# Work And Energy Formula Summary

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)mv2
- Net work done by the external force is equal to the change in the kinetic energy of the system
W=Kf-Ki

Work energy theorem states that
Wext=Kf-Ki=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
Uf-Ui=-∫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.E1+P.E1=K.E2+P.E2

### 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.