Lami's Theorem


  • From: Simon Erskine
  • Date: 17 April 1999
  • Subject: Three forces in equilibrium

A particle has a mass 125grams and hangs on a string.

The particle is pulled aside by a force of 0.75N so that the string makes
an angle of 30 degrees with the vertical.

In what direction is the force applied?

There are two possible answers.

Maths Help suggests:

Diagram of situation

As the diagram shows, we have three forces acting at a point which are in equilibrium.

This is an ideal situation to use Lami's Theorem, which is based on the sine rule.

T/(sin B) = 0.75/(sin 150) = W/(sin A)

Taking the second and third terms gives:

sin A = 0.125*g*sin(150)/0.75

And with g = 9.8:

A = 54.75 or 125.25 degrees
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