physics eq's 2 Flashcards
The formula for: average velocity?
v = displacement / time
The formula for: average acceleration?
a = velocity / time
The formula for: uniform accelerated motion –> solved for d (3)
d = 1/2 (Vo + V)t missing a d = Vot + 1/2at^2 missing V d = Vt - 1/2at^2 missing Vo
notice the difference in +/-
The formula for: solved for final velocity (2)
V^2 = Vo^2 + 2ad missing t V = Vo + at missing d
the area under a velocity vs. time graph gives?
displacement
newtons second law
Fnet = ma
if an object has constant velocity what is true of Fnet?
no acceleration (constant v) so Fnet = 0 (i.e. dynamic equilibrium)
formula for: weight?
w = mg (g is 10 unless on different planet)
formula for: gravitational pull between two objects
Fg = G x Mm / r^2
formula for g (force of gravity)?
we can combine w = mg with Fg = G x Mm / r^2
(note w = Fg)
we get: g = G x M/r^2
formula for static and kinetic friction
Fk = Fn x μk
Fsmax = Fn x μs
μs > uk always
what is the equation for the parallel force of gravity on an object sitting on an inclined plane?
sin slides down the slope
mgsinθ
the formula for: the centre of mass for a multi-mass object
Xcm = m1x1 + m2x2 +m3x3 / m1 + m2 + m3
x is the distance from a set point
the formula for: centripetal acceleration
a = V^2 / r
if r increases what happens to centripetal a?
it actually increases since r is proportional with v and v is squared in a = V^2 / r
the formula for: centripetal force
Fc = m x V^2 / r
formula for: torque (2)
T = F x d x sinθ
or
T = F x L L = lever arm
what decreases rotational inertia?
making the mass closer to the axis of rotation
the formula for? work?
W = F x d x cosθ
measured in joules
note: this opposes torque which is
T = F x r x sinθ
measured in Nm
the formula for? power?
P = W / t
P = F x v
if force is parallel to velocity
the formula for? kinetic energy and gravitational potential energy
KE = 1/2mv^2
PEgrav = mgh
t or f, ΔKE = total Work
true - work energy theorem
the formula for? conservation of mechanical energy
KE1 + PE1 = KE2 + PE2
in friction is involved
KE1 + PE1 + Work = KE2 + PE2
Work = Ff x d
the formula for? mechanical advantage
F needed without machine / F needed with machine
the formula for? momentum and impulse
p = mv
J = Δp = Δ(mv) = FΔt
I = ΔM = FΔt
I am fat
what occurs in an inelastic collision
KE is not conserved
p is conserved
if perfectly inelastic, objects stick together
first law of thermodynamics equation?
ΔE = Q - W
Q - heat - this is positive when heat flows into the system
W - work - this is positive when the system does work (e.g. a gas expanding and increasing volume)
The work done by a gas?
W = PΔV
what is an adiabatic process?
when Q=0
therefore ΔE = -W
formula for density ?
ρ = mass / volume
measured in kg/m^3
what is the density of water?
1000 Kg / m^3
1g / cm^3
1kg / L
what is specific gravity?
s.g. = ρ / ρH2O
density relative to gravity
weight of a fluid?
ρ = m / V
therefore, m = ρV
weight (w) = ρVg
formula for pressure?
P = F / A measured in N / m^2 = Pa
Force must be perpendicular to object
formula for hydrostatic gauge pressure
Pgauge = ρfluid x g x D
this is proportional to depth, total pressure is not
formula for total pressure ?
P total = Pgauge + Psurface
buoyant force formula? (Archimedes principle)
Fb = ρfluid x g x Vsubmerged
for a floating object, what is true of the buoyant force?
w = Fb
mg = Fb
ρobject x Vobject x g = ρfluid x Vsubmerged x g
for a floating object what is the relationship between the density of fluid and the object?
w = Fb
mg = Fb
ρobject x Vobject x g= ρfluid x Vsubmerged x g
Vobject / Vsub = = ρfluid / ρobject
Formula for apparent weight of a submerged object?
