1.8 Equations Flashcards
Hooke’s Law
F = kx F = Force K = Spring Constant X = Extenstion
Young’s Modulus
E= σ/ε E = Young’s Modulus σ = Stress ε = Strain
Stress
σ = F/A σ = Stress F = Force A = Cross Sectional Area
Strain
ε = x/L ε = Strain x = Extension L = Original Length
Springs in Series
F/K=F/K1 + F/K2
F = Force
K = Spring Constant
Springs in Parallel
K=K1 + K2
K = Spring Constant
Charles Law
V/T=k
V = Volume
T = Temperature in Kelvin
K = Constant
Boyles Law
PV=k
P = Pressure
V = Volume
K = Constant
Pressure Law
P/T=k
P = Pressure
T = Temperature in Kelvin
Ideal Gas Equation
pV=nRT P = Pressure V = Volume n = Number of moles of the gas R = Molar gas constant (8.31Jmol^-1K^-1) T = Temperature in Kelvin
pV=NkT
P = Pressure V = Volume N = No of molecules of the gas k = Boltzmann Constant (1.38 x 10^-23) T = Temperature in Kelvin
Mean Speed
{c} = (c1 + c2 + c3…)/N
C = Speed of Molecules in a gas
{c} = Mean Speed of molecules
N = Number of Molecules
Mean Square Speed
{c^2} = (c1^2 + c2^2 + c3^2….)/N
{c^2} = Mean Square Speed of Molecules
C^2 = Square Speed of single molecule
N = number of moleculesRoot Mean Square Speed
Crms = (c^2)^0.5/N
Crms = Root Mean Square Speed of Molecules
Gas Density
P = M/V = N x m/V
P = Density M = mass of the gas V = Volume N = Number of molecules m = mass of each molecule
Specific Heat Capacity
Q = mc∆θ
Q = Change in Heat Energy of the body M = mass of the body C = Specific Heat Capacity ∆θ = Change in Temperature of the body
Pressure of a Gas
P = 1/3(ρc^2)
P = Pressure ρ = density C^2 = Square Speed
pV = 1/3 Nm{c^2}
P = Pressure of the gas
V = Volume of the gas
N = Total Number of identical particles
M = mass of the gas
{c^2} = mean square speedMolecular Kinetic Energy Equation
1/2m {c^2} = 3/2 kT
m = Mass of individual molecule
{c^2} = Mean Square Speed
k = Boltzmann Constant (1.38x10^-23)
T = Temperature in Kelvin
The angle θ in radians
θ = s/r
θ = the angle S = the length of the arc R = the radius of the circle
Linear Velocity (V)
V = rω
V = Linear Velocity R = radius ω = angular velocity
Periodic Time (T)
T = s/v = 2πr/rω = 2π/ω
T = Time Period S = Length of the Arc V = Linear Velcotiy r = Radius ω = Angular Velocity
Frequency (F)
F = 1/T = ω/2π
F = Frequency T = Time Period ω = Angular Velocity
Simple Harmonic motion
a = -ω^2x
A = acceleration ω = angular frequency X = displacement from origin
Time Period Equations
T = 2π(L/g)^1/2
T = 2π(m/k)^1/2
T = Time Period L = length of string G = Acceleration due to gravity M = mass K = stiffness constant
Displacement from equilibrium (x)
X = A cos(ωt)
X = Displacement from equilibrium A = Amplitude/m ω = angular frequency t = time/s
Centripetal Acceleration Equations (a)
a = v^2/r a = rω^2
a = Centripetal acceleration V = linear speed R = radius ω = angular velocity
Resultant Force Equations (Fr)
Fr = mv^2/r Fr = mrω^2
Fr = Resultant Force V = Linear speed R = radius ω = angular velocity m = mass
Time taken for the displacement of a critically damped system to become 0
t = T/4
t = time T = Time Period
Radius of a Nucleus
r = r0A^1/3
r = Radius of a nucleus r0 = Radius of a proton A = Atomic mass number
Density of a nucleus
M = A x U then P = M/V
M = total mass of the nucleus A = Mass number U = 1.66x10^-27 V = Volume of the nucleus
Activity Equations
A = -λN A =A0e^-λt
A = Activity at time t λ = Decay Constant N = Number of Radioactive Nuclei A0 = Initial Activity at t= 0s t = time
Half Life Equation
T1/2 = ln(2)/λ
t1/2 = Half Life λ = Decay Constant
Number of Radioactive Nuclei Equation
N = N0 e^-λt
N = No of radioactive nuclei at time t N0 = No of radioactive nuclei at time t = 0s λ = Decay Constant t = time
