Work , Energy and Power (Quick Recap)

1. Work done by a constant force = F.S=FS cosθ
2. Work done by a variable force = ∫F.dS
3. 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.
4. Work done by conservative forces like gravitational and electrostatic forces does not depend on the path taken by the particle and only depends on the initial and final positions of the particles.
5. Work done by non conservative forces like frictional forces are path dependent.
6. Power is the rate of doing work.
       Average power = ΔW/Δt
       Instantaneous power = dW/dt = F.v
7. 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.
8. Kinetic energy = (1/2)mv²
9. Gravitational potential energy = mgh where m is the mass of the object, g is acceleration due to gravity and h is the hight of object above the referance level. PE of the object is positive when object is above the refrence level and negative when it is below the refrence level.
10. An object posess kinetic energy by virtue of its motion and it posess potential energy by virtue of its position.
11. Elastic energy of a spring is given by (1/2)kx² where k is the elastic constant for the spring.
12. Work energy theorem states that
       W_ext=K_f-K_i=ΔK
13. Law of conservation of energy states that " Total energy of the system always remains constant provided no external work is being done and energy of the system is not being converted to other forms of energy". Hence Energy can never be created or destroyed it can only be converted from one form of energy to another.

For full notes on Work energy and power visit the link

Work And Energy

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

Conservative And Non Conservative Forces
-If the workdone by the force in a closed path is zero,Then it is called conservative Force
-If the workdone by the force in a closed path is not zero,Then it is called non conservative Force
-Conservative Forces are gravtitional ,electrical force
-Non Conservative Forces are friction

Kinetic Energy:-It is the energy possesed by the body in motion
-it is defined as
K.E=(1/2)mv²
- Networkdone by the external force is equal to the change in the kinetic energy of the system
W=K_f-K_i


Potential Energy:
-It is the kind of energy possesed 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 gravtitional 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,intenal forces being conservative ,total energy of the system remains constant.
K.E₁+P.E₁=K.E₂+P.E₂