Forces, density and pressure

Learning objectives

Define the moment of a force and the torque of a couple, and locate the centre of gravity at which the whole weight of a body can be taken to act.

State the principle of moments and apply the two conditions for equilibrium — zero resultant force and zero resultant torque — to beams, ladders and other rigid bodies.

Draw a closed triangle of forces for three coplanar forces in equilibrium and use it, by scale drawing or trigonometry, to find an unknown force.

Define density and pressure, and derive and use Δp = ρgΔh for the change of pressure with depth in a fluid at rest.

Explain why a submerged object feels an upthrust — the fluid pressure on its lower surface exceeds that on its upper surface — and calculate the upthrust as ρgV, the weight of fluid displaced.