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Equations to know Flashcards

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1
Q

When trying to gauge the likelihood of a gene or a combination, how are they found?

A

If you wanted a homozygous tall plant from a TtPp the likelihood of that is 1/4 the likelihood is 1/16(1/4x1/4) so they are multiplied.

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2
Q

Whereas the likelihood of getting a certain trait found above can be added if there are multiple ways to receive it.

A

add the different likelihoods

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3
Q

How is the total lung capacity found?

A

Total lung capacity=residual volume+vital capacity

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4
Q

How is the Vital capacity found?

A

Vital capacity=tidal volume+expiratory reserve volume+inspiratory reserve volume

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5
Q

What is the hardy weiinberg equilibrium equation?

A

p^2+2pq+q^2=1

with only two possible choices at the gene locus p+q=1.

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6
Q

What is the equation for specific rotation?

A

α=αo/Cxl

or specific rotation=observed rotation/(concentration (g/mL)xlength(dm))

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7
Q

What is the equation to find frequency?

A

f=c/λ

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8
Q

What is the Henderson-hasselbach equation?

A

pH=pKa+log((conj base)/(conj acid))

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9
Q

What is the value of a charge of a proton/electron?

A

• (1.6 × 10− 19 C)

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10
Q

What is 1 atomic mass unit equal to/

A

•1amu=1.66 × 10− 24 grams

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11
Q

What is avogardro’s number?

A

• 1mol=Avogadro’s number: 6.022 × 1023

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12
Q

What is the electromagnetic energy and frequency equation?

A

•E=hf=hc/λ J=(Js)(1/s)=(Js)(m/s)(1/m). h=6.626x10^-34 Planck’s constant
c=speed of light 3x10^8

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13
Q

What is the equation for angular momentum?

A

•angular momentum=L=mvr kintetic energy=KE=1/2mv^2

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14
Q

How is the electromagnetic energy found from the energy levels?

A

E=hf=-RH((1/ni^2)-(1/nf^2))

n=quantum number, RH= rhydberg constant=2.18x10-18 J/electron, speed of light= c= 3x108 m/s
• n > 2 energy level to the n = 2 energy level is known, the Balmer series and includes four wavelengths in the visible region
• n > 1 to n = 1 (that is, the emissions of photons from the electron falling from the higher energy levels to the ground state) is called the Lyman series, which includes larger energy transitions and therefore shorter photon wavelengths in the UV region of the electromagnetic spectrum.

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15
Q

What is the angular momentum given the energy level of the series?

A

L=nh/2π

h=6.626x10-34 Planck’s constant

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16
Q

What is the maximum number of electrons that can exist in a subshell?

A

4l + 2
where l is the azimuthal number l=(0-3)

for any value of l there is a maximum 2l+l possible values for the magnetic quantum number ml. with each orbital holding -∞,0,∞

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17
Q

What is the pattern of the periodic table?

A
  • Left → Right
  • Atomic radius ↓
  • Ionization energy ↑
  • Electron affinity ↑
  • Electronegativity ↑
  • Top → Bottom
  • Atomic radius ↑
  • Ionization energy ↓
  • Electron affinity ↓
  • Electronegativity ↓
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18
Q

What is the equation for a vector quantity?

A

μ=qr

. μ =vector quantity. q=charge magnitude r=distance between two partial charges

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19
Q

What is the equation to find formal charge?

A

Formal charge= V-Nnonbonding-1/2Nnonbonding.

where v is the normal number of electrons in the atom’s valence shell, N nonbonding is the number of bonding electrons

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20
Q

What is the atmosphere conversion?

A

1atm=760mmHg=760torr=101.325kPa

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21
Q

What is the standard temperature and pressure, and the standard state conditions?

A

STP=273.17, (0C) and 1atm.

Standard state=298K, and 1atm

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22
Q

How can the average kinetic energy of gas particles be found?

A

KE=1/2mv^2=3/2kT
where k=boltzmann constant=1.3806488 × 10-23 m^2 kg s^-2 K^-1

J=(kg)(m/s)^2=(J/K)(K)

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23
Q

How can the resultant quantity of speed be found?