Wapp = Wtrue - Fb
Pascals law on fluids distributing external pressure?
F1 / A1 = F2 / A2
fluids perfectly distribute external pressures if they are confined
list what makes an ideal fluid
- incompressible (ρ is constant)
- negligible viscosity
- laminar flow
- constant flow rate
Bernoulli’s equation ?
P1 + 1/2ρv1^2 + ρgy1 = P2 etc…
flow rate equation?
f = Av
continuity law?
A1v1 = A2v2 if the fluid runs through the same pipe
what is true of two fluids are at the same height?
the faster running fluid has less pressure
Torcelli’s result for v-efflux?
this equation is used when a hole has been punctured in a container allowing fluid to leak from the bottom area. This equation explains velocity of efflux
v-efflux = (2gD)^1/2
square root of 2gD
stress equation?
stress = F / A but force does not need to be perpendicular like it does in pressure
what is the value of the elementary charge?
1.6 x 10^-19
What is Coulomb’s Law?
Felec = kQq / r^2
K = 9 x 10^9
formula for electric field due to a point charge?
E = KQ / r^2 where Q produces the field
which direction does a negative charge move in an electric field produced by a source charge?
negative charge will move opposite the direction of the field
formula for the force of an electric field?
F=qE where q feels the field.
formula for electric potential (φ)?
φ = kq / r
for electric potential (φ), where do positive charges move?
positive charges move to area’s of lower φ
negative charges move to area’s of higher φ
change in electrical potential energy is equal too?
ΔPE = qΔφ where q is the charge that is moving through the electric potential
work done by an electric field?
W = -ΔPE
kinetic energy of a particle in a field
ΔKE = -ΔPE
what is basic the formula for current?
I = Q / t
and note that often Q = # of electrons times e
the formula for resistance relative to the wire?
R = p L/A
p = resistivity, not density
the formula for Ohms law
V = IR
where R is equivalent resistance
the formula for connecting two resistors in parallel to get Req?
R1R2 / R1 + R2
can’t do this with more than two at a time
t or f, current is the same for resistors in series whereas voltage is the same for resistors in parallel.
true
what are the two main Kirchhoff rules
- junction rule –> current into a junction must equal current out
- voltage rule –> voltage drop of all resistors must sum up to the voltage gain of the battery
the formula for power dissipated by a circuit element.
where P = x = y = z
P = IV = I^2R = V^2 / R
just remember P = IV and then use V = IR to switch the terms
t or f, total power supplied to the circuit is equal to total power dissipated by the R’s?
true
true or false, the ground is at a potential of 0
true
the basic formula for a parallel plate capacitor?
Q = CV
Note: C is a constant therefore you can’t find it with this equation.
the formula for capacitance of a capacitor
C = K ε0 A / d
where K is the dielectric number
ε0 is the permittivity of free space constant
t or f, K can be less than 1
false. K is always greater than 1 and therefore, when a dielectric insulator is present, it increases the capacitance always
C = K ε0 A / d
what occurs when
- keep battery attached, insert dielectric
- disconnect the battery, insert dielectric
- keep battery attached, insert dielectric –> keeping it connected means voltage is constant. Since the dielectric is added, C increases. According to Q = CV, if C increases, but V stays the same, Q must increase.
- disconnect the battery, insert dielectric –> disconnecting it Q is constant. Since the dielectric is added, C increases. According to Q = CV, if C increases, but Q stays the same, V must decrease.
the formula for an electric field produced by a capacitor (which is uniform)
V = Ed
the formula for potential energy stored in a capacitor
PE = 1/2 QV
using Q = CV we can rearrange to
PE = 1/2 QV = 1/2CV^2 = Q^2 / 2C
t or f, the work done by a battery to charge a capacitor is equal to PE
true
t or f, capacitors have the same rules for capacitor equivalence (Ceq) as resistors do for equivalent resistor (Req)
false –> they are opposite
e.g. capacitors in series are added by their inverses
the formula for magnetic force
Fb = qvBsinθ
θ is in between v and B
if v and B are parallel, sinθ is 0, no force felt
if the charge is not moving, no force felt either
t of f, Fb is always perpendicular to B and v
true
t or f, in a solenoid, B is proportional to I and N/L
true
what is B proportional to when created by a long straight wire
B varies with I / r
r is distance from the wire
can a magentic force do work?
no!!! therefore is does not change the speed of the charge ever - only the direction
what is hookes law?
