Physics Equations Flashcards
Fluids: What is the equation for density and the units?
ρ = m / V where units are kg / m^3
Fluids: What is the “Weight” of a fluid in terms of an equation?
Wfluid = Vρg
ρ = density of fluid g = acceleration by gravity
Fluids: What is specific gravity?
density of a substance relative to water
Specific g = ρ / ρh2o
If something is twice as dense as water it has a specific gravity of 2
Fluids: What is the most simple formula for pressure?
P = F (perpendicular) / A
Fluids: what is the equation for gauge pressure?
Pgauge = ρfluidgD
D - depth from surface
Fluids: For an object immersed under fluid what is the equation for total pressure?
Pgauge + Psurface = Ptotal
where Pgauge = ρfluidgD
Psurface is probably 1 atm
Fluids: Archimedes principle states that the force acting upwards on a submerged object is equal to the weight of the fluid displaced by that object. What force is this and what is it in an equation?
Buoyant force
Fb = ρfluid x Vsubmerged x g
if the object if fully submerged then V is equal to the total volume of the object
Fluids: what is true of an object floating on a liquid?
Fnety = 0
therefore W = Fb
Fluids: What is the relationship of ρ and V for an object floating?
For a floating object W-object = Fb
ρobject x V object x g = ρfluid x V submerged x g
rearrange to find
ρobject V-Submerged
———– = ———————
ρfluid V-object
Fluids: What is flow rate of a fluid measured in?
Volume / time therefore m^3 / s
Fluids: What is the equation for flow rate if speed is constant for any given cross sectional area within the tube?
flow = Av
A = cross sectional area of any given point v = flow speed
m^2 x m/s = m^3 / s
Fluids: What is the law of continuity? What is it’s equation?
continuity = flow rate is constant throughout a pipe.
therefore for two sections f1 = f2
if f = Av then..
A1v1 = A2v2
Fluids: what 4 features make fluid have ideal flow?
- Fluid must be incompressible (ρ cant change)
- Viscosity must be negligible
- Flow must be laminar (no turbulence)
- Flow must be steady (volume/s is constant)
Fluids: for large changes in pressure, are gases ideal flowers?
no, gases are compressible often a high pressures violating an ideal flow law
fluids: What is Bernoulli’s equation?
P1 + ρgy1 + 1/2ρv1(^2) = P2 + ρgy2 + 1/2ρv2(^2)
first term = work
second term = PE
third term = KE
fluids: for fluids exposed to the Air, what is the pressure in Bernoulli’s equation?
Patm
fluids:
For fluids at the same height what is true about pressure and velocity?
For fluids at different heights what is true about pressure?
fluids at the same height are not subject to potential energy in Bernoulli’s equation. (ρgy term cancels)
Therefore, the faster a fluid is going (at the same height) the less pressure (on walls of pipe)
For fluids at different heights, the fluid at the higher height has less pressure.
Electrostatics: what is the value of the elementary charge (e)
1.6 x 10^-19 C
charge is quantized in e’s
Electrostatics: Equation for the electrostatic force felt between two charges?
q1q2
Fe = K ——–
r^2
Where K = 9 x 10^9
Note the equation for force felt between two charges is very similar to force felt between two masses.
m1m2 Fg = G --------
r^2
Electrostatics: true or false, Fe is stronger than Fg
true
Electrostatics: What is sin30? sin45? and cos60?
sin30 = 1/2
sin45 = square-root- 2 / 2
cos 60 = 1/2
Electrostatics: which direction do electric fields move?
they move from positive to negative charges. Therefore if you place a positive charge in an electric field, it will feel a force in the direction of the field.
Electrostatics: what is the equation for the electrostatic force in a defined electric field?
Fe = q x E
E = electric field q = charge
note: if q is positive than Fe is positive therefore it will feel a positive (in direction of field) force
Electrostatics: if you combine Fe = qE and
q1q2
Fe = K --------
r^2
What equation do you get?Kq
E = ——– the units are N / C
r^2
q is the source charge producing the electric field
note that this is very similar to electrostatic force (which includes one extra charge on top)
note: E is a vector. Also, you must account an E for every charge.
Electrostatics: true or false, for any force, Fnet = ma still applies.
True!!
Electrostatics: what is electric potential? what is its equation ?
Electric potential is a scaler field permeating around a charge. Changes to Electric potential influence potential energy.
Kq φ = -------- the units are J / C or Volts (V)
r
note that φ is very similar to electric field expect r is not squared (which it is in E) and φ is not a vector (E is)
Electrostatics: true or false, for every charge you must account for that charges personal contribution to total φ and to total E
true, except for φ you only account magnitude not direction.
Electrostatics: what is the equation for electrostatic potential energy?
ΔPEe = q x Δφ = qV
where Δφ and V are the same thing
Electrostatics: what is the relationship between work and ΔPEe?
Work done by the electric field = - ΔPEe = - qV
Electrostatics: what is true of kinetic energy in the absence of non-conservative (drag / frictions / etc.) forces?
ΔPEe = - ΔKE
Electrostatics: a negative ΔPEe is required for spontaneous things to occur.