A

Urms=√((3RT)/M)
R is the ideal gas constant=8.3144621 J K^−1 mol^−1

T is the temperature, and M is the molecular mass

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24
Q

What is Graham’s law and what does it determine?

A

r1/r2=√(M2/M1)
r=diffusion rates of gas 1 and 2, M=molar mass
equation used to determine the relative rates of diffusion or effusion

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25
Q

What does avogadro’s principle sate about gases at constant temperature and pressure?

A

n/V=k
n=moles of gas, V=volume
k=boltzmann constant=1.3806488 × 10-23 m^2 kg s^-2 K^-1

or n1/V1=n2/V2

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26
Q

What is the ideal gas law?

A

PV=nRT when comparing two gases withe the same moles the equations P1V1/T1=P2V2/T2 can be used

V2=(V1(P1/P2)(T2/T1))
where n is the number of moles found by n=m(mass in grams)/M(molar mass)
R=8.21 × 10-2 (L· atm)/(mol· K) or 8.314 J/(K· mol)

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27
Q

HOW can density be found?

A

density=mass/Volume. or m=dstp/Vstp=dstp/22.4L/mol

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28
Q

What is Boyle’s Law?

A

constant temperature.
PV=k or P1V1=P2V2

as pressure increases volume decreases

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29
Q

What is Charle’s Law?

A

constant pressure
V/T=k or V1/T2=V2/T2

as one increases so does the other

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30
Q

What is dalton’s law?

A

PT=PA+PB+PC+…

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31
Q

How is the partial pressure of a gas related to its mole fraction?

A

PA=PTX

where X=mole fraction
PA= the partial pressure of the gas

PT=total pressure

with the mole fraction found by XA=nA/nt or (moles of A/total moles of gases)

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32
Q

What is the Van der waals equation of state?

A

(P+((n^2a)/V^2))(V-nb)=nRT

where a and b are physical constants experimentally determined for each gas. The a term corrects for the attractive forces between molecules (a for attractive) and as such will be smaller for gases that are small and less polarizable He, larger for gases that are larger and more polarizable Xe, and largest for polar molecules. The b term corrects for the volume of the molecules themselves. Larger values of b are thus found for larger molecules. Numerical values for a are generally much larger than those for b.

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33
Q

What is the gram equivalent weight?

A

gram equivalent weight=molar mass/n

where n is the number of moles of something donated

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34
Q

What is the equation for equivalents?

A

equivalents=mass of compound/gram equivalent weight

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35
Q

What is the equation for molarity?

A

Molarity=Normality/n

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36
Q

How is normality found?

A

it is a measure of concentration and is measured in equivalents/liter, 1N solution has a concentration of hydrogen ions equal to 1 mole/liter

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37
Q

What is an empirical formula?

A

gives the simplest whole number ratio of the elements int he compound

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38
Q

What is a molecular formula?

A

gives the exact number of atoms of each element in the compound and is a multiple of the empirical

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39
Q

How is percent composition found?

A

% composiiton=(mass of X in formula/formula weight of compound) x100%

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40
Q

How is percent yield found?

A

percent yield=(actual yield/theoretical yield)x100%

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41
Q

What is the rate law?

A

-Δ(A)/aΔt=-Δ(B)/bΔt=-Δ(C)/cΔt=-Δ(D)/dΔt

where aA+bB=cC+dD

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42
Q

What is the rate equation?

A

rate=k(A)^x(B)^y

mole/Ls=k(mol/L)^x*(mole/L)^y

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43
Q

what is the equation for a zero order reaction?
first order?

second order?

mixed order?

A

rate=k(A)^0*(B)^0)=k

rate=k(A)^1 or rate=k(B)^1
with rate=-Δ(A)/Δt=kA and the At=(A0)e^-kt

rate=k(A)^1(B)^1 or rate=k(A)^0(B)^2=kB^2 or rate=k(A)^2*(B)^0=kA^2

rate=(k1(E)(A^2))/(k2+k3(A))

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44
Q

What is the rate of a reaction when there is an energy barrier given the requirement of activation energy?

