D'Alembert's principle converts a dynamic problem into an equivalent static problem by:
Choose the correct answer
Ignoring acceleration entirely
Adding a fictitious inertia force (-ma) to the real applied forces; the system is then in dynamic equilibrium (sigma F + (-ma) = 0)
Using energy methods only
Applying the principle of virtual work
Correct Answer
B. Adding a fictitious inertia force (-ma) to the real applied forces; the system is then in dynamic equilibrium (sigma F + (-ma) = 0)
Why is this the answer?
D'Alembert: F_net - ma = 0, written as sigma F = 0 if the inertia force (-ma) is treated as a real force. This allows free body diagram + static equilibrium methods to solve dynamics problems. Particularly useful for systems with constraints (connected bodies, pulleys, rotating systems). Equivalent to Newton's second law F_net = ma.
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