In this question, we build a truss — a supporting structure for something like a roof. These work by taking on a force (often a straight-down gravitational force, but sometimes it is angled) and distributing it to a couple of points attached to something that is very solid. A point that cannot move (e.g. at A below) experiences a force directly along the beam attached to it. A point that can move around, but is sitting on a surface due to gravity (e.g. at B) will experience a force in reaction to the gravitational pull — so the vector points straight up.

• A triangular truss is to be built. It will consist of a horizontal member AB, with A attached to a wall and B supported on a roller at a point 20 m away. The third joint, C, needs to be 10 m above AB. It will be subjected to 500 kN of force horizontally in the direction from A to B. If C can be placed above any point along the member AB, where should it be put to minimize the largest force on the truss?

• Repeat the question above, but this time with the force on C being angled down by 30°.