A

rate=fZ

Z is the total number of collisions occurring per second, f is the fraction of collisions that are effective

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45
Q

how is the equilibrium constant found? What is the law of mass action?

A

kf/kr=(B)(C)/(A) where kf and kr are constants and can in turn be used to find kc, kr/kr=Kc=Keq

keq=Kc=(k^1k^2k^3)/(k^-1k^-2k^-3)=((C)^c(D)^d)/((A)^a(B)^b)
units of concentration are mol/L

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46
Q

What is the equation for the reaction quotient?

In what instances is the reaction quotient different than the equilibrium constant and what does it suggest?

A

Qc==((C)^c(D)^d)/((A)^a(B)^b)

  • Qc < Keq, Δ G < 0, reaction proceeds in forward direction
  • Qc = Keq, Δ G = 0, reaction is in dynamic equilibrium
  • Qc > Keq, Δ G > 0, reaction proceeds in reverse direction
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47
Q

What is the equation for internal energy?

A

ΔU=Q-W

change in the total internal energy (Δ U) of a system is equal to the amount of heat (thermal energy) transferred (Q) to the system minus the amount of work (W) all in joules

no heat exchanged means
Δ Usystem + Δ Usurroundings = Δ Ucalorimeter = Qcalorimeter− Wcalorimeter = 0.

no work done so qsystem = − qsurroundings, and msteelcsteelΔ T + moxygencoxygenΔ T = − mwatercwaterΔ T.

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48
Q

What is the equation for specific heat?

A

q=mcΔT
J=(g)(J/G*K)(K)

where q is the heat absorbed or released, m is the mass, c is the specific heat, and T is the change in temperature

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49
Q

What is the equation for enthalpy change?

A

ΔH=Hproducts-Hreactants

J=J-J

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50
Q

What is the bond dissociation energy equation?

A

ΔH=ΣΔHbonds broken+ΣΔHbonds formed= total energy absorbed-total energy released

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51
Q

What is the equation to find the change in entropy of a reaction?

A

ΔS=Qrev/T

where Qrev is the heat that is gained or lost in the reversible process

kJ/molK

ΔSorxn=ΣΔSoproducts-ΣΔSoreactants

ΔS=ΔSfinal-ΔSinitial

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52
Q

What is the equation for the total change in entropy of the universe?

A

ΔSuniverse=ΔSsystem+ΔSsurroundings>0

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53
Q

What is the equation for Gibbs free energy?

A

ΔG=ΔH-TΔS

J/moll=(J/mol)-(K)(J/molK)

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54
Q

What is the standard gibbs free energy equation of a reaction?

A

ΔGorxn=Σ(ΔGoproducts)-Σ(ΔGoreactants)

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55
Q

What is the equation for the standard gibbs free energy of a particular reaction?

A

ΔGo=-RTlnKeq

J/mol=(J/molK)(K)(dimensionless)

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56
Q

What is the equation for the gibbs free energy of a particular reaction?

A

ΔG=ΔGo+RTlnQ

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57
Q

Wat is the gibes function of the gas-solid equilibrium?

A

ΔG=G(g)-G(s)

G(g)=G(s) because the change in gibbs free energy must be equal to zero in the phase equilibria

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58
Q

What is the equation for vapor pressure depression?

A

ΔP=PAo-PA

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59
Q

What is Raoult’s law?

A

ΔPA=XAPAo
XA is the mole fraction of the solute
atm=atm

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60
Q

What is the equation of the boiling point elevation?

A

ΔTb=iKbm

where i is the cant hoff factor or the moles of particles dissolved into a solution per mole of solute molecule, and Kb is a proportionally constant characteristic of a particular solvent m is the molality o the solution (molalilty=moles of solute/kg of solvent)

K=(K/molal)(molal)

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61
Q

What is the equation for freezing point depression?

A

ΔTb=iKfm

where i is the cant hoff factor or the moles of particles dissolved into a solution per mole of solute molecule, and Kf is a proportionally constant characteristic of a particular solvent m is the molality o the solution (molalilty=moles of solute/kg of solvent)

K=(K/molal)(molal)

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62
Q

What is the equation for osmotic pressure?

A

Π=iMRT

, defined as the osmotic pressure (Π ) where M is the molarity of the solution, R is the ideal gas constant, T is the absolute temperature (in Kelvin), and i is the van’t Hoff factor.

atm=(L/mol)(Latm/molK)(K)

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63
Q

What is the equation for dilutions?

A

M1V1=M2V2

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64
Q

What is the equation for solution equilibria?

A

Ksp=(A^n+)^M(B^m-)^n

by the reaction AmBn to mA^n+ + B^m-

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65
Q

What i the equation and units for I.P.?

A

I.P.=(A^n+)^M(B^m-)^n

mol/L

Ion product analogous to Q compared to Ksp in determining the behavior of the solution when not in equilibrium

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66
Q

What is the equation for finding the pH of a solution?

A

pH=-log(H+)=log(1/(H+))

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67
Q

What is the equation for finding the pOH of a solution?

A

pOH=-log(OH-)=log(1/(OH-))

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68
Q

What is the additive effects of the pHs

A

pH+pOH=14

pH=14-pOH=14-(-log(OH-)=14+log(1)=14+0=14

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69
Q

What is the equilibrium equation for hydrogen and hydroxide concentrations?

A

Ksp=(H3O+)(OH-)

Kn=(H3O+)(A-)/(HA)

or Kb=(B+)(OH-)//(BOH)

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70
Q

What equation is used to find the volume and normality when things are titrated?

A

NaVa=NbVb

Na and Nb are the normalities of the acid and base respectively

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71
Q

How can pKa and pKb be found?

A

pH=pKa+log(conj base/weak acid)

pOH=pKb+log(conj acid/weak base)

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72
Q

What is the equation for standard reduction potentials or standard electromotive force emf?

A

emfo=Eocell-Eoanode=Eored+Eooxid

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73
Q

What is the change in gibbs free energy of redox reactions?

A

ΔGo=-nFEocell=-RTlnK

or the change in chemical potential of a reaction, or the change in the amount of energy available in a chemical system to do work. n is the number of moles of electrons exchanged, F is faraday’s constants, and Ecell is the Emf of the cell

ΔG=-nFEcell

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74
Q

What is the equation to find the Ecell?

A

Ecell=Eocell-(RT/nF)lnQ

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75
Q

What equation is used to multiple vectors?

A

B=nA, when a vector A is multiple by a scalar value n, it produces a new vector B

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76
Q

What is the equation for velocity?

A

v=Δx/Δt

m/s

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77
Q

What is the equation for acceleration?

A

a=Δv/Δt

m/s^2

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78
Q

What is the gravitational equation?

A

F=(Gm1m2)/r^2

G=6.67384×10^-11 m^3 kg^-1 s^-2

N=((Nm^2/kg^2)(kg)(kg))/(m^2)

79
Q

What is the equation for torque?

A

t=rfsinθ

Nm=(m)(N)

80
Q

What is the equation for centripetal force and acceleration?

A

F=(mv^2)/r
N=(kg(m/s)^2)/m

a=(v^2)/r

81
Q

What is the equation for frictional force?

A

Fk=μkFn
Fs=μsFn

N=N

0<μs/kFn

82
Q

What is the equation for mechanical energy?

A

W=ΔE=ΔU+ΔK=

83
Q

What is the rule of conservation of mechanical energy?

A

E=U+K

84
Q

What is the equation for work?

A

W=Fdcosθ

J=Nm

85
Q

What is the equation for power?

A

P=W/t

Watt=J/s

86
Q

What is the work-energy theorem?

A

Wtot=ΔK=Kf-Ki

J

87
Q

What is the equation for momentum?

A

p=mv

kg*m/s

88
Q

What is the equation for impulse?

A

I=FΔt=Δp=mvf-mvi

kg*m/s=Ns=(kgm/s^2)(s)

89
Q

What is the conservation of kinetic energy present in completely elastic collision?

A

1/2mavai^2+1/2mbvbi^2=1/2mavaf^2+1/2mbvbf^2

90
Q

What is the conservation of momentum equation?

A

mavai+mbvbi=mavaf+mbvbf

91
Q

What is the equation for completely inelastic collisions?

