Static Equilibrium and Triangle of Forces

M

1

(kg)

10

M

3

(kg)

10

M

2

(kg)

10

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

F

i

whose norm is given by



F

i

=

M

i

g

, where

M

i

is the mass attached to the string and

g=9.81m/

2

s

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

F

i

. You can change the magnitude of each force by changing the corresponding mass

M

i

and observing how the directions of the forces adjust to maintain a triangle.