F = -kx
x = displacement k = spring constant
what is the elastic potential energy of a spring equation?
PE = 1/2kx^2
simple pendulum formula for frequency?
f = 1/2pi x squareroot (g / L)
wave equation?
v = f x λ
true or false, speed is dependent on λ and f
false!! although v = f x λ, speed depends on the medium it travels through and NOT on f or λ
therefore, if we change f then λ changes in the opposite way
how does v, f, and λ change when a wave changes media?
recall: wave speed is dependent on the medium
therefore v changes
NOTE: frequency always remains constant for a media change.
if frequency remains constant but v changes, λ must be proportional to v
v = f x λ
the equation for the wavelength of a standing wave?
λn = 2L / n
where n = the # of nodes - 1
where n = the number of harmonics (1/2 wavelengths)
what is the fundamental wavelength?
this is the wavelength of one harmonic, i.e. when n of λn = 2L / n is equal to 1.
if we know this value then we can simply multiply this wavelength by any integer to find any other harmonic
t or f, we can take λn = 2L / n and combine it with v = f x λ to get the harmonic frequency
true
t or f, λn = λ1 / n
and
fn = f1 /n
false,
λn = λ1/n is correct since if we extend the number of nodes over a distance L, the wavelength must be decreasing
(fn = f1 /n is incorrect) –> fn = f1 x n is correct since if wavelength is decreasing (above) then frequency must be increasing.
What is the formula for the harmonic wavelength for sound waves in an open pipe?
Each end of an open pipe is considered an anti-node
therefore, this is similar to a transverse standing wave.
λn = 2L / n
where n is the number of half wave lengths
What is the formula for the harmonic wavelength for sound waves in an closed pipe?
the closed en of the pipe is a node while the open side is an anti-node.
λn = 4L / n
BUT n can only be odd numbers (1,3,5, etc.)
what is beat frequency?
fbeat = f |f1 - f2|
absolute value is necessary
the formula for sound intensity
I = P / A I = j/s / m^2
what 2 important factors does sound intensity vary by?
since most sources produce sound that permeates a sphere, A = 4 pi r^2
therefore I varies with 1/r^2
I = P / A
power is a measure of energy and wave energy increases with amplitude
therefore, intensity varies with amplitude
what is the formula for sound level / intensity level?
B = 10 log (I / Io)
measured in decibels (remove the multiple of 10 and its just bels)
Io = the threshold of hearing = 10^-12 W / m^2
what two rules govern the equation B = 10 log (I / Io) in terms of manipulating I?
If we multiply I by 10 we add 10 to B
If we divide I by 10 we subtract 10 from B
if the intensity of a sound increases by 100, how did the sound level change?
sound level = intensity level
if intensity increased by 100 then it was multiplied by 10 twice (10 x 10 = 100). therefore B must have increased by 20dB
Doppler effect: when the source and the detector are..
a. approaching
b. receding
how does the perceived frequency change?
a. approaching –> when the distance between them is getting smaller the perceived frequency increases
b. receding –> when the distance between them is getting larger the perceived frequency decreases
what is the doppler equation?
(v +/- vd)
fd = fs ———-
(v -/+ vs)
fd = perceived frequency of detector fs = source frequency vd = speed of detector vs = speed of source v = speed of wave (340 m/s for sound)
explain the logic for when the source and the detector are both moving away from each other using the equation.