A

mavai+mbvbi=(ma+mb)vf

92
Q

What is mechanical advantage?

A

mech adv=Fout/Fin

93
Q

What is the equation for efficiency of machines?

A

Efficiency=Wout/Win=(load(load distance))/((effort)(effort distance))

94
Q

What is the center of mass?

A

X=(m1x1+m2x2+m3x3+…)/(m1+m2+m3+…)

m=kgm/kg

95
Q

What is the equation to find the temperature in celsius?

A

Tc=Tk-273

96
Q

What is the equation for the conversion of temperature in celsius to farenheit?

A

Tf=9/5Tc+32

97
Q

What is the equation for thermal expansion of a solid given its length?

A

ΔL=αLΔT

m=(K^-1)mK

98
Q

What is the equation for the thermal expansion of liquids and its volume?

A

ΔV=βVΔT

where β=3α

m^3=(k^-1)(m^3)K

99
Q

What is the calorie conversion to joules?

A

1 Cal=10^3cal=3.97Btu=4,184J

100
Q

What equation is used during a phase change?

A

cannot use Q=mcΔT, no change in temperature
Q=mL
where Q is the amount of heat gained or lost, m is the mass of the substance, and L is the heat of transformation of the substance.

101
Q

What is the equation to find the force on a piston?

A

F=PA

where F is force, P is pressure, and A is area

102
Q

What is the equation for work given the pressure and volume?

A

W=PΔV

J=(Pa)(m^3)=(N/m)(m^3)

103
Q

What are the equations used to find the areas under the pressure volume curve to find work?

A

A2=P2ΔV

A1=(1/2)is ΔVΔP

W=A1+A2

104
Q

What is the equation for an adiabatic process?
constant volume?
Closed cycle?

A

Q=0 ΔU=-W

W=0 ΔU=-Q

ΔU=0 Q=W

105
Q

What is the equation for entropy in terms of physics?

A

ΔS=Q/T=L(m/T)

where L is the latent heat (either heat of fusion or heat of vaporization), m is mass, and T is the constant temperature of the system and environment in Kelvin.

106
Q

What is Coloumb’s law?

A

F=(kq1q1)/(r^2)

k=8.99x10^9 (Nm^2)/C^2

107
Q

What is the equation to describe the force exerted from an electric field?

A

F=q0E
or E=F/q0=kq/r^2

N/C=((N/m^2)/C^2)(C)/m^2

When a test charge (q0) is placed in an electric field (E), it will experience an electrostatic force (F) equal to q0E. where E is the electric field magnitude, F is the force felt by the test charge qo, k is the electrostatic constant k=1/4πε0=8.99x10^9Nm^2/C^2, ε0=8.85x10^-12C^2/Nm^2, q is the source charge magnitude, and r is the distance between the charges.

With the total electric field equal to Etotal=Eq1+Eq2+…+

N/C

108
Q

What is the equation for electrical potential energy? what is the force exerted by this energy?

A

U=kqQ/r

J=Nm=(((NM^2)/C^2)(C)(C))/m

F=kqQ/r^2

found from U=W=Fd=Fr=(k(qQ/r^2))(r)

109
Q

What is the equation for electric potential concerning work?

A

V=W/q

Vb-Va=Wab/q0

V=kQ/r
V=kq/r1-kq/r2=kq((r2-r1)/r1r2)

with the total electric potential equal to Vtotal=Vq1+VqVq3

110
Q

What is the equation for electric dipole moments and electric potentials?

A

V=((kp)/(r^2))cosθ

where p is the magnitude of the dipole moment, p=qd or charge times distance, E is the magnitude of the uniform external electric field, theta is the angle the dipole moment makes with the electric field

111
Q

What is the equation for torque created from the rotational causation of the difference in electric potential?

A

τ=F(d/2)sinθ+F(d/2)sinθ=kq/r1-kq/r2=Fdsinθ=qEdsinθ=pEsinθ

112
Q

What is the equation for current?

A

I=Δq/Δt

A=C/s

113
Q

What is the equation to find the magnetic field strength of an infinitely long current carrying wire?

