Question

D’Alembert’s Principle is used to:

• A. Convert a dynamic problem into an equivalent static problem
• B. Determine the acceleration in dynamic systems
• C. Calculate the work done by a variable force
• D. Analyze the stability of rigid bodies

Hint:

Use D’Alembert’s Principle to simplify dynamic problems by introducing inertial forces, allowing the use of equilibrium equations like in statics.

Answer 1

The Correct Option is A

Step 1: D'Alembert's Principle is a fundamental concept in dynamics that allows dynamic systems to be analyzed using the methods of statics. It does this by introducing an inertial force equal and opposite to the product of mass and acceleration.
Step 2: Mathematically, it is stated as: \[ \sum \vec{F} - m \vec{a} = 0 \] This equation makes it appear as if the system is in static equilibrium by considering the inertial force \( -m\vec{a} \).
Step 3: This principle is useful in deriving the equations of motion using Newton’s second law and is widely applied in mechanical system analysis.
Why the other options are incorrect:

• (B) Although acceleration is involved, D’Alembert's principle does not determine it directly—it reformulates the system.
• (C) Work done by variable force is a different concept covered under work-energy methods.
• (D) Stability analysis is not the focus of D’Alembert’s principle.