Forces involved in principle of virtual work

In summary, the principle of virtual work states that for a system in equilibrium, the work done by external and internal forces during virtual displacements is zero. Key forces involved include applied forces, constraint forces, and reaction forces, which interact during virtual displacements to maintain equilibrium. The principle is used in mechanics and structural analysis to derive equations of motion and analyze stability, emphasizing the relationship between force systems and virtual displacements in a mechanical context.
  • #1
phantomvommand
282
39
Homework Statement
See picture below
Relevant Equations
Work done = Fd
Screenshot 2024-05-28 at 12.46.18 AM.png

The answer is as such: There’s only one way for the system to move: the rectangle can deform into a parallelogramso that the left horizontal arm moves up, and the right horizontal arm moves down by thesame amount. Then the total virtual work done on the scale by the weights is zero, so thesystem can be in equilibrium no matter where on the arms the weights are placed.

While I can understand this, this assumes that there is 0 work done by reaction forces at the joints, so the net work done on the system is entirely due to gravity. How fair is this assumption?
 
Physics news on Phys.org
  • #2
The forces in the joints are internal forces of the system. At a joint where two bars meet, the forces that the two bars exert on each other are action-reaction forces.
 
  • Like
Likes phantomvommand
  • #3
TSny said:
The forces in the joints are internal forces of the system. At a joint where two bars meet, the forces that the two bars exert on each other are action-reaction forces.
Oh right, forgot about that! Thanks!
 

FAQ: Forces involved in principle of virtual work

What is the principle of virtual work?

The principle of virtual work states that for a system in equilibrium, the total virtual work done by the forces acting on the system during a virtual displacement is zero. This principle is used in mechanics to analyze structures and mechanical systems by considering the work done by external and internal forces without needing to account for the actual motion of the system.

What types of forces are considered in the principle of virtual work?

The principle of virtual work considers both external forces, such as applied loads and reactions at supports, and internal forces, which are the forces that occur within the system due to interactions between its components. These forces include tension, compression, and shear forces in structural elements.

How does virtual work apply to rigid body equilibrium?

In rigid body equilibrium, the principle of virtual work can be applied to determine the conditions under which a rigid body remains at rest. By analyzing the virtual work done by all forces during a hypothetical small displacement, one can derive equations that represent the balance of forces and moments acting on the body, confirming that the sum of virtual work is zero.

Can the principle of virtual work be applied to non-conservative forces?

Yes, the principle of virtual work can be applied to non-conservative forces; however, one must account for the work done by these forces when calculating the total virtual work. Non-conservative forces, like friction, can affect the equilibrium conditions, and their work must be included in the analysis to ensure accurate results.

What are the advantages of using the principle of virtual work in engineering?

The principle of virtual work simplifies the analysis of complex systems by reducing the need for detailed motion analysis. It allows engineers to derive equilibrium conditions easily, apply it to various types of structures and systems, and provides a powerful tool for solving problems in statics and dynamics without requiring extensive calculations of forces and displacements.

Back
Top