The Law of Conservation of Energy states that the total energy of an isolated system remains constant. Energy can change form, but the total amount never changes.

Audio Explanation

Prefer to listen? Here's a quick audio summary of the conservation of energy.

Visual Representation

A diagram of a pendulum swinging, showing Total Mechanical Energy remaining constant while Potential and Kinetic energy fluctuate. Max PE KE = 0 Max KE Min PE PE_top = KE_bottom

Mechanical Energy

In many physics problems, we focus on Mechanical Energy ($E_{me}$), which is the sum of an object’s kinetic and potential energy.

\[E_{me} = KE + PE\]

If there are no non-conservative forces (like friction or air resistance), the mechanical energy at any point ($1$) is equal to the mechanical energy at any other point ($2$):

\[KE_1 + PE_1 = KE_2 + PE_2\]

Non-Conservative Forces

When friction is present, it does negative work on the system. This energy isn’t “gone”—it’s just converted into Thermal Energy (heat).

In these cases, the equation becomes: \(KE_1 + PE_1 + W_{ext} = KE_2 + PE_2\) (Where $W_{ext}$ is usually negative work done by friction)

Interactive Conservation Simulator

Adjust the friction and initial height of the block. Watch how the total energy stays the same (the height of the total energy bar), even as the proportions of Kinetic, Potential, and Thermal energy shift.

Energy Transformation Lab

None

Potential:

Kinetic:

Thermal:

Problem Solving Steps

Using energy conservation is often much easier than using $F = ma$. Follow these steps:

  1. Identify Two Points: Choose a “Start” and an “End.”
  2. List Energy Types: At each point, ask: “Is it moving ($KE$)?” and “Is it high up ($PE$)?”.
  3. Check for Friction: Is there a surface or air resistance doing work?
  4. Set Up Equation: $KE_i + PE_i = KE_f + PE_f + \text{Thermal}$.

Interactive Match: Energy Scenarios

Can you identify where the energy is going in these common situations?

Why Should I Care?

Conservation of energy is the “Ultimate Law.” It tells us:

  • Why “Perpetual Motion Machines” are impossible.
  • How to calculate the speed of a roller coaster at the bottom of a loop.
  • How hydroelectric dams turn the position of water into electricity for your phone.

💡 Quick Concept Check:

A ball is dropped from a height of 10 meters. If we ignore air resistance, how does its Kinetic Energy at the 5-meter mark compare to its initial Potential Energy at 10 meters?

Click to Reveal Answer
At the 5-meter mark (exactly halfway down), the ball has lost half of its initial Potential Energy. Because energy is conserved, that "lost" potential energy has been converted into Kinetic Energy. Therefore, its $KE$ at 5 meters is exactly **half** of its initial $PE$ at 10 meters.
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