(v +/- vd)
fd = fs ———-
(v -/+ vs)
if relative motion is away, then we know fd < fs
therefore the fraction must be as small as possible for this to hold true
therefore: v - vd
and
v + vd
note also the way the signs are positioned.
also may think top sign means toward
when a detector moves relative to a stationary source what changes out of
v
f
λ
when the detector moves, he’s changing his relative speed. Since the source is still, the wavelength fronts are the same
for v to change but λ to stay the same f must change too
e. g.
approaching: detector approaches the sound then the relative speed increases and so does the perceived frequency.
when a source moves relative to a stationary detector what changes out of
v
f
λ
when a source moves, the speed must stay the same. However, the moving source changes the wavelengths.
for wavelength to stay change while speed stays the same f must change too.
approaching: source approaches the detector then the wavelength is decreasing and so the frequency must increase
which waves require a medium out of
electromagnetic
sound
rope
electromagnetic - does not need a medium to propagate
sound - needs media
rope - needs media
t or f, sound waves are longitudinal and EM waves are transverse
true
t or f, the speed of an EM wave is the same regardless of the frequency in a vacuum and in a medium
false
the speed of an EM wave is the same regardless of the frequency in a vacuum
however, the speed is slightly different for each frequency in a medium. this accounts for dispersion of waves (prism)
what is the order from shortest to longest wavelength of EM waves
gamma rays < x rays < UV light < VBGYOR < IR waves < microwaves < radiowaves
EM waves: when is energy proportional to amplitude and when is it proportional to frequency?
as a wave - amplitude squared
as a particle / photon - frequency
what is the energy of a photon equation
E = hf
E = h c/λ
h = 6.6 x 10^-34
law of reflection: where is the angle measured
between the incidence ray and the normal (perpendicular line from the surface the ray is hitting)
t or f, the angle for refraction is also measured from the normal
true
t or f, media slows down EM waves
true
what is a mediums index of refraction
this is a measure of how much the medium slows down the EM wave.
speed in vacuum
IoR = ———————–
speed in medium
n = c / v
the bigger the n value, the more the medium slows down light
what is Snells law (equation)
n1sinθ1 = n2sinθ2
If n1 > n2 what is true about the θ’s? draw it.
if n1 > n2, and n1sinθ1 = n2sinθ2
then θ1 must be less than θ2 by Snell’s law
therefore when light travels from a slower medium (n1 in this case) to a faster medium (n2 in this case) then θ of refraction must be bigger then θ of incidence and therefore light bends away from the normal
when can total internal reflection occur?
ONLY when the second medium has a lower n value then the first medium. Think of when light tries to leave water into air.
what is the critical angle
the angle of incidence at which total internal reflection is about to occur. at the critical angle, light refracts along the media boundary making θ = 90 degrees with the normal. (draw it). if the angle of incidence exceeds the critical angle, then TIR will occur
what is the formula for the critical angle?
sinθ = n2 / n1
θ = critical angle
what is diffraction?
when light passes through a slit of similar size to the lights wavelength. the light will bend
what is polarization
when light has a restricted direction of electric fields
what is dispersion
when light is refracted through a medium in which the individual colours are refracted slightly differently due to slightly different speeds (since it is in a medium).
what colour is refracted (bent) the least in dispersion?
red
what is the equation for the focal length?
f = 1/2r
r = radius of the theoretical circle that a mirror / lens creates
mirrors: objects very distant from the mirror will have light rays converging?
at the focal point
mirrors: for a concave mirror, if the object is close but further away then the focal point the image will be real and the rays will intersect behind the focal point. If the object is within the focal point and the mirror, the image is virtual since lines intersect behind the mirror. t or f
true
mirrors: what is a real image? what is the value of i? virtual images?
if the rays actually intersect then the image is real and i is positive. if the rays theoretically intersect (like a convex mirror) then the image is virtual and i is negative.
what is the mirror equation?
