Chemical and Physical Foundations Flashcards
Units
Physical quantity, base units, symbol
lengyh
mass
time
electric current
temperature
frequency
sound intensity
length–> metre–> m
mass–> kilogram–> kg
time–> Second–> s
electric current–> Ampere–> A
magnetic field–> Tesla–> B
temperature–> Kelvin–> K
frequency–> Hertz–> Hz
sound intensity–> decibel–> dB
wehn your equation has a constant (gravitational constant, planck’s constant, etc) this is an indication that you must use ___ units
SI
Prefixes
prefix, symbol, order of magnitude
nano
micro
milli
centi
kilo
mega
giga
nano–> n–> 10^-9
micro–> μ–> 10^-6
milli–> m–> 10^-3
centi–> c –> 10^-2
kilo–> k–> 10^3
mega–> M–> 10^6
giga–>G –> 10^9
angstrom (Å), unit of length, equal to:
1x10^-10 or 0.1nm (nanometer)
to convert from km/h to m/s _______ by 3.6
divide
to convert from m/s into km/h ______ by 3.6
multiply
The speed of light is
c = fλ relates the speed of light (c), its frequency (f), and its wavelength (λ)
for scientific notation, making the coefficient a bigger number means the exponent must get
smaller (or more negative)
when adding or subtracting scientific notiation, you want coefficients to have the ___ exponent
for multiplying in scientific notation, we ___ exponents and ___ the coefficients
to divide in scientific notation, we ___ exponents and ___ the coefficients
same
add, multiply
subtract, divide
for scientific notation, making the coefficient a smaller number means the exponent must get
bigger (or more positive)
how do you round intermediate calculations?
one up and one down
ex: 8.9x11.1=9x11=99=100
then for the next calculation, round down: 100x1.14=114=110
with fractions, try to round the numerator and denominator in the ___ direction to maintain consistency and why
same
this consistency will be important for fractions, because differences in the direction of rounding can be compounded in fractions. if you round one up and the other down, you’ve done 2 manipulations to make the final answer larger.
ex: 118/9.81=120/10=12 (real answer is 12.03)
how do you multiply and divide fractions
with fraction multiplication, you multiply the numerators and the denominators
when we divide fractions, we multiply by the inverse: (2/4)/(5/6)=(2/4)x(6/5)=(12/20=(3/5)
converting between logarithmic and exponential form
loga(c)=b
a^b=c
when logs have no specified base (a is not written), the assumption is log base 10
what do you do when the term inside the logarithmic function has an exponent
the exponent can be pulled out to become the coefficient
ex: log(10^3)= 3log(10)
how to add logs
combine the terms by multiplying them
log(a)+log(b)=log(axb)
how to subtract logs
combine the terms by dividing them
log(a)-log(b)=log(a/b)
when the number inside the lpg is 1x10^n, the log of that number is
n
general approach to logarithmic estimation
Look at which exponents our number lies between
determine which of those two numbers our value is closer to
make an educated guess as to the approximate value
figure out which two logs your number is between and then figure out which of the two exponent numbers is closer to the original number and then pick the answer closest to that number
ex: -log(3.0x10^-4)
3.0x10^-4 is a number between 1.0x10^-4 and 10x10^-4 (1.0x10^-3)
Therefore, the answer must be between 3 and 4
Since 3.0x10^-4, the answer must be closer to 4, so pick the answer closer to 4
scalar quantities
only have magnitude, but no direction
these quantities describe motion, but do not take into account movement on a grid
relevant examples: speed, work, pressure, energy, mass, etc
vector quantities
have a magnitude and a direction
vectors take into account the 2 or 3 dimensional space (for the MCAT, it will be 2 dimensional) for the direction of motion
generally speaking, we must separate the x and y components and treat them separately
relevant examples: displacement, velocity, force, weight, etc
vector components are based off:
right angle triangles and SOH CAH TOA
SOH CAH TOA
sin(θ)=O/H
cos(θ)=A/H
tan(θ)=O/A
to combine the vector components to get the resultant vector, we employ the
pythagorean theorem
C^2=A^2+B^2
H^2=A^2+O^2
vector addition (highly unlikely to be tested explicitly on the MCAT)
