Analysis: Two-force objects

Before we look at centres of gravity, we need to see why our suspension method works. Here is an FBD of the triangular shape in this suspension test. It assumes there is no friction in the pin. It’s a two-force object, forces at two points only, and no couples. Can you see that the forces must be co-linear - that is, along the same line - opposite, and equal? For a formal proof, consider moments about the suspension point. With no friction at the pin, equilibrium tells us that this moment must be zero. The line of action of the weight must go through the pin, because force times moment arm must be zero, and force is equal to the weight.

Vertical equilibrium tells us that the forces must be equal and opposite. What happens if we have a couple acting? We saw this in our experiment when we pushed the pin in hard, so that it gripped the cardboard. It’s no longer a two-force object, and the forces need not be co-linear. Two-force objects appear in many engineering situations, and if you recognise them, it can be a great help. For example, trusses - like the ones you find in roofs - they can be considered to be made up of two-force objects, which makes design calculations easier. Now let’s interpret our experiments on finding the position of a centre of gravity.