Equilibrium of a Particle

Key Concept: Equilibrium of a particle (point mass) means that the net force (balance

of forces) on the particle sums to zero. It is common in engineering to refer to the net

force as the “resultant force”. So for equilibrium of a particle the resultant force must

equal zero. A particle can be thought of as a point mass.

In a Nut Shell: Sum all the forces acting on the particle and set the total to zero.

ΣF = F₁ + F₂ + F₃ + ● ● ● + F_n = 0

Among forces acting on a particle might be gravity and externally applied forces.

The best way to identify the forces on the particle is to construct a free body

diagram of the particle.

The figure below shows a FBD of a particle of mass, m, acted on by three external forces

including F, P, and the gravitational force (the weight of the particle, ˗ mg k .

So for equilibrium of the particle F + P + mg(-k) = 0

where F = F_x i + F_y j + F_z k and P = P_x i + P_y j + P_z k

Therefore F_{x +} P_x = 0, F_{y +} P_y = 0, F_{z +} P_z - mg = 0 for equilibrium (result)

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