Understanding Force Systems Classification

Forces are fundamental in mechanics, representing pushes or pulls on an object. To analyze the effect of multiple forces acting on an object, we classify them based on their arrangement in space and their points of application.

The question asks about forces that meet at one point and have their lines of action in different planes. Let's break down the classification terms:

• Concurrent Forces: Forces whose lines of action all pass through a single common point. This point may or may not be on the body itself.
• Non-concurrent Forces: Forces whose lines of action do not meet at a single common point.
• Coplanar Forces: Forces whose lines of action lie in the same plane.
• Non-coplanar Forces: Forces whose lines of action lie in different planes.

Combining Classifications to Define Force Systems

Based on whether forces are concurrent or non-concurrent, and whether they are coplanar or non-coplanar, we can define different types of force systems:

• Coplanar Concurrent Forces: Forces acting in the same plane and meeting at a single point. Example: Forces acting on a joint in a 2D truss.
• Coplanar Non-concurrent Forces: Forces acting in the same plane but not meeting at a single point. Example: Forces acting on a beam.
• Non-coplanar Concurrent Forces: Forces acting in different planes but meeting at a single point. Example: Forces acting on the apex of a tripod supporting a camera.
• Non-coplanar Non-concurrent Forces: Forces acting in different planes and not meeting at a single point. Example: Forces acting on a rigid body in 3D space, such as a car.

Analyzing the Question's Description

The question describes forces that:

1. Meet at one point: This means they are concurrent forces.
2. Have their line of action in different planes: This means they are non-coplanar forces.

Combining these two characteristics, the forces are non-coplanar concurrent forces.

Evaluating the Options

Let's look at how each option matches the description:

• Intersecting forces: This is a general term. Concurrent forces are a type of intersecting force system (they intersect at one point), but this term doesn't specify the plane condition.
• Non-coplanar non-concurrent forces: These forces are in different planes, but they do not meet at a single point. This does not match the "meet at one point" condition.
• Coplanar non-concurrent forces: These forces are in the same plane, but they do not meet at a single point. This fails on both the "different planes" and "meet at one point" conditions.
• Non-coplanar concurrent forces: These forces are in different planes AND meet at a single point. This exactly matches the description given in the question.

Therefore, the forces which meet at one point and have their line of action in different planes are called non-coplanar concurrent forces.

Revision Table: Force Systems

Additional Information on Concurrent and Non-coplanar Forces

Understanding non-coplanar concurrent forces is important in three-dimensional mechanics. When analyzing such systems, you often use vector notation to represent the forces and their directions in 3D space.

The equilibrium conditions for a system of non-coplanar concurrent forces are that the vector sum of all forces is zero. This means the sum of the force components along the x, y, and z axes must all be zero:

\(\sum \vec{F} = 0\)

Which expands to:

\(\sum F_x = 0\)

\(\sum F_y = 0\)

\(\sum F_z = 0\)

Since the forces are concurrent, they do not produce a net moment about the point of concurrency. Therefore, you only need to satisfy the force equilibrium equations to analyze a non-coplanar concurrent force system in equilibrium.