**Work:**-

Work done by the force is defined as dot product of force and displacement vector

- For constant Force

W=

**F**.

**s**

where F is the force vector and s is displacement Vector

-For variable Force

dW=

**F**.

**ds**

or W=∫

**F**.

**ds**

-It is a scalar quantity

If force acting on the body is along the direction of displacement of the body then work done can be calculated by calculating the area enclosed between F-S curve and displacement axis.

**Conservative And Non Conservative Forces**

-If the work done by the force in a closed path is zero,Then it is called conservative Force

-If the work done by the force in a closed path is not zero,Then it is called non conservative Force

-Conservative Forces are gravitational ,electrical force

-Non Conservative Forces are friction

-Work done by non conservative forces like frictional forces are path dependent.

**Kinetic Energy:**-It is the energy possessed by the body in motion

-it is defined as

K.E=(1/2)mv

^{2}

- Net work done by the external force is equal to the change in the kinetic energy of the system

W=K

_{f}-K

_{i}

Work energy theorem states that

W

_{ext}=K

_{f}-K

_{i}=ΔK

**Potential Energy:**

-It is the kind of energy possessed due to configuration of the system

-It is due to conservative force

-it is defined as

dU=-

**F**.

**dr**

U

_{f}-U

_{i}=-∫

**F**.

**dr**

Where F is the conservative force

**F**=-(∂U/∂x)

**i**-(∂U/∂y)

**j**-(∂U/∂z)

**k**

For gravitational Force

Change in Potential Energy =mgh

where h is the height between the two points

Mechanical Energy is defined as

=K.E+P.E

**Law Of conservation of Energy**

In absence of external forces,internal forces being conservative ,total energy of the system remains constant.

K.E

_{1}+P.E

_{1}=K.E

_{2}+P.E

_{2}

_{}

###
_{Power}

Power is the rate of doing work.

Average power = ΔW/Δt

Instantaneous power = dW/dt =

**F.v**

Slope of W vs t graph gives the power of the system and area between the P vs t curve and time axis gives work done by the system.

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