Equations Flashcards
dot product
A . B = |A| |B| cos θ
cross product
A x B = |A| |B| sin θ
velocity (v)
vector,
v = ∆X/∆t (m/s)
gravitational force between two objects
Fg = (Gm1m2)/r^2
where:
G = 6.67E-11 N*m^2/kg^2
static friction (fs)
fs ≤ μs*N
μs = coefficient of static friction (depends on two materials)
N = normal force, component force perpendicular to plane of contact
kinetic friction (fk)
fk = μk*N μk = coefficient of kinetic friction (depends on two materials)
weight (W)
W = m*g
m = mass
g (Fg) = 9.8 m/s^2 (approximately 10) (on earth)
center of mass/gravity of uniform object
x = ( (m1x1) + (m2x2) + (m3x3) + …) / (m1 + m2 + m3 + …)
same for y and z, just replace x
Newton’s laws
F = m*a , Fab = -Fba F = force m = mass a = acceleration Fab = force from a to b -Fba = equal and opposite reaction
acceleration (a)
vector,
a = ∆v/∆t (m/s^2)
equations of linear motion
x = v*t x = v(o)*t + (1/2) a*t^2 v = v(o) + a*t v^2 = v(o)^2 + 2*a*x
where v(o) = velocity initial
centripetal acceleration (Fc)
Fc = m*v^2 / r
torque (𝜏)
𝜏 = r*F = r*F sin θ r = length of lever arm F = magnitude of force θ = angle between lever arm and force vectors
kinetic energy (K)
K = 1/2 mv^2
unit: J = kg*m^2/s^2
gravitational potential energy (U)
U = mgh
unit: J = kg*m^2/s^2
elastic potential energy (U)
U = 1/2 kx^2
unit: J = kg*m^2/s^2
total mechanical energy (E)
E = U + K
conservation of mechanical energy
∆E = ∆U + ∆K = 0 W(conservative) = 0
work (W)
W = Fd cos θ
unit: J = kg*m^2/s^2
work for isobaric (constant pressure) process
W = P∆V
power (P)
P = W/t = ∆E/t
unit: watt (W) = J/s = kg*m^2/s^3
work-energy theorem
W(net) = ∆K = K(f) - K(i)
mechanical advantage
mechanical advantage = F(out) / F(in)
pulleys- what is relationship between tension and weight
T(total) = W
where T = tension
and W = mg
efficiency
efficiency = W(out) / W(in) = (load)(load distance) / (effort)(effort distance)
thermal expansion of solid
∆L = αL∆T
where:
L = initial length
α = coefficient of linear expansion (K^-1) = 1/3 β
thermal expansion of liquid
∆V = βV∆T
where:
V = initial volume
β = coefficient of volumetric expansion (K^-1) = 3 α
change in internal energy (U)
∆U = q - w
specific heat (c)
q = mc∆T
units of c = 1 cal/gK = 4.184 J/gK
heat of transformation/latent heat (L)
q = mL
entropy (S)
∆S = q(rev) / T
unit of S = J/mol*K
density (ρ)
ρ = m/V
pressure
P = F/A
absolute pressure
P = P(o) + ρgz
where: P(o) = incident/ambient pressure (at surface) ρ = density g = acceleration due to gravity z = depth of object
gauge pressure
P(gauge) = P - P(atm) = (P(o) + ρgz) - P(atm)
where: P(o) = incident/ambient pressure (at surface) ρ = density g = acceleration due to gravity z = depth of object below some point
Poiseuille’s law
Q = (π (r^4) ΔP) / (8ηL)
where: Q = flow rate r = radius of tube ΔP = pressure gradient η = viscosity L = length of pipe
critical speed (V(c))
V(c) = (N(R) η) / (ρD)
where: N(R) = Reynold's number η = viscosity ρ = density D = diameter of tube
continuity equation
Q = v(1) * A(1) = v(2) * A(2)
where:
Q = flow rate
v = linear speed
A = cross-sectional area
Bernoulli’s equation
P(1) + 1/2 ρv(1)^2 + ρgh(1) = P(2) + 1/2 ρv(2)^2 + ρgh(2)
where: P = absolute pressure ρ = density v = linear speed g = acceleration due to gravity h = height of fluid above some point
dynamic pressure
1/2 ρv^2
static pressure
P + ρgh
Coulomb’s law
F(e) = (k q1 q2) / r^2
where:
k = Coulomb’s constant (8.99 x 10^9 N*m^2/C^2)
q1 and q2 = magnitude of charges
r = distance between charges
ray diagrams for concave mirrors:
object is placed beyond F (focal point)
ray diagrams for concave mirrors:
object is placed at F (focal point)
ray diagrams for concave mirrors:
object is placed between F (focal point) and the mirror
ray diagram for convex mirrors:
isotopic notation
elements are preceded by their atomic number (Z) as a subscript and mass number (A) as a superscript
where:
X = element
A = mass number (corresponds to number of protons plus number of neutrons)
Z = atomic number (corresponds to number of protons)
radioactive decay:
alpha (α) decay balanced equation:
radioactive decay:
beta-negative (β-) decay balanced equation:
radioactive decay:
beta-positive (β+) decay balanced equation:
radioactive decay:
gamma (𝛾) decay balanced equation:
radioactive decay:
electron capture balanced equation:
