physics constants and equations Flashcards
kinematic equations
- V=Vo+at
- Δx=Vot+1/2at2
- V2=Vo2+2a(Δx)
Gravitational force btwn 2 objects
F=(Gm1m2)/r2
gravitational constant
6.67x10-11 N x m2/kg2
torque
t=rFsin(Θ)
centripetal foce
F=(mv2)/r
centripetal acceleration
a=V2/r
friction force
coefficient of static or kinetic friction times normal force
Kinetic energy
K=1/2mv2
Potential energy
U=mgh
Relating work to energy
W=ΔE=ΔK+ΔU
work
W=Fd cos Θ
power
P=w/t
net work
W=ΔK
momentum
p=mv
impulse
change in momentum
I= Δp (momentum) = FΔt = mvf-mvi
difference between elastic and inelastic collisions
kinetic energy is only conserved for elastic collisions
momentum is conserved for both
mechanical advantage
Fout/Fin
Efficiency
Wout/Win=[(load)(load distance)]/[(effort)(effort distance)]
effort and load in Newtons
center of mass
(m1x1 + m2x2 +…)/ m1 + m2 + …
Thermal expansion (ΔL)
ΔL = αLΔT
L is length, T is temp, alpha is a constant
volume expansion
liquids experience thermal expansion –volume expansion
ΔV=βVΔT
β=3α
change in the internal energy
equation and sign convention
ΔU = Q - W
Q is energy transfered through heat to system and W is work done by system.
Work done on the system (-) / work done by system (+)
heat flow out of system (-) / heat flow into system (+)
conversion between Cal, cal, Btu, and Joules
1 Cal = 1000 cal = 3.94 Btu = 4184 J
equation used to find heat gained or lost by a substance subjected to a change in temperature
Q=mcΔt
equation used to determine heat gained or lost by a substance when tehre is a change of phase
Q=mL
m is mass
L is heat of transformation
Q is heat gained or lost
Work done on or by a system that undergoes a change in volume at constant pressure
W=PΔV
entropy
ΔS=Q/T
entropy for a reversible process
ΔS=Q/T=L(m/T)
L = latent heat (either heat of fusion or heat of vaporization)
density
p=m/V
Work in terms of density
W=pVg
derivation: W=mg
m=pV
W=mVg
Pressure
Pressure = F/A
conversion between Pa, atm, torr, mm Hg
1.013 x 105 = 1atm = 760 torr = 760 Hg
Absolute pressure
the total pressure exerted on an object submerged in a fluid
P=Po+pgh
Po is pressure at the surface
pgh(density,gravity,height)
guage pressure
the difference between absolute pressure inside and atmospheric pressure outside
Pg=P-Patm = (Po + pgh) - Patm
pascals principle
P = F1/A1 = F2/A2
V=A1/d1=A2/d2 d is liquid displaced
W=PΔV so W=F1d1 = F2d2
buoyant force (for floating objects and for fully submerged objects)
Fbuoy= (Vfluid displaced)(pfluid)(g) = weight of object
for fully submerged objects, Fbuoy=(Vobject submerged)(pfluid)(g)
ciritical viscosity
critical velocity is the velocity at which, when exceeded, flow of fluid becomes turbulent
Vc=NRn/pD
NR is reynolds number, n is viscosity of the fluid, p is density of fluid and D is diameter of tube
Linear velocity at which fluid flows
measure of linear displacement of a fluid particle in a given amount of time
vA=V/time
v is velocity
V is volume
continuity equation
fluids flow more quickly through narrow passages than wide ones
v1A1 = v2A2 = constant
v is velocity
bernoulli’s equation
P1 + (ρv12 )/2+ ρgy1 = P2 + (ρv22)/2+ ρgy2
Young’s modulus
change of length due to stretching or pushing forc;e
Y=(F/A) / (ΔL/L)
shear modulus
S = (F/A)/(x/h)
Bulk modulus
degree to which a material will experience a change in volume in relation to applied pressure (gasses mostly)
B = (F/A) / (ΔV/ V)
what is the fundamental unit of charge
e=1.6 x 10-19
coulombs law
F=(kq1q2)/(r2)
constant electric field: F=Eq
what does K (coulombs constant) equal?
