PHYSICS FINAL REVIEW Flashcards
M, k, d, c, m, u, n, p prefixes
Mega, kilo, deci, centi, milli, micro, nano, pico
10^6, 10^3, 10^-1, 10^-2, 10^-3, 10^-6, 10^-9, 10^-12
Sin 0, 30, 45, 60, 90
Sin 0 = 0 Sin 30 = .5 Sin 45 = .7 Sin 60 = .9 Sin 90 = 1
Cos 0, 30, 45, 60, 90
Cos 0 = 1 Cos 30 = .9 Cos 45 = . 7 Cos 60 = .5 Cos 90 = .0
Tan 0, 30, 45, 60, 90
Tan 0 = 0 Tan 30 = .5 Tan 45 = 1 Tan 60 = 2 Tan 90 = undefined
velocity equation
average velocity ⊽= Δx/Δt
Δx = displacement, Δt = change in time
does not account for distance traveled
speed equation
average speed: v= distance/time
accounts for distance traveled
velocity vs speed
speed is a scalar quality, the rate at which an object covers distance; velocity is a vector quality, and the rate at which the position changes
Gravitational force equation
F = GMm / r^2
G= gravitational constant, M= mass 1, m= mass 2, r=distance between center of mass
pay attention to the relationship between r and force
as r doubles, force is divided by four
SI Units
Density Force Pressure Temperature Energy Power Charge Potential Current Resistance Magnetic Field
Density = kg/m^3 Force = N Pressure = Pa Temperature = K Energy = J Power = W Charge = C Potential = V Current = A Resistance = Ohm Magnetic field = Tesla
static friction and kinetic friction equations and application
static friction: fS MAX = ukN
stationary objects
- can experience the minimum static force (0) if the object is resting on a surface with no applied force
- when static friction is overwhelmed the object will move
kinetic friction: fK = ukN sliding objects (sleds, not tires)
Weight equation
Fg (weight) = mg
Acceleration equation
average acceleration
Δv/Δt
- change in velocity over time
- the value of speed/velocity, distance/displacement are interchangeable in this case
Newton’s first law equation
FNET = ma = 0
A body will remain in its motion unless a net force acts upon it
law of inertia
Newton’s second law equation
FNET = ma
Force is equal to change in momentum per change in time
Newton’s third law equation
FAB = -FBA
For every action there is an equal and opposite reaction
Linear motion equations (velocity, displacement, acceleration, and time)
V = V0 + at
final velocity = initial velocity + acceleration*time
x = V0t + 1/2at^2 displacement = initial velocity(time) + 1/2acceleration*time^2
v^2 = v0^2 + 2ax velocity^2 = initial velocity^2 + 2ax
x = vt displacement = average velocity * time
How to analyze projectile motion
analyze the vertical and horizontal values separately
vy will change at the rate of gravity as acceleration
vx will not change
Inclined planes, Force of gravity parallel to plane and perpendicular to plane
Fg (parallel to plane) = mgsinፀ
Fg (perpendicular to plane) = mgcosፀ
Circular motion equation
Fc= mv^2/r
centripetal force = mass * velocity^2 / radius
acceleration is therefore v^2/r
How to draw free body diagrams
make sure to draw for any calculation on forces
What is translational equilibrium
when the vector sum of all the forces acting on an object is zero
constant speed and constant direction, zero acceleration
What is rotational equilibrium
when the vector sum of all the torques acting on an object is zero
constant angular velocity (probably zero)
Equation for kinetic energy
K = ½ mv^2
units of Joules (like all energy)
Equation for gravitational potential energy
U= mgh
Equation for elastic potential energy
U=1/2kx^2
x is the magnitude of displacement from equilibrium
Equation for total mechanical energy
E = U + K
- energy is never created or destroyed, merely transformed
- this equation does not account for thermal energy so E can decrease
What are the conservative forces and what does that mean
Conservative forces are those that are path independent and that do not dissipate energy, △E = △U + △K = 0
Gravitational, Electrostatic, and Elastic
If the change in energy around any round-trip path is zero, or if the change in energy is equal despite taking any path between two points, then the force is conservative
What are nonconservative forces
Nonconservative forces are when total mechanical energy is not conserved
Wnonconservative = △E = △U + △K
Wnonconservative is the work done by the nonconservative forces only
Work equation for displacement vectors
Work is a form of energy. The transfer of energy by work or heat is the only way by which anything occurs
W = Fdcosθ
θ is the angle between the applied force vector and the displacement vector
Work equation for change in volume with constant pressure
Work is a form of energy. The transfer of energy by work or heat is the only way by which anything occurs
W = P△V for change in volume with constant pressure
if volume stays constant no work is done
Power equation
P = W/t = △E/t
unit is the watt, which is a J/s
Work equation for energy change
Work-energy theorem
Work equals change in kinetic energy
Wnet = △K = KEf - KEi
Mechanical advantage
Mechanical advantage = Forceout/Forcein
deals with forces
Efficiency equation
Efficiency = Workout/Workin
deals with work
=load(load distance) / effort(effort distance)
Zeroth law of thermodynamics
if A is in thermal equilibrium with B and C is in thermal equilibrium with C, A is in thermal equilibrium with C
Converting between temperature equation
F = 9/5C + 32
heat vs temperature
heat is the transfer of thermal energy between systems as a result of different temperatures
thermal expansion equations for length and volume
△L = αL△T
Change in length = (coefficient of thermal expansion)(Original length)(Temperature change in Celsius)
for liquids: △V = βV△T
beta is coefficient of volumetric expansion
Types of systems
Isolated systems
not capable of exchanging energy or matter with their surroundings
Closed systems
capable of exchanging energy, but not matter, with the surroundings
Open systems
can exchange both matter and energy with the environment
State functions
thermodynamic properties that are independent of the path taken to get to a particular equilibrium state
Pressure, density, temperature(not heat), volume, enthalpy, internal energy, gibbs free energy, entropy
Process functions on the other hand describe the path taken to get from one state to another
First law of thermodynamics
△U = Q - W
change in system’s internal energy = energy transferred as heat - work done by the system
change in internal energy = temperature
+q = heat into system
+w = work done by the system (expansion)
Three methods of heat transfer
Conduction is direct transfer of heat through molecular collisions
Convection is transfer of heat by the physical motion of a fluid over a material
Radiation is the transfer of energy by electromagnetic waves
Specific heat equation
q=mc△T
Cal to cal to J to BTU equation
1 Cal = 10^3 cal = 4200 J = 4 BTU
Heat of transformation equation
q=mL
L is latent heat
Types of thermodynamic processes
Isothermal - constant temperature
no change in internal energy
Adiabatic - no heat exchange
Isobaric - constant pressure
Isovolumetric (isochoric) - no volume change
Second law of thermodynamics
objects in thermal contact but not thermal equilibrium will transfer heat from higher temperature to lower temperature
-Isolated systems go towards higher entropy
Entropy equation
entropy is the heat gained or lost in a reversible process divided by the temperature in kelvin
△S = Qrev/T
when energy is distributed into a system at a steady temperature, entropy increases
Restating the second law in an equation
△Suniverse = △Ssystem + △Ssurroundings > 0
simple density equation, density of water (which unit is 1000?)
