Physics and Math Flashcards
Dot Product
gives the scalar resultant of vector multiplication
A*B = |A||B|cos(theta)
Cross Product
gives the vector resultant of vector multiplication
A X B = |A||B|sin(theta)
use right-hand rule to determine direction (face of palm is the resulting vector)
not the resultant vector is PERPENDICULAR to the plane created by vector A and B
How to differentiate a vector going into or out of the page?
Into the page: a circle with an X in the middle
Out of the page: a circle with a dot in the middle
The SI unit for force?
Newton (kg.m/s^2)
The magnitude of the gravitational force between two objects is …
Fg = Gm1m2/r^2
Kinetic Friction equation
coefficient of kinetic friction * N
N = normal force
note: the coefficient of static friction is ALWAYS larger than the coefficient of kinetic friction
unitless
Newton’s First Law
Fnet = ma = 0
an object will stay at rest unless a force is acted upon it
Newton’s Second Law
Fnet = ma
an object will move when a non zero force is acted upon it
Newton’s Third Law
Fab = -Fba
opposite and equal reaction
What are the four kinematic equations of linear motion?
v = v0 +at
x = v0t + 0.5at^2
v^2 = v0^2 + 2ax
x = vt
Circular motion equation
Fc = mv^2/r
Fc = centripetal force
m = mass
v = speed
r = radius
Torque Equation
torque = r x F = rFsin(theta)
Unit of energy?
Joule (J)
kg * m^2 / s^2
Equation for kinetic and potential energy.
K = 1/5mv^2
U = mgh
Elastic potential energy equation.
U = 1/2kx^2
k = spring constant
Conservative forces
those that are path independent and do not dissipate energy
GRAVITATIONALA ND ELECTROSTATIC FORCES
The conservation of mechanical energy can be expressed as…
deltaE = deltaU + deltaK = 0
Define Work and give the equation
the process by which energy is transferred from one system to another
W = F*d = Fdcos(theta)
Joule (J)
theta is the angle between the force vector and displacement vector
NOT A FORM OF ENERGY ITSELF
Positive work vs negative work?
+W = work done BY a system
-W = work done ON a system
e.g. gas expanding is +W (work was done by the gas)
Does an isovolumetric/isochoric process have negative or positive work?
NEITHER
no volume change means no work done
What is the formula for work in a isobaric process?
W = PdeltaV
isobaric = pressure remains constant
Definition and formula for power.
Power refers to the rate at which energy is transferred from one system to another
i.e. how fast is the work being done
P = W/t = deltaE/t
work over time … change in energy over time
Watt (W)
Work-energy theorem in respect to kinetic energy.
Wnet = deltaK
work is the equal to the change in kinetic energy
Mechanical advantage vs mechanical efficiency equation
Mechanical advantage = Fout/Fin
Efficiency = Wout/Win
Mechanical Advantage in terms of the work being done?
Work done by the machine is THE SAME to do the task without it
BUT, by changing the distance over which the force is applied, then we change the magnitude of the input force required
SI base units for force?
kg * m / s^2
NEWTON
What is the temperature of the human body in Fahrenheit and Celsius, respectively?
98.6 and 37
Conversion of Fahrenheit to Celsius?
F = (9/5)C + 32
Thermal Expansion equation
deltaL = alpha LdeltaT
deltaL = change in length
alpha = coefficient of linear expansion
L = original length
deltaT = change in temperature
Isolated System
not capable of exchanging energy or matter with their surroundings
total change in internal energy is ZERO
Closed System
capable of exchanging energy, but not matter, with the environment
i.e. movable piston
MOST OF TEST DAY
Open System
can exchange both matter and energy with the surroundings
State Function
thermodynamic properties that are a function of only the current equilibrium state of the system
independent of path
Process Functions
thermodynamic properties that are dependent on the path taken to get from one state to another
i.e. work and heat
What is the equation for the First Law of Thermodynamics
deltaU = Q - W
the change in total internal energy of a system is equal to the amount of energy transferred in the form of heat TO the system, minus the amount of energy transferred FROM the system in the form of work
heat in minus work out
What is the SI unit for heat? What is the alternative? Give the conversions.
SI unit is the Joule (J)
or
1 Calorie = 10^3 (1000) calories
1 cal is the amount of heat required to raise 1 g of water one degree Celsius
Define specific heat and give the equation.
q = mcdeltaT
q = heat gained or lost
m = mass
c = specific heat of a substance
deltaT = change in temperature
NOTE: then going through a phase change, this becomes q = mL
L = heat of transformation / latent heat
specific heat (c) – the amount of heat energy required to raise one gram of a substance by one degree Celsius or Kelvin
the specific heat of water is 1 cal/g*K
When would the specific heat of a system drastically change?
When going through a phase change!!!
heat added or removed from the system does NOT result in a change in temperature
First Law of Thermodynamics when the system is:
1. Isothermal
2. Adiabatic
3. Isovolumetric
- deltaU = 0; Q = W
- Q=0; delta U = -W
- W=0; deltaU = Q
Equation for the change in entropy?
deltaS = Qrev / T
Qrev = heat gained or loss in a reversible process
SI Unit of entropy (S) = J / mol * K
The Second Law of Thermodynamics
deltaS_universe = deltaS_system + deltaS_surroundings > 0
the energy in a closed system will spontaneously spread out and entropy will increase if it is not hindered from doing so
Formula for density
p (density) = m/V
SI units for density
kg/m3/ , g/mL , g/cm3/
Density of Water
1 g/cm3 OR 1000 kg/m3
What is the weight of a fluid?
Fg = pVg
p (rho) = density
What is the formula and SI unit for pressure?
P = F / A … force over area
SI = Pascal (Pa) or N/m2
What is the hydrostatic pressure? I.e. what is the pressure exerted on a submerged object?
P = P0 + pgz
P0 = ambient pressure (on the surface)
z = depth of the object
p = density
What is gauge pressure?
difference between the hydrostatic pressure inside a closed container and the atmospheric pressure outside
Pgauge = P - Patm
Equation for buoyant force?
FB = pairgV
pair = density of air
g = acceleration due to gravity
V = volume
Real vs Virtual Images
Lens physics
CONVEX lenses form REAL images
CONCAVE lenses form virtual images
What is the equation for the radius of curvature of a lens?
R = 2f
f = focal length of the lens
What is the equation for equilibrium partial pressure of a reaction?
Kp = Pproductsm / Preactantsn
Concave vs Convex Lens
Concave bends DIVERGING light (bends light OUTWARD)
Convex bends light IN
Nearsightedness? also called what?
called MYOPIA
light bends too much!
image formed in FRONT of retina
Strength of a lens equation?
S = 1/o + 1/i
S = strenght of lens (Diopter // D)
o = object distance from lens
i = image distance from lens
Single split diffraction pattern equation?
sin(theta) = m*lambda / alpha
theta = angle of dark bands
lambda = wavelength of the light
alpha = width of the slit
m = integer
What is the gas constant?
R = 0.082 L * atm / K * mol