With the equation ΔPEe = q x Δφ
explain the difference between positive and negative charges and electric potentials.
the charges want to be on the lowest energy state possible which means ΔPEe must drop (be negative)
ΔPEe = q x Δφ
positive charge the equation is (+) (?) = (-)
to lose potential energy, positive charges move to area’s of a negative change in electric potential (- Δφ)
negative charges look like (-)(?) = (-)
negative charges must move to areas of a positive change in electric potential (+ Δφ) to loose potential energy.
Electrostatics:
Work done on the system will ?
Work done by the system will?
work done on the system will increase PE
Work doen by the system will decrease PE
W done by E = - ΔPEe
The more work the system (E) does, the bigger the fall in ΔPEe.
Electricity: What is a capacitor? What is the equation for it?
A capacitor is a device which stores electrical charge. It is two conducting plates separated by an insulator called a dielectric.
C = Kε0 x A / d
Where K is the dielectric number (essentially measures how polarized the insulator gets in between)
ε0 is the permittivity of free space usually given
A area of each plate (only input area of one of them)
d is distance between plates
C is the capacity of charge the capacitor can hold
C is measured in F called farads
Electricity: Explain a battery (+ terminal, - terminal, charge movement, etc.)
a battery provides a voltage (change in potential).
The long line side is the positive terminus indicating higher potential
the short line side is the negative terminus indicating lower potential
electrons wont to go to area’s of high potential to satisfy
ΔPEe = qV. Therefore electrons would flow out of the negative terminal toward the positive.
Positive charges do the opposite
Electricity: The equation of charge stored in a capacitor?
Q = CV
V = voltage across the capacitor not the battery (Although often they are the same)
Electricity: Electric field created by a capacitor or any parallel planes of charge
V = Ed
V = voltage between capacitor plates d = separation of those plates E = electric field created by capacitor
Note: this is a uniform constant field
Electricity: If V = Ed for a capacitor’s electric field, what is the equation for electric field felt by a point charge?
E = kq / r^2
electric potential = kq / r
note that in these equations r is variable but in V = Ed, d is a constant.
Electricity: what is the kinematic equation if distance is missing and final velocity is solved for.
v = vi + at
Electricity: what is the kinematic equation if final velocity is missing and distance is solved for
d = vit + 1/2at^2
note this equation is the same if missing vi but its subtraction instead. (vt - blahblah)
Electricity: what is the kinematic equation if time is missing and final velocity is solved for?
v^2 = vi^2 +2ad
Electricity: what are the three eqautions for PE of a capacitor
PEcap = 1/2qV = 1/2CV^2 = q^2 / 2C
Note this equation is just manipualting the charge found in a capacitor equation: Q = CV
q=Q
Electricity: Voltage vs. charge graph. What is the slope of the graph? What occurs when…
A. You hold voltage constant and change the slope
B. You hold charge constant and change the slope
Voltage (x) vs. charge (y) graph has a slope = C
Area under the curve = PE
A. If you hold voltage constant and increase the slope (increase C) then you increase PE
B. IF you hold charge constant and increase C, then PE must decrease
Q = CV and PE = 1/2qV = 1/2CV^2 = Q^2 / 2C
Electricity: If you were to pull a disconnected (from a battery) capacitor’s plates to a distance of 2d are you doing positive or negative work?
Since work is being done on the system it is positive work
positive work increases potential energy so we can prove this with the following.
Since the battery becomes disconnected V is not constant (batteries maintain constant V)
Since you are changing D, then C is not constant
since no battery supplies V, no charge movement so
Q IS CONSTANT
Now we need to relate the constant to a non-constant. We no nothing of V but we no that
d –> 2d and C = Kε0 A / d than C–> 1/2 C
so we need an equation relating PE with C and Q
PE = Q^2 / 2C
IF C is getting smaller, PE is getting bigger indicating positive work
Work on system = +
work by system = -
for physics at least
Electricity: If a capacitor is connected to a battery what is constant?
Voltage. therefore when finding PE or work changes, use voltage + some variable (C or Q)
Electricity: explain in 5 sentences how a dielectric works?
A dielectric is an insulating material placed into a capacitor. The Electric field of the capacitor causes the charges in the dielectric to polarize in the opposite direction of the field therefore inducing an opposite direction electric field. According to V = Ed, the reduction in E (due to the opposing E of the dielectric) causes the capacitor voltage to drop making Vb > Vc. For a moment, the battery voltage can now place more charge into the capacitor (increasing C) then it could before. Therefore dielectrics increase the capacitance of capacitors which is why K is in their equation.
Electricity: upon inserting a dielectric into a capacitor, What is the difference between when you do it and the capacitor is plugged into a battery and when its not?
battery connect means V is constant
Q = CV the increase in C will increase the Q
No battery connected means Q is constant
Q = CV the increase in C means a decrease in V
Electricity: What is ohms law?
V = IR
note I = C / s
Electricity: what is the equation for resistance a given size of a given material
R = ρ L / A
note: ρ is resistivity not density.
