IAL MECHANICS 2 – WORK & ENERGY

IAL M2-Work , Energy & Power

1. The Work-Energy Principle

The Work-Energy Principle links the net forces acting on an object directly to its change in speed.

The Core Rule:

The net work (W_net) done by all forces combined equals the object's change in kinetic energy (ΔKE).

W_net = ΔKE = KE_f - KE_i = ½mv_f² - ½mv_i²

Positive Net Work (W_net > 0): Energy is added. The object speeds up.
Negative Net Work (W_net < 0): Energy is removed (e.g., braking). The object slows down.
Zero Net Work (W_net = 0): Kinetic energy stays constant. The object maintains a steady speed.

2. Conservative vs. Non-Conservative Forces

Forces are categorized by how they handle the total mechanical energy of a system.

A. Conservative Forces

These forces conserve mechanical energy. Instead of wasting energy as heat, they store it as potential energy which can be fully recovered later.

Path Independence: The work done depends only on the starting and ending points.
Closed Loops: Returning to the starting point means the net work done is exactly zero.
Examples: Gravity, ideal spring force, electrostatic force.

B. Non-Conservative Forces

These forces permanently dissipate mechanical energy from the system, converting it into heat or sound.

Path Dependency: The longer or more winding the path, the more work is done.
Examples: Friction, air resistance (drag), tension, human push/pull.

3. Why Gravitational Potential Energy (GPE) "Disappears"

You don't see GPE on the work side of the baseline formula because its effect is already accounted for as work done by gravity.

The Logic Split:

You can treat gravity as an external force doing work, OR as stored internal potential energy—never both at once, or you double-count it:

W_gravity + W_other = ΔKE
Since W_gravity = -ΔGPE → (−ΔGPE) + W_other = ΔKE
Rearranging gives: W_other = ΔKE + ΔGPE (Conservation of Mechanical Energy)

💡 Summary Cheat Sheet

Concept	The Big Idea	Key Formula
Work-Energy	Total work equals change in kinetic speed.	W_net = ΔKE
Conservative	Path independent; energy is perfectly stored.	W_loop = 0
Non-Conservative	Path dependent; energy is lost as heat.	W_f = −f_k • d
GPE Rule	Count as work OR potential energy, not both.	W_g or ΔGPE = mgh