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