1.8 Equations

Question 1

Hooke’s Law

Answer 1

F = kx
F = Force
K = Spring Constant
X = Extenstion

Question 2

Young’s Modulus

Answer 2

E= σ/ε
E = Young’s Modulus
σ = Stress
ε = Strain

Question 3

Stress

Answer 3

σ = F/A
σ = Stress
F = Force
A = Cross Sectional Area

Question 4

Strain

Answer 4

ε = x/L
ε = Strain
x = Extension
L = Original Length

Question 5

Springs in Series

Answer 5

F/K=F/K1 + F/K2
F = Force
K = Spring Constant

Question 6

Springs in Parallel

Answer 6

K=K1 + K2

K = Spring Constant

Question 7

Charles Law

Answer 7

V/T=k
V = Volume
T = Temperature in Kelvin
K = Constant

Question 8

Boyles Law

Answer 8

PV=k
P = Pressure
V = Volume
K = Constant

Question 9

Pressure Law

Answer 9

P/T=k
P = Pressure
T = Temperature in Kelvin

Question 10

Ideal Gas Equation

Answer 10

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

Question 11

pV=NkT

Answer 11

P = Pressure
V = Volume
N = No of molecules of the gas
k = Boltzmann Constant (1.38 x 10^-23)
T = Temperature in Kelvin

Question 12

Mean Speed

Answer 12

{c} = (c1 + c2 + c3…)/N

C = Speed of Molecules in a gas
{c} = Mean Speed of molecules
N = Number of Molecules

Question 13

Mean Square Speed

Answer 13

{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 molecules

Question 14

Root Mean Square Speed

Answer 14

Crms = (c^2)^0.5/N

Crms = Root Mean Square Speed of Molecules

Question 15

Gas Density

Answer 15

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

Question 16

Specific Heat Capacity

Answer 16

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

Question 17

Pressure of a Gas

Answer 17

P = 1/3(ρc^2)

P = Pressure
ρ = density
C^2 = Square Speed

Question 18

pV = 1/3 Nm{c^2}

Answer 18

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 speed

Question 19

Molecular Kinetic Energy Equation

Answer 19

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

Question 20

The angle θ in radians

Answer 20

θ = s/r

θ = the angle
S = the length of the arc
R = the radius of the circle

Question 21

Linear Velocity (V)

Answer 21

V = rω

V = Linear Velocity
R = radius
ω = angular velocity

Question 22

Periodic Time (T)

Answer 22

T = s/v = 2πr/rω = 2π/ω

T = Time Period
S = Length of the Arc
V = Linear Velcotiy
r = Radius
ω = Angular Velocity

Question 23

Frequency (F)

Answer 23

F = 1/T = ω/2π

F = Frequency
T = Time Period
ω = Angular Velocity

Question 24

Simple Harmonic motion

Answer 24

a = -ω^2x

A = acceleration
ω = angular frequency
X = displacement from origin

Question 25

Time Period Equations

Answer 25

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

Question 26

Displacement from equilibrium (x)

Answer 26

X = A cos(ωt)

X = Displacement from equilibrium
A = Amplitude/m
ω = angular frequency
t = time/s

Question 27

Centripetal Acceleration Equations (a)

Answer 27

a = v^2/r a = rω^2

a = Centripetal acceleration
V = linear speed
R = radius
ω = angular velocity

Question 28

Resultant Force Equations (Fr)

Answer 28

Fr = mv^2/r
Fr = mrω^2

Fr = Resultant Force
V = Linear speed
R = radius
ω = angular velocity
m = mass

Question 29

Time taken for the displacement of a critically damped system to become 0

Answer 29

t = T/4

t = time
T = Time Period

Question 30

Radius of a Nucleus

Answer 30

r = r0A^1/3

r = Radius of a nucleus
r0 = Radius of a proton
A = Atomic mass number

Question 31

Density of a nucleus

Answer 31

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

Question 32

Activity Equations

Answer 32

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

Question 33

Half Life Equation

Answer 33

T1/2 = ln(2)/λ

t1/2 = Half Life
λ = Decay Constant

Question 34

Number of Radioactive Nuclei Equation

Answer 34

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