Question

The virtual work done by external active forces on an ideal mechanical system in equilibrium is ______ for any and all virtual displacements consistent with the constraints.

• A. Zero
• B. Unit
• C. Twice
• D. Thrice

Hint:

The Principle of Virtual Work is extremely powerful because it allows us to solve complex equilibrium problems for multi-body mechanisms without calculating internal constraint forces.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question asks for the fundamental statement of the Principle of Virtual Work as applied to ideal mechanical systems in static equilibrium.

Step 2: Key Formula or Approach:
The Principle of Virtual Work states that for any ideal mechanical system in equilibrium, the total virtual work done by all active external forces during any virtual displacement consistent with constraints is equal to zero:
\[ \delta W = \sum \vec{F}_i \cdot \delta \vec{r}_i = 0 \]

Step 3: Detailed Explanation:

• A virtual displacement ($\delta \vec{r}_i$) is an imaginary, infinitesimal change in the coordinates of the system occurring at a constant instant of time.

• It must be compatible with the geometric constraints of the mechanical system.

• In an ideal system, the virtual work done by constraints (such as normal reactions of frictionless surfaces or tension in inextensible cords) is zero.

• Therefore, only the active external forces perform net virtual work on the system.

• For the system to remain in static equilibrium, the net active force in any allowable direction must be zero, which mathematically guarantees that the sum of the virtual work is zero.

Step 4: Final Answer:
The virtual work done by external active forces on an ideal mechanical system in equilibrium is zero.