Electricity: What is constant in series circuits and parallel circuits?
circuits in series have constant current (I) throughout
Circuits in parallel have constant voltage across each resistor
Electricity: What is the voltage rule of circuits?
Voltage created by the battery must be equal to the net drop on in voltage across all resistors in the same loop.
in a simple parallel circuit each resistor would have a voltage drop = to the voltage of the battery
In a simple series circuit, each resistor would combine to equal the voltage drop of the battery.
this rule applies to each “loop”
Electricity: t or f, power output by battery is chemical energy converted to electrical energy. Power dissipated by resistors is thermal energy usually
true
Electricity: Explain pivit-rvter
pronounced pivot - rifter
mnemonic for power associated with circuits . t = ^2
P = IV = I^2R = V^2 / R
note: this equation is manipulating ohms law
just like the equation for capacitor PE manipulates
Q = CV
Electricity: power = work / time t or f?
true
Random: True or false,
If net distance is increasing - observed frequency is less then real frequency
If net distance is decreasing between two listeners then frequency observed is more than real f.
true
Random: if a bus is travelling at 50km / h and a cyclist is moving in the same direction at 40 km / hour and observes the frequency of the bus engine to be 1000Hz what is the real frequency approx?
without having to make any calculation: We know the bus is travelling slightly faster then the cyclist. Therefore the distance between them is gradually increasing.
If distance is increasing, observed frequency is less then real frequency.
Therefore if cyclist observes 1000Hz, the real f must be greater than this value.
random: when a wave changes medium its frequency changes too.
false, changing medium does not change frequency.
random: what angle makes sinx and cox equal to one and equal to 0?
sin 90 = 1 and sin 180 = 0
cos90 = 0 and cos 360 = `1
Magnetism: What is the magnetic force equation?
FB = qvBsin0
Where q is the charge magnitude (sign is not included)
v is speed of charge moving
B is magnetic field
theta is angle between B and v
Magnetism: What is true of..
a. particles with no charge
b. particles with no speed
c. particles moving parallel with a magnetic field
d. particles moving perpendicular with a B
FB = qvBsin0
a. no charge means no magnetic force felt
b. no speed means no magnetic force felt
c. sin180 and sin0 both equal 0. Therefore particles in the same or opposite direction to B feel no FB
d. sin90 is 1. Therefore the particle will feel force.
Magnetism: What is the right hand rule for magnetic force (FB)
note: this is not the same as the one for B
- point thumb in direction of velocity
- point straight fingers in direction of B
- palm points to direction of FB that a positive charge would feel. (opposite direction, i.e. back of hand direction, for a negative charge)
Magnetism: What is the equation for centripetal force and acceleration?
Fc = mv^2 / r
ac = v^2 / r
Magnetism: t or f, centripetal forces do not perform work.
true!! since W = delta PE or delta KE and an object in circular motion has no net change in either.
Magnetism: Explain when does FB = Fc
when a charge moves thru a magnetic field, the charge feels a changing FB which makes it go into a circle.
Note: This means that magnetic fields do not do work. IF asked “Calculate the work done by FB or Fc” the answer is 0.
Magnetism: what is a magnetic field
a vector field created by movement of charge (current)
Magnetism: what is the right hand rule for B created by current?
- place thumb in direction of current (note: current is for positive charges. Therefore if question refers to electron direction, you must change the direction of current so it applies to a positive charge)
- curl fingers in direction of B
therefore, B curls around wires with current
Magnetism: t or f, all magnets are dipoles which have magentic fields going from N to S
true! no magnetic is a monopole unlike electric field which can be.
springs: what is Hookes law?
F = - Kx
where F is a restoring force
k is the spring constant
x is displacement from equilibrium
springs: what is frequency/period relationship?
f = 1/T
T = 1/f
f = cycles per second T = time / cycle
note: 3 beats per second = 3 Hz
springs: what is the equation for elastic PE in a spring?
PE spring = 1/2kx^2
note: KE = 1/2mv^2
and KE of a fluid is 1/2ρv^2
springs: Work done by a spring =?
- PE
Waves: what is the equation for frequency of a pendulum?
f = 1/2pi x root ( g / L)
Where L is length of rope to the mass swinging
Waves: what is the equation for the restoring force of a pendulum?
F = mgsin0
where theta = angle between the vertical and the rope
Waves: what is the equation for wave speed?
What is true for
a. a given type of wave (UV, sound, etc.) in a given medium
b. a given type of wave changing medium.
v = λ x f and for light its c = λ x f
- a given wave in a given medium does NOT change its speed. v is constant.
- a given wave changing medium does NOT change its frequency. f is constant
also: frequency varies with energy of a wave
Waves: what isi the beat frequency?
fb = |f1 - f2|
for sounds with two different frequencies.
Waves: what is the equation for
a. Intensity of a wave
b. intensity of a spherical wave?
I = Power / area
I of a spherical wave: I = power / 4pi x r^2
Waves: t or f, I varies with 1/r^2 and varies with A^2
true.
if you move 3 times further from a sound source then..
r –> 3r therefore I –> 1/9I
I varies with A^2 then root I = 1/3
therefore amplitude decreases by 3