1/f = 1/o + 1/i
note: o is always positive - distance the object is from mirror
i - distance of image from mirror
when is i and f positive for mirrors and lenses?
when the observer is on the same side as the image, the image is real and positive.
draw a mirror and lens to see
magnification equation?
m = -i / o
think: if i is positive, then the image is real, which means the observer is on the same side as the image.
real image then must be inverted since m is negative
t or f virtual images are upright images
true, since i of a virtual image is negative and
m = -i/o
how can we find the height of the image?
multiply the height of the object by the magnification number
concave mirrors
concave lenses
convex mirrors
convex lenses
list whether the focal length is +/- for each.
a focal length is positive if the image results from the actual intersection of rays
concave mirrors –> positive
concave lenses –> (diverging lens) –> negative
convex mirrors –> negative
convex lenses –> (converging lens) –> positive
plane mirrors produce what kind of image?
a virtual image (therefore a negative i value, upright image)
t or f, the equations for mirrors apply to lenses
true
what is lens power and what is its equation?
lens power explains how strong a lens bends light. the more it bends light the more power has
P = 1 / f
focal length (f) must be in meters
unit = diopters (D)
what unit for focal length do we use for lens power
meters
t or f, for consecutive lenses we add the powers
true and note that negative power does exist. for example, a diverging/concave lens has a negative focal length and thus negative power
what is myopia?
what do they see
where do rays converge
how do we correct it
myopia = shortsightedness
people can see nearby things
the rays converge before the retina
corrected with a diverging lens
what is hyperopia?
what do they see
where do rays converge
how do we correct it
hyperopia = farsightedness
people can see far away things
the rays converge after the retina
corrected with a converging lens
Stats: what is the mean?
the average of a sample. here you sum up all the values and divide by the number of components.
the mean is not necessarily a number seen in the sample
Stats: what is the median?
the middle number in the data set. put the numbers in consecutive order and find the one literally in the middle.
If there is an even amount of numbers, we then average the two closest to the middle
XXYYXX –> we average the Y’s
Stats: what is the mode?
the most frequently recurring number in a data set.
32, 65, 66, 67, 68, 68, 69, 70, 70, 70, 70 ,71
70 is the mode
Stats: what is the mode for a sequence of numbers that never repeat?
if no numbers occur more than once, there is no mode!!
Stats: what is the standard deviation?
it is a measure of how much each individual number differs from the mean
Stats: for standard deviation, what is a normal distribution?
large sets of data form a symmetrical, bell shaped curve when graphed by frequency (# of instances).
the measure is on the y axis (weight, grades, etc) and the frequency is on the x
Stats: what is a low standard deviation?
most data points are close to and similar to the mean
Stats: what is a high standard deviation?
data is more spread out
Stats: what is the significance of the values 34%, 68%, and 13.6%?`
a normal distribution has a set structure. We can therefore break up the graph into chunks of certain meaning.
34% of components fall 1 S.D. above the mean
34% of components fall 1 S.D. below the mean
thus, 68% of components fall within 1 S.D. of them mean.
13.6% of components fall between 1 and 2 S.D.’s and so on.
Stats: t or f, for a normal distribution, essentially all data falls within 3 standard deviations of the mean
true
Stats: what is an independent and dependent variable?
dependent variable is a function of the independent variable.
Stats: what is statistical power?
statistical power is the likelihood that you have enough subjects to accurately prove your hypothesis is true within an acceptable margin of error
small sample sizes influence this
Stats: what is sampling bias?
when a group of people being tested was not randomly selected and therefore may unintentionally skew results.
Stats: what is
specific real area bias
self-selection bias
pre-screening / advertising bias
healthy user bias
these are all forms of sampling bias
specific real area bias –> when you select people close in proximity. (like standing in the arc where you get extrovert answers but no introvert answers)
self-selection bias –> when the study allows people to choose to participate or not (like surveys which may only reach out to highly opinionated people on the topic)
pre-screening / advertising bias –> volunteers how succumb to advertising of a research may acquire only people highly motivated in the research. e.g. smoking cessation may only get people who are v serious about quitting
healthy user bias –> when the study population is likely healthier than the general population.
Stats: t test measures what? whats important about it?
t test measures significance of a correlation between stats.
significant findings have a p value of less than 0.05
Stats: what is inter-rater reliability?
when two separate raters (researchers) examine someone, they should have similar findings for the same study.
what are confounding factors?
these are hidden variables not directly tested for, that correlate in some way with either the independent or dependent variable and thus may impact results.
this may effect internal validity –> can we prove a causal relationship between the two variables being tested
Stats: what is external validity?
this is asking if we can take the info of the study and generalize it to other situations.
