Conservative forces:
If the work done by a force in moving a body between two positions is independent of the path followed by the body, then such a force is called as a conservative force.

*Conservative forces and non-conservative forces*

*Conservative forces*

*If the work done by a force in moving a body between two positions is independent of the path followed by the body, then such a force is called as a conservative force.*

*Examples : force due to gravity, spring force and elastic force.*

*The work done by the conservative forces depends only upon the initial and final position of the body.*

*The work done by a conservative force around a closed path is zero.*

*Non conservative forces*

*Non-conservative force is the force, which can perform some resultant work along an arbitrary closed path of its point of application.*

*The work done by the non-conservative force depends upon the path of the displacement of the body*

*(e.g) Frictional force, viscous force, etc.*

*Law of conservation of energy*

*The law states that, if a body or system of bodies is in motion under a conservative system of forces, the sum of its kinetic energy and potential energy is constant.*

*Explanation*

*From the principle of work and energy,*

*Work done = change in the kinetic energy*

*( i.e) W1â†'2 = E**k2 **- E**k1 ** ...(1)*

*If a body moves under the action of a conservative force, work done is stored as potential energy.*

*W1â†'2 = - (EP2 - EP1) ...(2)*

*Work done is equal to negative change of potential energy.*

*Combining the equation (1) and (2),*

*Ek2 - Ek1 = -(EP2 - EP1) (or) EP1 + Ek1 = EP2 + Ek2 ...(3)*

*which means that the sum of the potential energy and kinetic energy of a system of particles remains constant during the motion under the action of the conservative forces.*

*Power*

*It is defined as the rate at which work is done.*

*power = work done/ time*

*Its unit is watt and dimensional formula is ML2 T-3.*

*Power is said to be one watt, when one joule of work is said to be done in one second.*

*If dw is the work done during an interval of time dt then,*

*power = dw/ dt ...(1)*

*But dw = (F cos Î¸) ds ...(2)*

where Î¸ is the angle between the direction of the force and displacement. F cos Î¸ is component of the force in the direction of the small displacement ds.

Substituting equation (2) in (1)

power = (F cos Î¸) ds / dt

=( F cosÎ¸) ds / dt= F( cos Î¸) v

âˆ´ power = (F cos Î¸) v

If F and v are in the same direction, then

power = F v cos 0 = F v = Force x velocity

It is also represented by the dot product of F and v.

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