📚 Work, Energy, and Power – Formula Sheet for NEET

✅ 1. Work

Definition of Work:

W=F⋅d⋅cos⁡θ

Where:
W = Work done (Joule)
F = Force applied (N)
d = Displacement (m)
θ = Angle between force and displacement

Conditions for Work:
- Force must be applied.
- Displacement should occur.
- Component of force in the direction of displacement: F⋅cos⁡θ
Unit of Work:
- SI Unit: Joule (J)
- 1 J=1 N⋅1 m
- CGS Unit: Erg
- 1 J=107 erg
Work Done by a Constant Force:

W=F⋅d⋅cos⁡θ

Work Done by a Variable Force:

W=∫F⋅dx

Work Done in Circular Motion:

W=0

(Because force and displacement are perpendicular)

Work Done by Gravitational Force:

W=m⋅g⋅h

Where:
m = Mass (kg)
g = Acceleration due to gravity (9.8 m/s²)
h = Height (m)

Work Done by Friction:

W=−f⋅d

Where:
f = Frictional force
d = Displacement

Work Done in Lifting an Object:

W=m⋅g⋅h

✅ 2. Energy

Definition of Energy:
The capacity of a body to do work.
Kinetic Energy (KE):

K.E=1/2mv²

Where:
m = Mass (kg)
v = Velocity (m/s)

Change in Kinetic Energy:

ΔK.E=1/2m(v_f² – v²_i )

Where:
vf = Final velocity
vi = Initial velocity

Potential Energy (PE):

P.E=m⋅g⋅h

Where:
m = Mass
g= Acceleration due to gravity
h = Height

Potential Energy in a Spring:

P.E=1/2 kx²

Where:
kk = Spring constant
xx = Displacement from the mean position

Total Mechanical Energy:

E=K.E+P.E

✅ 3. Work-Energy Theorem

Statement:
The work done by the net force on an object is equal to the change in its kinetic energy.

W=ΔK.E

W=1/2m(v_f² – v²_i )

✅ 4. Power

Definition of Power:
The rate at which work is done or energy is transferred.

P=W/t

Where:
P = Power (Watt)
W = Work done (Joule)
t = Time (s)

Instantaneous Power:

P=F⋅v

Where:
v = Velocity

Average Power:

Pavg=ΔWΔtPavg=ΔtΔW

Power in Rotational Motion:

P=τ⋅ω

Where:
τ= Torque
ω = Angular velocity

Unit of Power:
- SI Unit: Watt (W)
- 1 W=1 Joule/second1W=1Joule/second
- CGS Unit: Erg/sec
- 1 W=107 erg/sec1W=107erg/sec
- Bigger Units:
- 1 kW=1000 W1kW=1000W
- 1 MW=106 W1MW=106W

✅ 5. Relation Between Power and Energy

Power in Terms of Energy:

P=E/t

✅ 6. Efficiency

Definition:
The ratio of useful work output to total energy input.

η=Useful Power OutputTotal Power Input×100η=Total Power InputUseful Power Output×100

Efficiency of an Engine:

η =W/Q * 100

Where:
W = Work done by the engine
Q = Heat supplied

✅ 7. Collision and Energy Conservation

Perfectly Inelastic Collision:

v= m₁u₁ + m₂u₂ / m1+m2

Perfectly Elastic Collision:

v1=(m1−m2)u1+2m₂u₂/m1+m2

v2=(m2-m1)u2+2m₁u₁/m1+m2

Loss of Kinetic Energy in Inelastic Collision:

ΔK.E=1/2(m1m2/m1+m2)(v1-v2)²

✅ 8. Motion in Vertical Circle

Kinetic Energy at the Bottom:

K.E= 1/2 mv²

Potential Energy at the Top:

P.E=m⋅g⋅2r

Minimum Velocity at the Highest Point:

v= √gr

✅ 9. Power and Work in Different Scenarios

For Constant Force:

W=F⋅d

For Variable Force: