Static Equilibrium and Triangle of Forces

Forces are vectors, which means that they have both a magnitude and direction. To illustrate this concept, this Demonstration shows a mechanical system composed of three weights connected by strings and pulleys. The equilibrium position can be found by analyzing the forces acting on the central knot. Each force is a vector whose norm is given by , where is the mass attached to the string and is the acceleration of gravity. According to Newton's second law, at static equilibrium the vector sum of all the forces acting on the central knot should be zero. This is illustrated in the inset by constructing a triangle of forces from the three vectors . You can change the magnitude of each force by changing the corresponding mass and observing how the directions of the forces adjust to maintain a triangle.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Static equilibrium cannot be attained for every set of values of the masses , , and . This is related to the fact that the sides , , of a triangle must satisfy the triangle inequality . In practice, even more stringent limits must be put on the values of the masses to avoid any accident like the central knot passing over the pulleys, or the weight falling below the visible area. In this Demonstration, the masses and are restricted to avoid such an accident and automatically readjusted if necessary.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+