Dynamic equilibrium form of Newton’s second law Let P be the net applied force on a mass m producing acceleration f. The relation P − m f = 0 is called what in mechanics?

Introduction / Context:
Newton’s second law, P = m f, is often rewritten for analysis as P − m f = 0 by transferring inertia to the left-hand side. This rearrangement is widely known as the equation of dynamic equilibrium or D’Alembert’s principle, enabling dynamic problems to be treated as if in static equilibrium with an added inertial force.

Given Data / Assumptions:

• Net applied force P acts on a body of mass m.
• Resulting acceleration is f (vector).
• Classical (nonrelativistic) mechanics.

Concept / Approach:

D’Alembert’s principle introduces an inertial force F_in = − m f, and imposes equilibrium: ΣF + F_in = 0. This converts a dynamics problem to a statics form, simplifying free-body analysis and allowing the use of equilibrium methods (ΣF = 0, ΣM = 0) with the inertial force included.

Step-by-Step Solution:

Verification / Alternative check:

Applying the method to a translating block or rotating link yields the same accelerations as direct second-law application, confirming equivalence.

Why Other Options Are Wrong:

(a) names the original Newtonian form, not the rearranged equilibrium form; (c) applies only when accelerations are zero; (d) and (e) do not describe this specific mechanical identity.

Common Pitfalls:

Forgetting the inertial force is fictitious and used for analysis convenience; mixing signs when moving m f across the equality.

Final Answer:

Equation of dynamic equilibrium (D’Alembert’s form)