Question

D'Alembert's Principle is used to

• A. Convert dynamic problems into static problems
• B. Solve fluid dynamics problems
• C. Analyze chemical reaction dynamics
• D. Study heat transfer

Hint:

D'Alembert's Principle. Transforms a dynamics problem (\(F=ma\)) into a statics problem by introducing an inertial force (\(-ma\)) such that the sum of external forces and the inertial force is zero (\(F + (-ma) = 0\)).

Answer 1

The Correct Option is A

D'Alembert's principle is a reformulation of Newton's second law of motion (\(\vec{F} = m\vec{a}\)).
It states that the vector sum of the external forces (\(\vec{F}\)) acting on a body and the inertial force (or fictitious force) \( -m\vec{a} \) is zero.
$$ \sum \vec{F} - m\vec{a} = 0 $$ By introducing the inertial force (\(-m\vec{a}\)), which acts opposite to the acceleration, the dynamic problem (\(\sum \vec{F} = m\vec{a}\)) is transformed into an equivalent problem of static equilibrium (\(\sum \vec{F}_{effective} = 0\)).
This allows methods of statics to be applied to problems involving motion (dynamics), often simplifying the analysis, particularly in complex systems.
It is fundamental in mechanics, not specifically fluid dynamics, chemical reactions, or heat transfer.