The simplest resultant of a spatial parallel force system is always _______.

Explanation:

Spatial parallel force system:

• A spatial parallel force system consists of forces that:
  • Act in parallel directions,
  • Are located in different planes or positions in 3D space.
• Even though the forces are parallel, they do not necessarily pass through the same point, which means:
  • They will not cancel each other out, and
  • Their lines of action will generally cause a resultant moment about a point.

Varignon’s Principle of moments (or the law of moments)

• It states, “If a number of coplanar forces are acting simultaneously on a particle, the algebraic sum of the moments of all the forces about any point is equal to the moment of their resultant force about the same point.”

MO' = R × r = F1 × r1 + F2 × r2

Additional Information

Lami's theorem

• Lami's theorem states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces. Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β, and γ with each other.

Therefore, \(\frac{{{F_A}}}{{sin\alpha }} = \frac{{{F_B}}}{{sin\beta }} = \frac{{{F_C}}}{{sin\gamma }}\)

D’ Alembert's principle:

• It states that a moving body can be brought to equilibrium by adding inertia force to the system whose magnitude is equal to the product of mass and acceleration.
• This inertia force is in the opposite direction to that of acceleration, i.e. F = ma

Polygon Law of Forces

• It is an extension of Triangle Law of Forces for more than two forces, which states, “If a number of forces acting simultaneously on a particle, be represented in magnitude and direction, by the sides of a polygon taken in order; then the resultant of all these forces may be represented, in magnitude and direction, by the closing side of the polygon, taken in the opposite order.”