To illustrate a vector construction with 3 vectors (3 forces).The area of Mechanics that studies solids at rest is called Statics.Ĭlick and drag the points A and B to modify the position of the dynamometers. This corresponds to Newton’s Law of Inertia: “All bodies will maintain their state of rest or of uniform motion in a straight line that they are already in, unless acted upon by a force that would cause them to change their state of motion.” divide the second equation by the first to give tan4.258.113,0.524 (to 3d.p.). Objectives: To determine required forces for equilibrium condition of concurrent force. To solve problems about particles in equilibrium we resolve the forces. The resulting moment has three components. , F x,, F y, and F z are components of the force. This state of equilibrium continues as long as the sum of the forces applied to the body remains zero. where is the vector sum of all forces acting on the particle. Here,, r x,, r y, and r z are components of the vector describing the distance from the point of interest to the force. 002 Components of forces with given slope up 004 Components of a 3D force with given angles. P is the point of intersection and the vector sum of the forces is zero at all times. that the weighted position vectors relative to this point sum to zero. In the animation, the forces are contained in the plane Pxy. In physics, the center of mass of a distribution of mass in space is the unique point where. The vector sum of these forces is equal to the zero vector.The lines of action are convergent (they cross at the same point) Coordinate direction angles (used for 3D models): - alpha ( ) - against the x-axis )( cos - beta ( ) - against the y-axis ( )cos - gamma ( )- against the z-axis )( cos Unit-Force Vectors - used to calculate a Force along a material of specific length, such as a rod/rope.The lines of action are coplanar (in the same plane).A solid body submitted to three forces whose lines of action are not parallel is in equilibrium if the three following conditions apply :

Equilibrium 3d vectors