Equilibrium of a Particle in 2D & 3D

Study Notes

A particle is in equilibrium when the vector sum of all forces acting on it is zero.
The equations of equilibrium ensure that the net force along each axis (x, y, and z) equals zero.
The three scalar equations of equilibrium are: ΣFx = 0, ΣFy = 0, and ΣFz = 0.
These equations are valid for any point in equilibrium and can be used to solve for up to three unknowns.
Free body diagrams are essential for visualizing the forces acting on a particle and applying the equations of equilibrium.

Example 1: The text provides a scenario involving forces acting on a particle in 2D space with a known angle. The solution involves applying the equations of equilibrium to find the unknown forces.
Example 2: This example showcases a scenario with forces acting on a particle in 2D space. The solution involves using the equations of equilibrium to determine the unknown force components.
Example 3: This example involves finding the forces acting on a particle in 2D space, where the particle is at equilibrium. The solution involves applying the equations of equilibrium to determine the unknown values.
Example 4: This example showcases a scenario in 3D where forces are acting on a particle at equilibrium. The solution involves using the equations of equilibrium in all three dimensions to calculate unknown force components.
Example 5: This example focuses on a particle in 3D space experiencing multiple forces. The solution utilizes the equations of equilibrium to determine the unknown force magnitudes and angles.
Example 6: This example involves a particle in 2D space subjected to multiple forces. The solution relies on drawing a free body diagram to visualize the forces acting on the particle and using the equations of equilibrium to find unknown forces.