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A system of connected rigid bodies is in equilibrium, provided the virtual work done by all the external forces and couples acting on the system is _______ for each independent virtual displacement of the system.
- a)One
- b)zero
- c)infinite
- d)twice the external force
Correct answer is option 'B'. Can you explain this answer?
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A system of connected rigid bodies is in equilibrium, provided the vir...
Equilibrium of a System of Connected Rigid Bodies
Introduction
When a system of connected rigid bodies is in equilibrium, it means that the system is not experiencing any net external forces or couples that would cause it to accelerate or rotate. In other words, the system is in a state of balance.
Virtual Work
Virtual work is a concept used to analyze the equilibrium of a system by considering the work done by external forces and couples. It involves considering virtual displacements, which are hypothetical, infinitesimally small displacements applied to the system.
Equilibrium Condition
For a system of connected rigid bodies to be in equilibrium, the virtual work done by all the external forces and couples acting on the system must be zero for each independent virtual displacement of the system. This condition is based on the principle of virtual work, which states that the work done by external forces and couples during a virtual displacement is equal to zero in equilibrium.
Explanation
In the given question, the correct answer is option 'B', which states that the virtual work done by all the external forces and couples acting on the system is zero for each independent virtual displacement of the system.
This means that in equilibrium, the work done by the external forces and couples is balanced and cancels out each other. The system remains at rest or in a state of uniform motion.
If the virtual work done by the external forces and couples was non-zero for a virtual displacement, it would imply that there is a net external force or couple acting on the system, causing it to accelerate or rotate. This would violate the condition of equilibrium.
Conclusion
In conclusion, for a system of connected rigid bodies to be in equilibrium, the virtual work done by all the external forces and couples acting on the system must be zero for each independent virtual displacement of the system. This condition ensures that the system is balanced and not experiencing any net external forces or couples.
Introduction
When a system of connected rigid bodies is in equilibrium, it means that the system is not experiencing any net external forces or couples that would cause it to accelerate or rotate. In other words, the system is in a state of balance.
Virtual Work
Virtual work is a concept used to analyze the equilibrium of a system by considering the work done by external forces and couples. It involves considering virtual displacements, which are hypothetical, infinitesimally small displacements applied to the system.
Equilibrium Condition
For a system of connected rigid bodies to be in equilibrium, the virtual work done by all the external forces and couples acting on the system must be zero for each independent virtual displacement of the system. This condition is based on the principle of virtual work, which states that the work done by external forces and couples during a virtual displacement is equal to zero in equilibrium.
Explanation
In the given question, the correct answer is option 'B', which states that the virtual work done by all the external forces and couples acting on the system is zero for each independent virtual displacement of the system.
This means that in equilibrium, the work done by the external forces and couples is balanced and cancels out each other. The system remains at rest or in a state of uniform motion.
If the virtual work done by the external forces and couples was non-zero for a virtual displacement, it would imply that there is a net external force or couple acting on the system, causing it to accelerate or rotate. This would violate the condition of equilibrium.
Conclusion
In conclusion, for a system of connected rigid bodies to be in equilibrium, the virtual work done by all the external forces and couples acting on the system must be zero for each independent virtual displacement of the system. This condition ensures that the system is balanced and not experiencing any net external forces or couples.
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Community Answer
A system of connected rigid bodies is in equilibrium, provided the vir...
- Virtual work is the work done by a real force acting through a virtual displacement or a virtual force acting through a real displacement.
- A virtual displacement is any displacement consistent with the constraints of the structure, i.e., that satisfy the boundary conditions at the supports.
- A virtual force is any system of forces in equilibrium.
- The principle of virtual work states, for bodies in equilibrium, for a small arbitrary displacement, the total work done by the system is zero.
- In this method, the system is displaced through a small amount about a reference point and the work done by all the forces about the reference point is summed to zero to find the unknown reactions if any.
∴ The principle of virtual work states that, for a body to be in equilibrium, the virtual work should be zero.
⇒ A system of connected rigid bodies is in equilibrium, provided the virtual work done by all the external forces and couples acting on the system is zero for each independent virtual displacement of the system.
⇒ A system of connected rigid bodies is in equilibrium, provided the virtual work done by all the external forces and couples acting on the system is zero for each independent virtual displacement of the system.
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A system of connected rigid bodies is in equilibrium, provided the virtual work done by all the external forces and couples acting on the system is _______ for each independent virtual displacement of the system.a)Oneb)zeroc)infinited)twice the external forceCorrect answer is option 'B'. Can you explain this answer?
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