# Virtual work and constraint forces

• I
• Ahmed1029
In summary, the conversation discusses the principle of virtual works and its application to a system of constrained particles. The speaker is considering a system of N particles with less than 3N generalized coordinates, and wants to calculate the virtual work done by constraint forces on a single particle that is virtually displaced. They question whether this work can be non-zero, as the book they are reading asserts that the net virtual work of all particles must be zero. The principle of virtual works states that the total virtual work is indeed zero.
Ahmed1029
Suppose I'm considering a system of N particles that are constrained in their possible motions and so there are less that 3N generalized coordinates. Suppose now I perform a virtual displacement on one particle, which due to some constraints might force some other particles to more virtually with it, like the case of an atwood machine. I now want to calculate the virtual work done by the constraint forces on the particles that move as a corrolary to the movement of this single particle plus the work done on this particle itself, can I get a non-zero result? I'm asking because the book I'm reading assers that the virtual work done by virtually moving ALL the particles has to be zero, and not necessarily the work done to move a single particle has to be zero.

vanhees71 and Ahmed1029

## 1. What is virtual work?

Virtual work is a concept in mechanics that describes the work done by a force on a system that undergoes a virtual displacement. It is a theoretical tool used to analyze the behavior of a system without having to consider the actual forces and displacements involved.

## 2. How is virtual work related to constraint forces?

Virtual work is closely related to constraint forces because it allows us to analyze systems that are subject to constraints, such as objects moving on a curved surface or connected by a rigid rod. By considering virtual displacements, we can determine the forces exerted by the constraints on the system.

## 3. What is the principle of virtual work?

The principle of virtual work states that the work done by all the forces acting on a system undergoing a virtual displacement is equal to zero. This means that in a state of equilibrium, the sum of the virtual work done by all the forces must be equal to zero.

## 4. How is virtual work used in engineering and physics?

Virtual work is used in engineering and physics to analyze and solve problems involving constraints and equilibrium. It allows us to simplify complex systems and determine unknown forces or displacements without having to consider the actual forces and displacements involved.

## 5. What are some real-life applications of virtual work and constraint forces?

Virtual work and constraint forces have many real-life applications, such as in structural engineering, where they are used to design and analyze buildings, bridges, and other structures. They are also used in the design of mechanical systems, such as machines and vehicles, to ensure that they are in a state of equilibrium and can function properly.

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