What happens when three coplanar non-parallel forces are in equilibrium?

Analysis

The question asks for the geometric condition that must be satisfied for three coplanar (acting on the same plane) and non-parallel forces to be in equilibrium.

Concept Explanation

In physics, for an object to be in equilibrium under the influence of forces, two conditions must be met:

1. Translational Equilibrium: The vector sum of all forces must be zero ($\sum F = 0$).
2. Rotational Equilibrium: The sum of the moments (torques) about any point must be zero ($\sum \tau = 0$).

When you have three coplanar, non-parallel forces acting on a body, the only way to ensure there is no rotation (the body doesn't spin) is if the lines of action of all three forces intersect at a single common point. If they did not meet at a point, the forces would create a resultant moment, causing the object to rotate.

Step-by-Step Solution

1. Visualize the forces: Imagine three forces, $F_1$, $F_2$, and $F_3$, acting on an object in the same plane.
2. Check for rotation: If the lines of action of $F_1$ and $F_2$ intersect at a point $P$, the object will rotate around $P$ unless the third force $F_3$ also passes through that same point $P$.
3. Apply the Triangle Law: When three forces are in equilibrium, they can be represented by the sides of a closed triangle taken in order. For this to hold true for non-parallel forces, their lines of action must be concurrent (meet at a single point).
4. Evaluate the options: • A is incorrect because the forces are explicitly stated as "non-parallel." • B and C are incorrect because forces are vector quantities requiring both magnitude and direction. • D correctly describes the condition for rotational equilibrium for three coplanar forces.

Conclusion

Exam Tip

Whenever you see a question about "three forces in equilibrium," immediately think of the Triangle of Forces. If the forces are coplanar and non-parallel, they must be concurrent (meeting at a point) to prevent the object from rotating. This is a classic JAMB concept, so keep it in your memory!