p = m/V
density =mass/volume
density of water = 1g/cm^3 or 1000kg/l^3
Finding the density of a fluid from weight and volume, or vice versa
Fg(weight) = pVg
Weight = density * volume * gravity
(F=ma with m = density*volume)
Specific gravity
Specific gravity is a unitless ratio of density/density of water
Ex: 877kg/m^3 =.877 specific gravity
Simple pressure equation
P = F/A
Absolute pressure and equation
Absolute pressure (hydrostatic) is the total pressure exerted on an object that is submerged in fluid (both liquid and gas)
P = p0 + pgh
P is absolute pressure, P0 is incident or ambient pressure, p is density of fluid, g is acceleration due to gravity, and h is depth
P0 is often atmospheric pressure but not always
Fluid pressure equation
Pf = pgh
density of fluid * gravity * depth
Conversion between Pa, mmHG, torr, and atm
10^5 Pa = 760mmHG =760 torr = 1 atm
Gauge pressure and equation
Gauge pressure in the difference in atmospheric pressure and absolute pressure
Pgauge = Pressure - Patm = (pgh) - Patm
pgh = densitygravitydepth
(Absolute pressure is gauge pressure measured in a vacuum)
Hydraulic systems principles equations
a change in pressure will be transmitted undiminished to every portion of the fluid an to the walls of the containing vessel
Hydraulic systems
P = F1/A1 = F2/A2
force and area are a fixed ratio for both sides of a hydraulic system (the force is proportional to the area)
V = A1d1 = A2d2
(Area)(distance) on both sides is equal (the distance is inversely proportional to the area)
Archimedes principle equation (Force of bouyancy)
Fbouyancy = pfluidVsubmergedg
Bouyancy force = weight of displaced fluid
Surface tension
results from cohesion between molecules due to IMFs
adhesion is the attractive force that a molecule of the liquid feels toward the molecules of some other substance
A meniscus occurs due to adhesion with the side of the container, a convex meniscus occurs when the adhesive forces are greater than cohesive forces
viscosity
viscosity (η) is the resistance of a fluid to flow
increased viscosity increases its viscous drag
-analogous to air resistance
those with lower viscosities behave more like ideals fluids, which are inviscid
-we assume this for the MCAT
Poiseulle’s Law (Laminar flow)
Laminar flow, can be modeled through Poiseuille’s Law
Q = ΔPπr^4 / 8ηl
pay attention to:
radius to the fourth power and pressure change on the numerator
viscosity and length are the denominator
Turbulent flow
Turbulent flow is rough, causes formation of eddies
eddies are swirls of fluid of varying sizes
laminar flow occurs at the boundaries in a boundary layer
can arise when the speed of the fluid exceeds a certain critical speed
critical speed equation
vc = Nrη / pD
vc is the critical speed Nr is a constant called the Reynolds number η is viscosity p is density of the fluid D is diameter of the tube
Most likely just need to understand the concept/relationships
flow rate and linear speed through a pipe equation
Q (flow rate) = v1 (linear speed) * A1 (cross sectional area)
Area = pi*r^2
Bernoulli’s equation
P + 1/2pv^2 + pgh = CONSTANT
Pressure energy + Kinetic energy + pressure is constant
P is absolute pressure, p is density, v is linear speed, g is gravity, h is average height of flow
velocity and pressure are inversely related
electrostatic force between two charges
Fe = kq1q2/r^2
similar to gravitational force, with k instead of G and q instead of m
quantities the magnitude
repulsive forces lead to positive electrostatic force
Energy of an electric field equation
E = Fe / q = kQ / r^2
equal to the electrostatic force divided by charge placed in the electric field
Q is stationary source charge that creates the electric field
Electric potential energy equation
U = kQq/r
similar to gravitational energy in the same way as the electrostatic force is similar to the gravitational force
energy ends with /r, force ends with /r^2
repulsive forces lead to positive energy
Electric potential equation
a charges potential energy divided by the magnitude of its charge
V = U/q = kQ/r
measured in volts
Potential difference
Difference in electric potential
potential difference between two charges gives voltage
ΔV = Vb - Va = Wab/q
Wab is the work needed to move a test charge q through an electric field from point a to b