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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
KE
0 J
PE
156.96 J
Total E
156.96 J

Parameters

kg
m/s²
m
m
m

Energy Distribution

Kinetic0 J
Potential156.96 J
Total156.96 J
Energy Stack
PE

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.

KE1+PE1=KE2+PE2KE_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.

KE1+PE1=KE2+PE2+WfrictionKE_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=12mv2KE = \frac{1}{2}mv^2

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

PE=mghPE = 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.

PEspring=12kx2PE_{\text{spring}} = \frac{1}{2}kx^2
Variables
  • kk is the spring constant (stiffness, in N/m)
  • xx is the compression or extension distance (in m)

A stiffer spring (larger kk) or greater compression (larger xx) 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.

Wnet=ΔKE=KEfKEiW_{\text{net}} = \Delta KE = KE_f - KE_i

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

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

where μ\mu is the friction coefficient and dd is the distance traveled along the surface.

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