K = (1/4)πεo
=8.99 x 109 (Nxm2)/C2
Electric field
E=F/qo = kq/r2
f is the force felt by test charge qo
Force generated by electric field
E=Eq1 + Eq2 + Eq3 + …
F=qoE
electric potential energy
U=kqQ/r
potential energy between two charges separated by distance r
potential energy due to constant electric field
U=Vq and U=qED
electric potential
V = W/qo
V=kQ/r
J/C=NxM/C
constant electric field: V=Ed
potential difference
Voltage between points a and b = Vb-Va = Wab/qo
εo
8.85 x 10−12
conversion between tesla and gauss and units of tesla
1 Tesla =1 N x s/m x C = 104 gauss
gauss is smaller
determine total electric current passing through a conductor per unit time
i=Δq/Δt
unit is 1 Ampere = 1 C/s
magnetic field produced by straight current carrying wire
B=(µoi)/2πr
magnetic field generated by a circular loop of current carying wire at the center of the loop
B=(µoi)/2r
Force on a moving charge throguh an external magnetic field
F=qvB sin θ
q is charge (including sign) v is the velocity and b is the magnetic field
µo
permeability of free space
= 1.26 x 10-6 T x m/A
force on a current carrying wire in a uniform external magnetic field
F = iLB sin θ
i is the current, L is length and b is magnetic field
resistance
R=pL/A
p is resistivity, L is length and A is cross sectional area
ohms law
V = iR
actual voltage supplied by a cell to a circuit
V = εcell - irint
r int is the internal resistence = 0 when there is no currentg
εcell is voltage supplied
Power of a resistor
P=IV = I2R = V2/R
total voltage and resistance for resistors in series
Vs=v1 + v2 + v3 + ….+Vn
Rs = R 1 + R2 + R3 + …+ Rn
total resistance and voltage when resistors are connected in parallel
Vp=V1 = V2 = V3 =…=Vn
1/Rp=1/R1 + 1/R2 + 1/R3 + … + 1/Rn
capacitance
C=Q/V
C=εo (A/d)
Electric field at a point in space between plates of a parallel plate capacitor
E=V/d
potential energy stored in a capacitor
U=1/2 CV2
increase in capacitance due to a dialectric material
C’=KC
voltage and capacitance of capacitors in seris
1/Cs=1/C1 + 1/C2 + 1/C3 + ….
Vs=V1 + v2 + v3 + …
voltage and capacitance of Capacitors in parallel
Cp=C1 + C2 + C3 + …
Vp = V1 = V2 = V3 =…
rms current
Irms = Imax/root2
rms voltage
Vrms = Vmax/root2
restoring force of a spring
F=-kx
angular frequency of a spring
ω=2πf
ω=sqt(k/m)
potential energy of a spring
u=1/2kx^2
angular frequency of a pendulum
ω=2πf=sqt(g/L)
frequency
sqt(1/T) or sqt(ω/2π)
spring system kmax occurs at?
x=0
pendulum system kmax occurs at?
theta=0 (vertical position)
max potential energy of spring system
x=+/- X
max potential energy of pendulum
max value of theta
max acceleration of spring system
x= +/- X
max acceleration of pendulum
max value at theta
speed of a wave
v=fλ
sound intensity
I = P/A power over area
sound level
β=10 log I/Io
calculate new sound level
βf=βi + 10 log ( If / Ii )
( If / Ii ) = ratio of final to initial intensity
beat frequency
Fbeat=|F1-F2|
doppler effect
f’=[(v±Vd) / (v∓Vs )]
wavelength of a standing wave on a string
λ=2L/n
frequency of a standing wave on a string
f=nv/2L
fundamental frequency or first harmonic
lowest frequency longest wavelength of a standing wave
open pipes
act like strings
n=number of half waves
λ=2L/n
f=nv/2L
closed pipes
λ=4L/n
f=nv/4L
speed of light
c=fλ
c=3 x 10^8
wavelength of red light
760 nm
law of reflection
Θ1=Θ2
mirror equations
1/o + 1/i=1/f
f=(1/2)r
magnification
m=-i/o
|m|
|m|>1 image is enlarged
|m|=1 image is the same size
snells law
n1sinΘ=n2sinΘ
n=c/v
c is the speed of light in a vacuum and v is the speed of light in the medium
n for air = 1
lens power
P=1/f
diopters
formula for lenses
1/o+1/i=1/f
m=-i/o
lensmaker’s equation
use for thick lenses
1/f=(n-1)(1/r1-1/r2)
n is the index of refraction for lens material r1 is the radius of curvature for first and 2nd lens
multiple lens systems
for lenses in contact
1/f=1/f1 + 1/f2+1/f3…
P= P1 + P2 + P3…
for lenses not in contact
M=m1 x m2 x m3….
peak wavelength at a given temperature
(λpeak)(T) = 2.9 x 10^-3
peak wavelength means wavelength that radiates greatest energy. not highest wavelength possible (both higher and lower wavelengths will be admitted
energy of a photon
E=hf
λ=c/f
maximum kinetic energy of an electron ejected by an incident photon
Kmax=hf-W
energy of an electron with given quantum number in joules
E=-RH/n^2
rydberg constant
2.18 x 10 & -18
estimate energy of an electron with given quantum number n in electron volts
En=-13.6/n^2
change in energy due to absorbtion or emission of a photon
hf=Ef-Ei
alpha decay
emission of a helium nuclius
beta particle decay
B- decay means nutron becomes a proton
0
B
-1
positron decay
proton becomes positron and neutron
0
B
+1
exponential decay
rate = Δn/Δt
n=n0e-λt
λ=ln/half life = 0.693/half life
wavelength of violet light
380 nm
potential energy of a pendulum
u=mgh
doppler effect approximation
Δf/fs=v/c
Δλ/λs = v/c
