Most Important And Most Frequently Used Formulas in Physics (2)~PHYSICS PROBLEMS AND SOLUTION

Physics Problem Solving For High School - Formula, Definition and explanations - Some of the most important and most frequently used formulas in physics lessons at our school are presented and explained below. We look forward to helping you solve physics problems in school.

Springs, Hooke's Law and Potential Energy
Formula, Definition and explanations

\[F_s = k x\]

F is the force applied to compress or stretch a spring
k is the spring constant
x is the length of extension or compression of the spring

\[E_s = \frac{1}{2} k x^2\]

Es is the potential energy stored in a spring when compressed or extended
k is the spring constant
x is the length of extension or compression of the spring

Period of Simple Harmonic Motions
Formula, Definition and explanations

\[T_s = 2\pi \sqrt{\frac{m}{k}}\]

Ts is the time period of motion
k is the spring constant
m is the mass attached to the spring

\[T_p = 2\pi \sqrt{\frac{L}{g}}\]

Ep is the time period of motion
L is the length of the pendilum
g is the acceleration due to gravity

Gravitational Fields and Forces
Formula, Definition and explanations

\[= G \frac{m_1 m_2}{r^2}\]

F is force of attraction
G is the universal gravitational constant
$m_1$ and $m_1$ are the masses of the two objects attracting each other
r is the distance separating the centers of the two objects

\[g_r = \frac{G m}{r^2}\]

$g_r$ gravitational field intensity at a distance r
G is the universal gravitational constant
m is the mass
r is the distance (from mass m) where the field is measured

\[E_p = -\frac{G M m}{r}\]

Ep gravitational potential energy of mass m
G is the universal gravitational constant
G is the mass of the attracting body
m is the mass being attracted
r is the distance separating the centers of the masses M and m

Satelite motion, orbital speed, period and radius
Formula, Definition and explanations

\[v = \sqrt{ \frac{G M}{r} }\]

v is the orbital speed of the satellite
G is the universal gravitational constant
M is the mass of the attracting body (Earth for example)
r is the distance from the center of mass M to the position of the satellite

\[T = \sqrt{ \frac{4\pi^2r^3}{G M} }\]

T is the orbital period of the satellite
G is the universal gravitational constant
m is the mass
r is the distance from the center of mass M to the the position of the satellite

\[v = \frac{2\pi r }{T}\]

v is the orbital speed of the satellite
r is the distance from the center of mass M to the the position of the satellite
T is the orbital period of the satellite

Electric forces, fields and potentials
Formula, Definition and explanations

\[F = k \frac{q_1 q_2}{r^2}\]

F is the electric force
k is a constant
q1 and q1 are the charges attracting or repulsing each other
r is the distance separating the two charges

\[F = q E\]

F is the electric force
q is the charge
E is the eletcric field

\[E = k \frac{q}{r^2}\]

E is the electric field due charge q
k is a constant
q is the charge
r is the distance from the charge q where E is being calculated

\[E_p = k \frac{q_1 q_2}{r}\]

Ep is the electric potential energy for a system of two charges
k is a constant
q1 and q1 are the charges
r is the distance separating the two charges

\[V = k \frac{q}{r}\]

V is the electric potential
k is a constant
q is the charge
r is the distance from the charge q

\[E = \frac{V}{d}\]

E is the electric field between two large, oppositely charged, conducting parallel plates
V is the electric potential difference between the plates
d is the distance separating the two plates

Magnetic fields and forces
Formula, Definition and explanations

\[= \frac{\mu _0 I}{2 \pi r}\]

B is magnetic field due to current I in a long conductor of length L
μo is permeability in vacuum
I the current in the conductor
L is the length of the conductor
r is the distance from the conductor to where the field B is calculated

\[B = \frac{\mu _0 N I}{L}\]

B is the magnetic field (in the center of the solenoid) due to current I in a solenoid of length L
μo is permeability in vacuum
I the current in the solenoid
L is the length of the solenoid
N is the number of turns of the solenoid

\[F_m = q v B \sin(\theta)\]

Fm is the magnetic force (due to B) on a charge q moving at a velocity v
B the magnetic field
θ is the angle between B and the direction of motion of q

\[F_m = I L B \sin(\theta)\]

Fm is the magnetic force (due to B) on a wire with current I and length L
B the magnetic field
θ is the angle between B and the wire

\[F_m = \frac{ \mu _0 I_1 I_2 L }{2 \pi r}\]

Fm is the magnetic force of attraction or repulsion between two parallel wires
μo is permeability in vacuum
I1 and I2 are the currents in the two wires
L is the common length between the two wires

Waves
Formula, Definition and explanations

\[v = \lambda f\]

v is the wave velocity
λ is the wavelength
f is the frequency

\[f = \frac{1}{T}\]

f is the wave frequency
T is the period of the wave

Optics
Formula, Definition and explanations

\[v = \frac{c}{n}\]

v is the velocity of light in a medium of index n
c is speed of light in vacuum ( = 3.0 × 108m/s)
n is the index of refraction of the medium

\[n_1 \sin \theta_1 = n_2 \sin \theta_2\]

n1 is the index of refraction of medium 1
n2 is the index of refraction of medium 2
θ1 is the angle of incidence in medium 1
θ2 is the angle of refraction in medium 2

\[\theta_c = \sin^{-1}(\frac{n_2}{n_1})\]

θc is the critical angle such that when the angle of incidence is bigger that θc all light is reflected to medium 1
n1 is the index of refraction of medium 1 (medium of incidence)
n2 is the index of refraction of medium 2 (medium of refraction)

\[\frac{1}{D_o} + \frac{1}{D_i} = \frac{1}{F}\]

Do is the distance to the object
Di is the distance to the image
F is the focal length

Photoelectric Effects
Formula, Definition and explanations

\[E = h f\]

E is the energy of the photon
h is Plank's constant
f is the wave frequency of the photon

\[E_k = h f - \phi\]

Ek is the kinetic energy
h is Plank's constant
f is the wave frequency of the photon
φ is the work function of the metal (minimum work required to extract an electron)

\[p = \frac{h}{\lambda}\]