Engineering Mechanics: Statics
Lami's Theorem Formula
P/sinα = Q/sinβ = R/sinγ
Resultant of Many Forces Formula
R = √((∑Fx)²+(∑Fy)²)
Resultant Formula
R = √(P² + Q² + 2PQcosα)
Force System
a number of forces acting on a body.
Force
a pull or push, which acting on a body changes or tends to change, the state of rest or uniform motion of the body. Measured in Newton (N).
Statics
a science which deals with the action of forces on bodies, the forces being so arranged that they are in equilibrium.
Principle of Transmissibility of a Force
states that if a force acts at any point of a rigid body it may be considered to act at any other point in its line of action provided the point is rigidly connected with the body.
Polygon Law of Forces
states that if any number of forces acting at a point be represented in magnitude and direction by the sides of a polygon taken in order, the forces shall be in equilibrium.
Lami's Theorem
states that if three coplanar forces acting at a point are in equilibrium, each is proportional to the sine of the angle between the other two forces.
Triangle Law of Forces
states that if three forces acting at a point b e represented in magnitude and direction by the sides of a triangle taken in order, they will be in equilibrium.
Parallelogram Law of Forces
states that if two forces acting at a point be represented in magnitude and direction by the adjacent sides of a parallelogram, their resultant is represented in magnitude and direction by the diagonal of the parallelogram passing through that point.
Collinear Forces
the coplanar forces having a common line of action.
Coplanar Forces
the forces acting on a body lying in the same plane.
Resultant of Many Forces
the resultant of any number of forces acting in a body can be calculated by resolving them along two perpendicular directions and then taking the square root of the sum of the square of their components.
Concurrent Forces
the system of forces intersecting at a common point.
Parallel Forces
those forces having parallel lines of action.
Angle at which Resultant Acts Formula
θ = tan⁻¹(Qsinα/P+Qcosα)
Angle in which Resultant of Many Forces Act Formula
θ = tan⁻¹(∑Fy/∑Fx)
