Principle of Virtual Work topics include: Work, conservative forces, potential energy, equilibrium potential energy criterion and stability configurations. The principle of virtual work (PVW) states that the virtual work of the forces applied to a system is zero when the system is in equilibrium.  The PVW states that the stress, body force, and traction are in equilibrium if and only if the IVW equals the EVW for every virtual displacement field.  The PVW was originally used to examine systems of rigid structures. It is a powerful method for solving problems involving several connected... Show more

Principle of Virtual Work topics include: Work, conservative forces, potential energy, equilibrium potential energy criterion and stability configurations.

The principle of virtual work (PVW) states that the virtual work of the forces applied to a system is zero when the system is in equilibrium. 

The PVW states that the stress, body force, and traction are in equilibrium if and only if the IVW equals the EVW for every virtual displacement field. 
The PVW was originally used to examine systems of rigid structures. It is a powerful method for solving problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. 

The PVW was also known as “the law of lever” and was used by the Greeks, medieval Arabs, and Latins.

The potential energy criterion for equilibrium states that for systems with multiple degrees of freedom, the partial derivative of potential energy with respect to each coordinate must be zero for equilibrium. 

The stability at the equilibrium configuration remains as long as its potential energy is minimum at that configuration.

A stable configuration is a state that is not subject to variation. It is also known as a state of minimum energy.

 

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Engineering Mechanics Practice Test: Principle of Virtual Work

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25 Questions

1. Work done by the couple is best given by___________

dU = MdθdU = M.dθdU = MxdθdU = Mθ

2. What is not the criteria for the equilibrium in potential energy free body diagram?

∑Fy=0∑Fz=0∑F≠0∑Fx=0

3. If the resolved force for the stability of equilibrium configuration or the force which you get as the answer after solving the question is negative, then what does this implies?

The force component is not possibleThe force is possible, but in the direction perpendicular to the resultant forceThe force is not in the reverse direction w.r.t the direction set in the free body diagramThe force is in the reverse direction w.r.t the direction set in the free body diagram

4. Potential energy is stored in the body if some work is done on it. Work done is best given by:

dU = FdrdθdU = FdrcosθdU = FdrsinθdU = Fdrcotθ

5. The net moment of the body is zero that means the distance between the force and the rotational axis is zero thus the stability of equilibrium configuration.

The first part of the statement is true and other part is true tooThe first part of the statement is false and other part is false tooThe first part of the statement is false and other part is trueThe first part of the statement is true and other part is false

6. The supports in the 3D are having more than three reaction forces. Because they are having three axis on which the components of the work done need to be zero.

The first part of the statement is true and other part is true tooThe first part of the statement is false and other part is trueThe first part of the statement is true and other part is falseThe first part of the statement is false and other part is false too

7. Which of the following needs to zero for the perfect equilibrium for the calculation of the work?

∑F=0, ∑M≠0 and ∑θ = 0∑F=0, ∑M=0 and ∑θ = 0∑F=0, ∑M=0 and ∑θ≠0∑F≠0, ∑M=0 and ∑θ = 0

8. If solving the question in 3D calculations is difficult, then use the 2D system and then equate the total net force to zero as the criteria of the potential energy for equilibrium.

MaybeFalseTrueDon't Know

9. What is Mechanics?

Branch of science which deals with failure analysisBranch of science which deals with conditions of rest or motion of bodiesBranch of science which deals with the study of bodies only under motionBranch of science which deals with the study of bodies only under rest

10. The single pin, single bearing and single hinge resist _______ so as to attain potential energy equilibrium.

Couple momentsInertiaForceBoth force and couple moments

11. The moment is the cross product of which of the following two vectors/scalars?

Force and Radius scalarsRadius and Force scalarsRadius and Force vectorsForce and Radius vectors

12. What does Newton’s third law states for the conservative forces?

The body is rest until a force is appliedFor every reaction there is an opposite reactionThe body is tend to be rotated if the force is applied tangentiallyThe rate of change of momentum is equal to the force applied

13. If the supports are properly aligned then the reaction forces developed under the potential energy diagrams are adequate to support the body.

Statement is true only in 1DStatement is true only in 3DStatement is true only in 2DStatement is true throughout

14. Find the tension in the cable AC.

55N89N-29N23.6N

15. What is Engineering Mechanics?

Application of mechanics to issues involving common engineering aspectsStudy of bodies only under restStudy of bodies under motion without considering forcesStudy of bodies only under motion

16. Calculate the Normal force developed between the body and the surface due to the work done by the force.

611N116N100N180N

17. The net force of the body is zero that means the force are not being applied to the body at all and hence the body has achieved stability.

The first part of the statement is true and other part is falseThe first part of the statement is true and other part is true tooThe first part of the statement is false and other part is false tooThe first part of the statement is false and other part is true

18. If five forces are acting on the single particle and having an angle of 72˚ between each and are collinear, then_____________

The net force acting on the body is horizontalThe net force acting on the body is vertical but net work done is non-zeroThe net force acting on the body is at an angle of 45The net force acting on the body is zero and the net work done is also zero

19. Which statement is right for conservative force vector F = Ai + Bj + Ck?

In rectangular components representation of any vector we have vector F = Ax + By + CzIn rectangular components representation of any vector we have vector F = Fi + Fj + FkIn rectangular components representation of any vector we have vector F = Fx + Fy + FzIn rectangular components representation of any vector we have vector F = Ai + Bj + Ck

20. The net moment of the body is zero that means the work done by the force and the rotational axis is zero.

The first part of the statement is false and other part is false tooThe first part of the statement is true and other part is true tooThe first part of the statement is true and other part is falseThe first part of the statement is false and other part is true

21. We often determine the work done by the couples. A couple moment is developed when _______ of the attached member is prevented.

RotationAdditionSubtractionTranslation

22. For stability of equilibrium configuration the net force acting on the body is zero.

Don't KnowFalseTrueMaybe

23. What is Newton’s second law for work?

The rate of change of distance is equal to the force appliedThe rate of change of momentum is equal to the force appliedThe rate of change of momentum is equal to the moment appliedThe rate of change of momentum is equal to the work applied

24. Which of the following is the characteristic of force?

Point of application of forceDirection of application of forceAll of the mentionedMagnitude of force

25. For the conditions of the stability of equilibrium configuration of the body, i.e. the body only the external forces defines the equilibrium. Because the internal forces cancels out so not to be considered.

The first part of the statement is true and other part is falseThe first part of the statement is true and other part is true tooThe first part of the statement is false and other part is trueThe first part of the statement is false and other part is false too