Outcomes for a body acted upon by coplanar, non-concurrent forces In elementary engineering mechanics, if several forces lie in one plane but their lines of action do not meet at a single point (non-concurrent), what motions or states can the body exhibit under such a system?

Introduction / Context:
Coplanar non-concurrent force systems are common in structures and machines. Because the forces do not intersect at a single point, their combined effect can be a pure force (resultant through the center of mass), a pure couple (net moment only), a general force-couple system, or zero (equilibrium). Understanding all possible outcomes is essential for analyzing beams, frames, and rigid bodies.

Given Data / Assumptions:

• Forces lie in a single plane (coplanar).
• Lines of action are not concurrent.
• Rigid body assumption; small deformations are neglected.
• No frictional complications unless implied by the net effect.

Concept / Approach:

Any system of forces on a rigid body can be reduced to an equivalent resultant force R acting at a chosen reference point, plus a resultant moment M at that point. Special cases arise: R = 0 with M ≠ 0 gives a pure couple (tendency to rotate); M = 0 with R ≠ 0 gives pure translation; both nonzero give general plane motion; both zero give equilibrium.

Step-by-Step Solution:

Verification / Alternative check:

Replace the system by a single force at the center of mass and a couple. Kinematics of rigid bodies confirms the motion classes correspond exactly to the force–moment combinations above.

Why Other Options Are Wrong:

Each individual option lists only one possible outcome; in reality, all listed outcomes are possible depending on ΣF and ΣM. Hence only “All of the above” is comprehensive and correct.

Common Pitfalls:

Assuming non-concurrency always causes rotation; forgetting that geometry and magnitudes can cancel to yield equilibrium; ignoring that a pure couple can exist with zero net force.

Final Answer:

All of the above