Virtual work of constraint forces

In summary: The issue with the model of a rigid body is that it assumes that the constraints can exert forces without any deformation of the body. This is not entirely realistic as in the real world, constraint forces only exist during deformations of the body. Therefore, the concept of virtual work may not accurately represent the behavior of a rigid body.
  • #1
tomjones11
1
0
On a rigid body we usually use the formula δL=F*δP to calculate virtual work. My problem is about the force. This kind of force exists only before the contact. If I imagine a movement δP of the constrained body outside ,in the free space, I will have δL≥0 but as soon as P moves the force F disappears (and δL=0). Removing the contact, even the force should be removed. We can't have movement and force together
I think the problem is related to the model of rigid body. I don't think a rigid body can exert constraint forces without some trick in the model. If it is rigid, it can't be deformed and so it can't return work. In real world constraint force exist only during the deformations of the body, but here?
I don't understand how I should treat the model of the rigid body in this case.
Thanks (and sorry for my english)
 
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  • #2
The concept of virtual work is based on the idea that the forces applied to a system can be considered to be acting instantaneously at an arbitrarily small displacement δP. The force F is assumed to remain constant over this small displacement and can therefore be used to calculate the work done by the system. In the case of a rigid body, the force F is assumed to act instantaneously due to the constraints imposed by the body itself. Therefore, when considering a displacement δP in the free space outside of the rigid body, there will be no force acting on the system and therefore no work done (δL=0).However, if the rigid body is subjected to external forces, such as those generated by contact with another object, then the force F will not disappear upon moving the body. In this case, the forces must be taken into account when calculating the work done, and the equation δL=F*δP can be used to calculate the work done by the system.
 

Related to Virtual work of constraint forces

1. What is virtual work of constraint forces?

Virtual work of constraint forces is a concept in classical mechanics that describes the work done by a system of forces that keep an object constrained within a specific path or motion. It is used to analyze the equilibrium state of a system and determine the forces acting on it.

2. How is virtual work of constraint forces calculated?

The virtual work of constraint forces is calculated by taking the dot product of the constraint forces and the virtual displacements of the object. This can be represented mathematically as W = F·δx, where W is the virtual work, F is the constraint force, and δx is the virtual displacement.

3. What is the significance of virtual work of constraint forces?

The virtual work of constraint forces is significant because it allows us to determine the stability of a system and understand the forces that keep an object in equilibrium. It also helps in the design and analysis of mechanical systems, such as bridges and buildings.

4. Can virtual work of constraint forces be negative?

Yes, virtual work of constraint forces can be negative. This occurs when the constraint forces and virtual displacements are in opposite directions. A negative virtual work indicates that the object is moving away from the equilibrium state and the constraint forces are not strong enough to keep it in place.

5. How is virtual work of constraint forces related to potential energy?

Virtual work of constraint forces is related to potential energy through the principle of virtual work. This principle states that the virtual work done by constraint forces is equal to the change in potential energy of the system. Therefore, the virtual work of constraint forces can be used to calculate the potential energy of a system in equilibrium.

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