Work And Energy Formula Summary

Work done by the force is defined as dot product of force and displacement vector
- For constant Force

where F is the force vector and s is displacement Vector
-For variable Force


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

Work energy theorem states that

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

Where F is the conservative force


For gravitational Force
Change in Potential Energy =mgh

where h is the height between the two points

Mechanical Energy is defined as

Law Of conservation of Energy

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


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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