A

B=μ0i/2r

T=((Tm/A)(A))/m

114
Q

What is the equation to find the magnetic field strength of a circular loop of current carrying wire?

A

B=μ0i/2πr

T=((Tm/A)(A))/m

115
Q

What is the equation for the magnetic force on a moving charge?

A

F=qvBsinθ

where q is the charge (including the sign of the charge), v is the velocity of the charge, B is the magnitude of the magnetic field, and θ is the smallest angle between the vector qv and the magnetic field vector B.

N=(C)(m/s)(T)=(C)(m/s)(Ns/mC)

116
Q

What is the force on a current carrying wire?

and its relation to the force on a magnetic field.

A

F=ILBsinθ

F=(Δq/Δt)LBsinθ=Δq(L/Δt)Bsin=qvbsinθ

F=qvB=(mv^2)/r

117
Q

What is the equational relation of the electric field and radii?

A

r=mv/qB

B=mv/qr

v=qrB/m

118
Q

What is the characteristic equation that determines the resistance of a resistor?

A

R=ρL/A

The number that characterizes the intrinsic resistance to current flow in a material is called the resistivity (ρ ), for which the SI unit is the ohm-meter (Ω · m). Resistivity is the proportionality constant that relates a conductor’s resistance (R) to the ratio of its cross-sectional area (A) to the length of the resistor (L).

Ω=(Ω · m)(m)/m^2

119
Q

What is Ohm’s Law?

A

V=IR

V=AΩ

J/C=(C/s)(Js/C^2)

120
Q

Wht is the equation for the electromotive force and the electric potential?

A

V=Ecell-IRint

V=V-(A)(Ω)

121
Q

What is the equation for power?

A

P=E/Δt

122
Q

What is the equation for power in circuits?

A

P=IV=I^2R=(V^2)/R

J/s=(C/s)(J/C)=(C/s)^2(Js/C^2)=(J/C)^2/(Js/C^2)

123
Q

what is the equation for resistance in a series circuit?

A

Rtot=R1+R2+R3+…

124
Q

what is the equation for capacitance in a series circuit?

A

1/Ctot=1/C1+1/C2+…

125
Q

what is the equation for

voltage in a series circuit?

A

Vtot=V1+V2+V3+…

126
Q

what is the equation for resistance in a parallel circuit?

A

1/Rtot=1/R1+1/R2+…

127
Q

what is the equation for capacitance in a parallel circuit?

A

Ctot=C1+C2+…

128
Q

what is the equation for voltage in a parallel circuit?

A

Vtot=V1=V2=V3=…

129
Q

How is capacitance calculated?

How can you determine the capacitance of a parallel plate capacitor?

A

C=Q/V
F=C/V

C=ε0(A/d)
F=(F/m)(m^2/m)

130
Q

How do you determine the electric field at a point in space between the plates of a parallel plate capacitor?

A

E=V/d

N/C=V/m=(Nm/C)/m

131
Q

What is the equation for the potential energy stored in a capacitor?

A

U=1/2C(V^2)

J=(F)(V^2)=(C/V)(J/C)^2=(C/(J/C))(J^2/C^2)

132
Q

What is the equation for the capacitance in dielectric materials?

A

C’=KC where K is the dielectric constant or a measure of the insulation of the particular dielectric material.

133
Q

what is the equation for alternating current?

A

i=Imaxsin(2πft)=Imaxsinωt)

the current flows in the opposite direction. where i is the instantaneous current at the time t, Imax is the maximum current, f is the frequency, and ω is the angular frequency ( ω = 2π f).

134
Q

What is the equation for RMS current?

A

Irms=Imax/√2

135
Q

What is the equation for RMS voltage?

A

Vrms=Vmax/√2

136
Q

What is the angular frequency of a spring?

A

(ω = 2π f = π /T, where T is the period, ,1/f the time to complete one cycle), and t is time.

rad/s=rad(1/s)(hz)

ω = √k/m

rad=√((kg/s^2)/kg)

137
Q

What is the restoring force?

A

F=-kx

N=(N/m)m
kgm/s^2=(kg/s^2)(m)

138
Q

What is the equation for displacement?

