Work, Energy and Power – JEE Mains Physics

• by Zenith LMS
• Updated April 2025

1. Work Done by a Constant Force

• Work (W) = Force (F) × Displacement (d) × cosθ, where θ is the angle between force and displacement.
• Work is a scalar quantity and can be positive, negative, or zero.

2. Work Done by a Variable Force

• When force varies with position, work is calculated as:

  W = ∫ F(x) dx

  where F(x) is the force as a function of position x.

3. Kinetic and Potential Energies

• Kinetic Energy (K.E.) =

  (1/2)mv²

  where m = mass and v = velocity.
• Potential Energy (P.E.) is the energy possessed by a body due to its position or configuration.

4. Work-Energy Theorem

• The net work done by all forces on a particle equals the change in its kinetic energy.
• Mathematically:

  Wnet = ΔK.E. = K.E.final - K.E.initial

5. Power

• Power is the rate at which work is done.
• Average Power = Work done / Time taken.
• Instantaneous Power =

  P = F·v

  where F = force and v = velocity.
• Units: Watt (W).

6. Potential Energy of a Spring

• For a spring obeying Hooke's law:

  F = -kx

  where k = spring constant and x = displacement.
• Potential Energy stored:

  U = (1/2)kx²

7. Conservation of Mechanical Energy

• In the absence of non-conservative forces (like friction), the total mechanical energy (K.E. + P.E.) of a system remains constant.
• Mathematically:

  K.E. + P.E. = Constant

8. Conservative and Non-Conservative Forces

• Conservative Forces: Work done is independent of path (e.g., gravitational force, spring force).
• Non-Conservative Forces: Work done depends on path (e.g., friction, air resistance).

9. Motion in a Vertical Circle

• Analyzing an object (like a pendulum) moving in a vertical circle involves conservation of energy and forces acting at different points.
• At the topmost point:
  • Minimum speed to maintain circular motion:

    v = √(gR)

    where g = gravitational acceleration and R = radius.

10. Elastic and Inelastic Collisions

• Elastic Collision:
  • Both momentum and kinetic energy are conserved.
  • Example: Ideal collisions between hard spheres.
• Inelastic Collision:
  • Momentum is conserved, but kinetic energy is not.
  • Some energy is converted into heat, sound, deformation, etc.

11. Collisions in One and Two Dimensions

• One-Dimensional Collision (Head-on collision):
  • Analyze using conservation of momentum and kinetic energy (if elastic).
• Two-Dimensional Collision:
  • Momentum conservation applied separately along x and y axes.
  • Common example: Collision of billiard balls.