Work, Energy and Power — Class XI Physics Notes | eduPhysics
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Class XI · Chapter 05

Work, Energy and Power

Three everyday words, given exact physics definitions — and the conservation law that lets you skip force calculations entirely for a huge range of problems.

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1Work Done by a Constant Force

In physics, "work" has a precise meaning, narrower than its everyday use: force alone doesn't do work — displacement in the direction of that force does.

Work
W = F · d = Fd cos θ
θ = angle between the force and the displacement. Push a wall as hard as you like — if it doesn't move, you've done zero work on it, however tiring it feels.
Sign Matters Work can be positive (force helps the motion), negative (force opposes it, like friction), or zero (force perpendicular to displacement — like gravity on a horizontally-moving object).

2Work Done by a Variable Force

Many real forces (springs, gravity over large distances) change with position, so the simple W = Fd formula doesn't directly apply. Instead, work is found by summing up tiny contributions over each small displacement.

Work by a Variable Force
W = ∫ F dx
Geometrically, this is the area under a force-versus-position graph — a useful way to estimate work even without doing the integral explicitly.

3The Work-Energy Theorem

Work-Energy Theorem
Wnet = ΔKE = KEf − KEi
The total work done by all forces on an object exactly equals its change in kinetic energy. This single relation connects force-based mechanics to energy-based mechanics, and often solves problems far faster than working through Newton's laws directly.

4Kinetic Energy

Kinetic Energy
KE = ½ m v²
The energy an object has purely because of its motion. Note it scales with the square of speed — doubling speed quadruples kinetic energy, which is exactly why higher speeds are disproportionately more dangerous in a collision.

5Potential Energy

Potential energy is stored energy associated with position or configuration — available to be converted into kinetic energy (or other forms) later. It only makes sense for conservative forces (gravity, spring force), where the work done depends only on start and end position, never on the path taken.

Gravitational Potential Energy (near Earth's surface)
U = mgh
h is height measured from any chosen reference level — only differences in potential energy are physically meaningful, not its absolute value.

6Conservation of Mechanical Energy

Conservation of Mechanical Energy
KE + PE = constant (when only conservative forces act)
A dropped ball trades potential energy for kinetic energy in exact lockstep, with the sum unchanged throughout the fall — this is often the fastest route to a problem's answer, skipping the need to work out acceleration or time at all. The moment a non-conservative force like friction or air resistance gets involved, mechanical energy is no longer conserved (though total energy, including heat, always still is).

7Potential Energy of a Spring

A stretched or compressed spring stores elastic potential energy, following Hooke's Law: F = −kx (the restoring force is proportional to displacement from natural length, and opposes it).

Elastic Potential Energy
U = ½ k x²
k = spring constant, x = displacement from the spring's natural (unstretched) length. Since this depends on x², the energy stored quadruples if you double the compression or extension.

8Power

Average and Instantaneous Power
P = W/t (average), P = dW/dt (instantaneous)
Power measures how quickly work is done or energy is transferred — the same amount of work done faster means more power, even though the total energy delivered is identical.
Power in Terms of Force and Velocity
P = F · v
Especially useful for problems involving engines or motors moving at a given speed against a known resistive force.

9Collisions

Collisions always conserve total momentum (Chapter 4) — but kinetic energy is a different story.

  • Elastic collision: both momentum and kinetic energy are conserved — the objects bounce off cleanly, with no energy lost to heat, sound, or deformation. A close real-world approximation is billiard balls colliding.
  • Inelastic collision: momentum is conserved, but kinetic energy is not — some is converted to other forms during the collision (heat, sound, permanent deformation).
  • Perfectly inelastic collision: the extreme case — the colliding objects stick together and move as one afterward, losing the maximum possible kinetic energy while still conserving momentum.
Special Case Worth Remembering In a 1D elastic collision between two objects of equal mass, where one is initially at rest, the objects simply exchange velocities — the moving object stops, and the stationary one takes off at the original speed.

Formula Summary

Work
W = Fd cosθ
Work-Energy Theorem
W_net = ΔKE
Kinetic Energy
KE = ½mv²
Gravitational PE
U = mgh
Spring PE
U = ½kx²
Mechanical Energy
KE + PE = const
Power
P = W/t = F·v

Solved Examples

Example 1 · Work-Energy Theorem

A 2 kg block moving at 3 m/s has 20 J of work done on it by a net force. Find its final speed.

Solution: W = ΔKE = ½m(vf² − vi²) → 20 = ½×2×(vf² − 9) = vf² − 9.

vf² = 29, so vf ≈ 5.39 m/s.

Example 2 · Elastic Collision, Equal Masses

A 1 kg ball moving at 4 m/s collides elastically, head-on, with a stationary 1 kg ball. Find both velocities after the collision.

Solution: Since the masses are equal and the collision is elastic, the balls simply exchange velocities.

The first ball comes to rest (v₁′ = 0); the second ball moves off at the original speed (v₂′ = 4 m/s).

Quick Check

1. The work done by a force acting exactly perpendicular to an object's displacement is:
Maximum
Negative
✓ Zero (correct)
Equal to the force magnitude
2. In a perfectly inelastic collision, which quantity is conserved?
Kinetic energy only
✓ Momentum only (correct)
Both momentum and kinetic energy
Neither
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Laws of Motion

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System of Particles and Rotational Motion

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