Energy Conservation Explorer

Drag the position slider to move an object along a track and watch the energy bars shift between kinetic and potential energy. Add friction to see energy lost as heat. All calculations run in your browser.

Track

Speed

0 m/s

Height

8 m

0 J

156.96 J

Total E

156.96 J

Parameters

Scenario

Position along track

Mass

Gravity

m/s²

Start height

Valley height

End height

Friction coefficient (μ)

Presets

Energy Distribution

Kinetic0 J

Potential156.96 J

Total156.96 J

Energy Stack

Reference Guide

Conservation of Energy

In a closed system with no friction, the total mechanical energy stays constant. Energy transforms between forms but is never created or destroyed.

KE_1 + PE_1 = KE_2 + PE_2

When friction is present, some mechanical energy converts to thermal energy (heat). The total energy (including heat) is still conserved.

KE_1 + PE_1 = KE_2 + PE_2 + W_{\text{friction}}

Kinetic and Potential Energy

Kinetic energy is the energy of motion. The faster an object moves, the more KE it has.

KE = \frac{1}{2}mv^2

Gravitational potential energy depends on height. The higher an object is, the more PE it has.

PE = mgh

As an object slides down a frictionless hill, PE converts to KE. It speeds up going down and slows down going up.

Spring and Elastic Energy

A compressed or stretched spring stores elastic potential energy. When released, this energy converts to kinetic energy.

PE_{\text{spring}} = \frac{1}{2}kx^2

Variables

$k$ is the spring constant (stiffness, in N/m)
$x$ is the compression or extension distance (in m)

A stiffer spring (larger $k$ ) or greater compression (larger $x$ ) stores more energy and launches the object faster.

The Work-Energy Theorem

The net work done on an object equals its change in kinetic energy. This connects forces to energy.

W_{\text{net}} = \Delta KE = KE_f - KE_i

Friction does negative work (it opposes motion), removing kinetic energy and converting it to heat.

W_{\text{friction}} = -\mu m g \cdot d

where $\mu$ is the friction coefficient and $d$ is the distance traveled along the surface.