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Equation for Force

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Simply, we can say that force is an influence which causes the motion of particles. So, forces are essentially pushes or pulls and they are responsible for the direction changes of a moving object. We may not be see them, but we can feel the effect of force. Hence, force plays an important role in everyday life. It changes the direction of moving objects. Forces hold together the atoms which is a building block of every materials. The force is responsible for every kind of motions. The human body is always consisting so many forces. We are always influenced by the gravitational force. which is a most recognized type of force. We can classify the forces depending upon their effect on any object. Different forces can act on an object at same time. According to the types of forces, the equations are also different. The different kinds of forces and their corresponding equations are mentioned below.
Tug of War

Equation for Force of Gravity

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Gravity is the attraction or a pull of earth towards its center. The force corresponding to this attraction is known as the gravitational force.
The equation for force of gravity is given by,
F = $\frac{GMm}{R^{2}}$

Where G is the universal gravitational constant
M is the mass of first body
m is the mass of the second body
R is the distance between the two masses

We know that F=mg
So,
mg = $\frac{GMm}{R^{2}}$

g = $\frac{GM}{R^{2}}$
This is the equation for gravity.

Frictional Force Equation

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Frictional force is a force which resist or prevent the motion of a body on a surface. The mathematical representation of the frictional force is given by,

$F_{friction}$= N$\mu $

Where $F_{friction}$ is the frictional force
N is the normal force
$\mu $ is the coefficient of friction

Electric Force Equation

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Electric force is defined as the force which acts on a charged particle in an electric field. So the equation of the electric force is given by,

F = qE

Where F is the electric force
q is the net charge of the particle
E is the net electric field

Electrostatic Force Equation

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When two charged particles are subjected to a non time varying electric field, it exhibit electrostatic attraction or repulsion. This attractive or repulsive force can be explained by Coulomb's law. It states that, the force of attraction or repulsion between the two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between the two charges. The equation of electrostatic force is given by,

F= $\frac{1}{4\pi \varepsilon _{0}}$ $\times$ $\frac{q_{1}q_{2}}{r^{2}}$

Where $\frac{1}{4\pi \varepsilon _{0}}$ is the proportionality constant, the value is given as 9$\times$ $10^{9}$N$m^{2}$
$q_{1}$ is the charge of the first particle
$q_{2}$ is the charge of the second particle
r is the distance between the charges

Electromagnetic Force Equation

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Electromagnetic force is experienced when the particle is placed in a mutually perpendicular electric and magnetic fields. Electromagnetic force is also known as the Lorentz force. Which is given by,

F = q(E+v$\times$ B)

Where F is the Lorentz force
q is the charge of the particle
E is the electric field
v is the velocity of the particle
B is the magnetic field

Magnetic Force Equation

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Magnetic force gives an idea about the force between the magnetic poles. It is given by the formula,

F = $\frac{\mu q_{m1} q_{m2}}{4\pi r^{2}}$

Where F is the magnetic force
$\mu$ is the permeability of the medium
$q_{m1}$ and $q_{m2}$ are the magnetic poles
r is the distance of separation

Average Force Equation

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We know that, force is defined as the rate of change momentum. If the time interval is very small we can not calculate the rate of change of momentum. So, we need to consider the average force. It is given as the rate of change of momentum over an interval of time. The equation is,

F = $\frac{m(v_{f}-v_{i})}{\Delta t}$

Where m is the mass of the object
$v_{f}$ is the final velocity
$v_{i}$ is the initial velocity
$\Delta$ t is the time interval

Buoyant Force Equation

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Buoyancy is the upward push or force exerted by a fluid which opposes the weight of an immersed body. The equation for the buoyant force is,

F = PA

Where P is the pressure
          A is the area
In terms of volume and height it can be represented as

F = gρV = ρghA

Where g is the gravity
          ρ is the density of the fluid
          V is the volume of the immersed part
          h is the height
          A is the area

Buoyant Force

Centripetal Force Equation

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Centripetal force is a kind of force which makes a body to follow a circular path. The direction of this force is towards the center. The mathematical representation is given by

F = $\frac{mv^{2}}{r}$


Where F is the centripetal force
          m is the mass of the object
          v is the velocity of the object
          r is the radius of the curvature of the circular path

Centripetal Force

Centrifugal Force Equation

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Centrifugal force is a type of force which pushes a rotating body towards the edge of the circular path or it pulls from its center. The equation of the centrifugal force is same as that of the centripetal force. Only the direction is different. In the case of centripetal force, it is towards the center whereas the direction of centrifugal force is away from the center.

Impulse Force Equation

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Impulse is defined as the integral of force with respect to the time interval. This gives the change in the momentum of an object. Impulse is denoted by J. It is given by,

J = F$\Delta$ t = $\Delta$ P

Where J is the impulsive force
F is the force
t is the time interval
P is the momentum

Spring Force Equation

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Hooke's law tells about spring force. The law states that, in case of an elastic material the stress is directly proportional to the strain. So the equation is,

F = -kx
Where F is the amount of force applied
           k is the spring constant or force constant
           x is the distance by which the elastic material stretched

Spring Force

Tension Force Equation

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Tension is a pulling force which is exerted by an elastic material on another material. It is denoted by T. So the equation is given as,

T = $\sum$ F-mg, if the system is in equilibrium
T = $\sum$ F+mg, if the system is not in equilibrium

Where $\sum$ F is the sum of all forces
m is the mass of the body
g is the acceleration due to gravity

Impact Force Equation

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Impact is defined as the high force which applied to an object with in a short interval of time when two bodies are colliding. The equation is,

F = $\frac{1}{2}$$\frac{mv^{2}}{r}$


Where F is the impact
m is the mass of an object
v is the velocity of an object
r is the distance traveled by the object

Normal Force Equation

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The equation of normal force is given by Newton's second law. The equation of normal force is given below.

F = ma

Where F is the force
m is the mass of an object
a is the acceleration of that object

Net Force Equation

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Net force or resultant force is the vector sum of all forces acting on an object. So the equation is given by,

$\left | F \right |$= $\sqrt{f^{2}_{x}+f_{y}^{2}}$

Where $f_{x}$ is the sum of horizontal component of all forces
$f_{y}$ is the sum of the vertical component of all forces