Force
Category : JEE Main & Advanced
(1) Force is an external effect in the form of a push or pull which
(i) Produces or tries to produce motion in a body at rest.
(ii) Stops or tries to stop a moving body.
(iii) Changes or tries to change the direction of motion of the body.
Various condition of force application

Body remains at rest. Here force is trying to change the state of rest.  
Body starts moving. Here force changes the state of rest.  
In a small interval of time, force increases the magnitude of speed and direction of motion remains same.  
In a small interval of time, force decreases the magnitude of speed and direction of motion remains same.  
In uniform circular motion only direction of velocity changes, speed remains constant. Force is always perpendicular to velocity.  
In nonuniform circular motion, elliptical, parabolic or hyperbolic motion force acts at an angle to the direction of motion. In all these motions. Both magnitude and direction of velocity changes. 
(2) Dimension : Force = mass x acceleration
\[[F]=[M][L{{T}^{2}}]=[ML{{T}^{2}}]\]
(3) Units : Absolute units : (i) Newton (S.I.) (ii) Dyne (C.G.S)
Gravitational units : (i) Kilogramforce (M.K.S.) (ii) Gramforce (C.G.S)
Newton : One Newton is that force which produces an acceleration of \[1\,m/{{s}^{2}}\] in a body of mass 1 Kilogram.
\[\therefore 1\]Newton \[=1kg\,m/{{s}^{2}}\]
Dyne : One dyne is that force which produces an acceleration of \[1cm/{{s}^{2}}\] in a body of mass 1 gram.
\[\therefore \] 1 Dyne\[=1gm\,cm/{{\sec }^{2}}\]
Relation between absolute units of force 1 Newton \[={{10}^{5}}\] Dyne
Kilogramforce : It is that force which produces an acceleration of \[9.8m/{{s}^{2}}\] in a body of mass 1 kg.
\[\therefore \] 1 kgf = 9.80 Newton
Gramforce : It is that force which produces an acceleration of \[980cm/{{s}^{2}}\] in a body of mass 1gm.
\[\therefore \] 1 gmf = 980 Dyne
(4) \[\vec{F}=m\vec{a}\] formula is valid only if force is changing the state of rest or motion and the mass of the body is constant and finite.
(5) If m is not constant \[\vec{F}=\frac{d}{dt}(m\vec{v})=m\frac{d\vec{v}}{dt}+\vec{v}\frac{dm}{dt}\]
(6) If force and acceleration have three component along x, y and z axis, then
\[\vec{F}={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}+{{F}_{z}}\hat{k}\] and \[\vec{a}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}+{{a}_{z}}\hat{k}\]
From above it is clear that \[{{F}_{x}}=m{{a}_{x}},\,\,{{F}_{y}}=m{{a}_{y}},\,{{F}_{z}}=m{{a}_{z}}\]
(7) No force is required to move a body uniformly along a straight line with constant speed.
\[\overrightarrow{F}=m\vec{a}\] \[\therefore \overrightarrow{F}=0\]
(As \[\vec{a}=0\])
(8) When force is written without direction then positive force means repulsive while negative force means attractive.
Example : Positive force  Force between two similar charges
Negative force  Force between two opposite charges
(9) Out of so many natural forces, for distance \[{{10}^{15}}\]metre, nuclear force is strongest while gravitational force weakest.
\[{{F}_{\text{nuclear}}}>{{F}_{\text{electromagnetic}}}>{{F}_{\text{gravitatio}\text{nal}}}\]
(10) Ratio of electric force and gravitational force between two electron's
\[{{F}_{e}}/{{F}_{g}}={{10}^{43}}\] \[\therefore {{F}_{e}}>>{{F}_{g}}\]
(11) Constant force : If the direction and magnitude of a force is constant. It is said to be a constant force.
(12) Variable or dependent force :
(i) Time dependent force : In case of impulse or motion of a charged particle in an alternating electric field force is time dependent.
(ii) Position dependent force : Gravitational force between two bodies \[\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\]
or Force between two charged particles \[=\frac{{{q}_{1}}{{q}_{2}}}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\].
(iii) Velocity dependent force : Viscous force \[(6\pi \eta rv)\]
Force on charged particle in a magnetic field \[(qvB\sin \theta )\]
(13) Central force : If a position dependent force is directed towards or away from a fixed point it is said to be central otherwise noncentral.
Example : Motion of Earth around the Sun. Motion of electron in an atom. Scattering of aparticles from a nucleus.
(14) Conservative or non conservative force : If under the action of a force the work done in a round trip is zero or the work is path independent, the force is said to be conservative otherwise non conservative.
Example : Conservative force : Gravitational force, electric force, elastic force.
Non conservative force : Frictional force, viscous force.
(15) Common forces in mechanics :
(i) Weight : Weight of an object is the force with which earth attracts it. It is also called the force of gravity or the gravitational force.
(ii) Reaction or Normal force : When a body is placed on a rigid surface, the body experiences a force which is perpendicular to the surfaces in contact. Then force is called 'Normal force' or 'Reaction'.
(iii) Tension : The force exerted by the end of taut string, rope or chain against pulling (applied) force is called the tension. The direction of tension is so as to pull the body.
(iv) Spring force : Every spring resists any attempt to change its length. This resistive force increases with change in length. Spring force is given by \[F=Kx\]; where x is the change in length and K is the spring constant (unit N/m).
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