Vector addition is simply connecting two vectors tip to tail, and the resultant vector is simply the line that connects the starting point and the end point
vector subtraction (highly unlikely to be tested explicitly on the MCAT)
all you’re doing with vector subtraction is adding the negative version of the second vector
in other words, A-B is equivalent to A+(-B)
with vectors, the negative version is simply a vector pointing in the opposite direction
sin and cos 90
sin(90)=1
cos(90)=0
sin and cos 0
sin(0)=0
cos(0)=1
sin and cos 30
sin(30)= 1/2= 0.5
cos(30)= √3/2= 0.866= 0.9
sin and cos 60
sin(60)= √3/2= 0.866=0.9
cos(60)= 1/2= 0.5
relevant trigonometric identities to remember
tan(θ)= sin(θ)/cos(θ)
slope
rise/run= Δy/Δx = units of y/units of x
area under the graph
regardless of the shape, the area can be simplified to bsexheight
equates to (units of x) multiplied by (units of y)
basic motion graphs: displacement vs time
y axis: has a unit of m
x axis: has a unit of s
the slope=m/s
slope represents velocity
the area under the graph: (units of x) x (units of y) = (m)(s)
nothing recognizable, so likely not relevant
basic motion graphs: velocity vs time
y axis: has a unit of m/s
x axis: has a unit of s
the slope: m/s^2
the slope represents acceleration
the area under the graph: (units of x)(units of y) = (m/s)x(s)= m
the area represents the change in displacement
basic motion graphs: acceleration vs time
y axis: has a unit of m/s^2
x axis: has a unit of s
the slope: m/s^3
nothing recognizable, so likely not relevant
the area under the graph: (units of x)(units of y) = (m/s^2)x(s) = m/s
area represents the change in velocity
what is a force
a force is something that pushes or pulls an object. to be more specific, a force will change the acceleration of an object
if acceleration and velocity are in the same direction, the object will _______
if acceleration and velocity are in opposite directions, the object will _______
if an object changes direction due to the acceleration, although its velocity may momentarily be 0, the acceleration is ______
speed up
slow down
constant
constructing a free body diagram
define your system and draw all the relevant sources
is there an applied force? if so, include it
is there gravity? chances are… yes!
does it make contact with another surface? if so, there is a normal force perpendicular to the point of contact
is there friction? if so, frictional force will oppose motion (be pointed in the opposite direction of velocity or the direction the object will want to move)
Any other special situations? (attached rope for tension force, magnetic or electric forces acting at a distance, thrust, etc)
newton’s first law (the law of inertia)
an object in motion will stay in motion unless acted upon by an outside force
a force will impart acceleration to the object causing it to speed up or slow down
lacking that external force, an object will have 0 net acceleration. two scenarios under which the acceleration will be zero:
—constant velocity (Δv=0)
—at rest (v=0)
newton’s second law
the force acting on an object is directly proportional to the mass of the object and the acceleration produced
F = ma, where F (force) and a (acceleration) are both vector quantities
this law describes the relationship between force, mass, and acceleration.
if you apply a force to an object, the object will accelerate.
the amount of acceleration depends on the force applied and the mass of the object
—for example: if you push a lightweight object with the same amount of force as a heavier object, the lightweight object will accelerate more because it has less mass
newton’s third law
for every action, there is an equal and opposite reaction
F_AB = -F_BA
or
F_AonB=F_BonA
this law is all about balance, which is a recurring theme in physics
the fundamental tenet of thermodynamics is that energy cannot be created or destroyed, simply changed from one form to another
this ensures that total energy within the universe is unchanged
in essence, all energy is balanced and this is where action-reaction pair forces stem from
in order for a pair of forces to qualify as action-reaction pair forces they must:
1. be equal in magnitude
2. be opposite in direction
3. be the same type of force
