Question

4. State and explain the principle of virtual work and apply it to find the excess
pressure over the curved liquid membrane.
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Answer 1

Answer: According to the virtual work principle, a system has zero virtual work when it is in equilibrium. According to Newton's laws, the applied forces are equal to and in opposition to the reaction, or constraint, forces at equilibrium. This implies that the constraint forces' virtual work must also be zero.

Explanation:

Step :1 Because the pressure on the concave side of the curve must balance the pressure on the convex side and the net inward force produced by surface tension, it will be higher than the pressure on the convex side of the curve. The total virtual work of forces operating on a particle when it is in equilibrium is zero for any virtual displacement. The total virtual work of external forces acting on a rigid body when it is in equilibrium is zero for any hypothetical displacement of the body.

Step :2 The surface is under different pressures. We can infer that if there is extra pressure on the concave side of a curved surface, the liquid will be in equilibrium. A Curved Liquid Surface Under Too Much Pressure (surface tension notes). According to this theory, the increase in work performed by the forces external to the body is equal to the increase in stored strain energy if an elastic body subject to a system of external forces is given a tiny virtual displacement.

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