A

x=Xcos(ωt)

139
Q

What is the potential energy of a spring?

A

U=1/2kx^2

J=kgm/s^2=)kg/ms^2)(m^2)

140
Q

What is the equation for energy in relation to kinetic energy and potential energy?

A

E=K+U=constant

U=mgh

141
Q

What is the equation for angular frequency for a pendulum?

A

ω=2πf=√(g/L)=2π/T

142
Q

What is the force of a pendulum?

A

F=-mgsinθ

143
Q

What is the equation for the force constant k for a mass-spring?

A

spring constant k

144
Q

What is the equation for the force constant k for a simple pendulum?

A

mg/L

145
Q

What is the equation for the period T of a mass-spring?

A

2π√(m/k)

146
Q

What is the equation for the period T of a simple pendulum?

A

2π√(L/g)

147
Q

What is the angular frequency of a mass spring?

A

√(k/m)

148
Q

What is the angular frequency of a simple pendulum?

A

√(g/L)

149
Q

What is the frequency f of a mass-spring and simple pendulum?

A

1/T or ω/2π

150
Q

What is the kinetic energy, K of a mass-spring and simple pendulum?

A

1/2mv^2

151
Q

What is the maximum kinetic energy of mass-spring and simple pendulum?

A

x=0 and θ=0 vertical position

152
Q

What is the equation for potential energy for the mass-spring?

A

1/2kx^2

153
Q

What is the equation for potential energy for the simple pendulum?

A

mgh

154
Q

What is the potential energy maximum and max acceleration for the mass-spring and simple pendulum?

A

x=±X or

a max value of θ

155
Q

What is the equation of the displacement of a particle in a wave?

A

y=Y sin(kx-ωt)

displacement y of a particle in a wave may be plotted at each point x along the direction of the wave’s motion. Y is the amplitude (maximum displacement), k is the wavenumber, ω is the angular frequency, and t is the time. the displacement of a spring at time t.

156
Q

What is the equation for the speed of a wave?

A

v=fλ

m/s=(1/s)m

157
Q

What is the velocity of a wave?

A

v=fλ=w/k=λ/T

158
Q

What is the equation for intensity?

A

I=P/A

W/m^2=(J/s)/m^2

159
Q

What is the equation for sound level?

A

β=10 log (I/Io)

Btot=BE+10 log (If/Ii)

sound waves of the same amplitude and frequency that have traveled 1 meter from their source. sound level (β ), measured in decibels (dB). where Io is a reference intensity set at the threshold of hearing, 1 × 10− W/m2. When the intensity of a sound is changed by some factor

160
Q

What is the frequency of a beat?

A

fbeat=(f1-f2)

161
Q

What is the equation for the perceived frequency from the doppler effect?

A

f’=f((v±vo)/(v±vs))

162
Q

What is the wavelength of open pipes?

A

λ/2, 2λ/2, 3λ/2

λ=2L/n

163
Q

What is the frequency of open pipes?

A

f=v/λ, f=nv/2L

164
Q

What is the wavelength and frequency of closed pipes?

A

λ=4L/n

f=nv/4L

165
Q

What is the equation for density?

A

ρ=m/v

kg/m^3

g/mL

166
Q

What is the equation for work and density in relation?

A

W=mg

m=ρV

W=ρVg

167
Q

What is the equation for pressure?

A

P=F/A

Pa=N/m^2

168
Q

What is absolute pressure?

A

P=Po+ρgh

N/m^2=N/m^2+(g/m^3)(m/s^2)m

PB=P-Patm+(Po+ρgh)-Patm

169
Q

What is Pascal’s principle?

A

P=F1/A1=F2/A2

170
Q

What is the buoyant force?

A

Fbuoy=(Vfluiddisplaced)(ρfluid)(g)=weight of object

Fbuoy=(Vobjectsubmerged)(ρfluid)(g)

N=kgm/s^2=(m^3)(kg/m^3)(m/s^2)

171
Q

What is the equation for work in the case of a hydraulic lift?

A

W=PΔV=F1d1=F2d2

172
Q

What is the equation for critical velocity?

