File:Trigonometric forces acting on a piano lid.png

English: Force vectors on a piano lid. The prop resists the moment of the lid tending to turn on its hinge. The value of the moment is MGR.cosØ where M=mass of lid, G = gravitational constant, R = distance from hinge to center of gravity of lid, Ø = angle of elevation of lid. The force P exerted by the prop on the lid may have two components: P.sine@ and P.cos@ where @ is the angle between the prop and the lid. P.cos@ is a force parallel to the underside of the lid and, if present, it will cause the top of the prop to slide against the lid unless this is prevented by a block, notch or hole. P.sine@ counteracts the lid turning moment which implies that MGR.cosØ = PS.sine@ where S = distance from hinge to prop contact. The situation @ = 90 degrees is interesting because P.cos(90 degrees) = 0 meaning the prop has no tendency to slide against the lid. Nothing here requires R = S so the lid angle Ø can be chosen by the prop length.