A

vε=(Nεη)/(ρD)

m/s=((N*s)/(m^2))/((kg/m^3)(m))

173
Q

What is the equation of young’s modulus?

A

ϒ=(F/A)/(ΔL/L)

174
Q

What is the equation for shear modulus?

A

S=(F/A)/(x/h)

175
Q

What is the equation for Bulk modulus?

A

B=(F/A)/(ΔV/V)

176
Q

What are the Em sperctums and what do they describe?

A

EM spectrum term described the full range of frequency and wavelength of electromagnetic waves. following units are often used when quoting wavelengths: 1 mm = 10− 3 m, 1 μ m = 10− 6 m, 1 nm = 10− 9 m, and 1 Å (angstrom) = 10^− 10 m. The full spectrum is broken up into many regions, which in descending order of wavelength are radio (109 m− 1 m), microwave (1 m− 1 mm), infrared (1 mm− 700 nm), visible light (700 nm− 400 nm), ultraviolet (400 nm− 50 nm), x-ray (50 nm− 10− 2 nm), and gamma rays (less than 10^− 2 nm). Electromagnetic waves vary in frequency and wavelength, but in a vacuum, all electromagnetic waves travel at the same speed, called the speed of light. This constant is represented by c and is approximately 3 × 10^8 m/s. electromagnetic waves also travel in air with this velocity. In reference to electromagnetic waves, the familiar equation v = fλ. where c is the speed of light in a vacuum and, to a first approximation, also in air.

177
Q

What is the focal length of a mirror?

A

f=r/2

178
Q

What is the mirror equation?

A

(1/o+1/i)=(1/f)=(2/r)

the o, object is positive when the object is in front of the mirror (R side), the o is negative when the object is behind the mirror (V side)

the i is positive or the image is in front of the mirror (R side), the negative i the image is behind the mirror (V side)

where r is the positive or a concave mirror, where r is negative meaning a convex mirror

where f is the positive and indicates a concave mirror, and negative means convex mirror.

where m the magnification is positive the image is upright or erect, the magnification is negative or the image is inverted

179
Q

What is the equation for magnification?

A

m=-i/o

180
Q

What is snell’s law? the law of refraction?

A

n1sinθ1=n2sinθ2

181
Q

What is the equation for total internal reflection?

A

n1sinθ1=n2sin90=n2sinθc=n2/n1

or 1/f(n-1)(1/r1-1/r2)

182
Q

What is the equation for the diffraction grating?

A

asinθ=nλ n=1,2,3,…

183
Q

What is the maxima of a black body radiation?

what is the minima?

A

dsinθ=mλ m=-0,1,2

dsinθ=(m+1/2)λ

184
Q

What is the stefan-boltzmann law?

A

Et=σT^4

W/m^2=(J/(sm^2K^4))(K^4)

185
Q

What is the max kinetic energy?

A

Kmax=hf-W

J=(Js)(S^-1)-J

where work W=hft

186
Q

What is the equation for the energy levels?

A

En=-13.6eV/n^2
eV=eV

or E=-RH/n^2
J=J

where ΔE=Ef-Ei

187
Q

What is the equation for mass and energy?

A

E=mc^2

J=kg(m/s)

188
Q

What is the equation for alpha decay?

A

Zdaughter=Zparent-2

Adaughter=Aparent-4

where A is the mass number, and Z is the atomic number

189
Q

What is the equation for beta decay?

A

azX=az+1Y+β-
Zdaughter=Zparent+1
Adaughter=Aparent

azX=az-1Y+β+
Zdaughter=Zparent-1
Adaughter=Aparent

190
Q

What is the equation for gamma decay?

A

Zparent=Zdaughter

Aparent=Adaughter

191
Q

What is the equation for exponential decay?

A

Δn/Δt= -λn

or

ln(n)=ln(no)e^-λt

λ(s^-1) and t (s)

192
Q

What is the equation for the wavelength of radioactive decay half-life?

A

λ=ln2/T1/2=.693/T1/22

193
Q

What are the units for tesla?

A

1T=Ns/mC

MCAT (6 decks)

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