Question

With what minimum acceleration can a fireman slide down a rope whose breaking strength is 2/5th of his weight

Answer 1

Sum of the forces acting = ma. These types of questions can also be easily solved by drawing a free body diagram as shown below. If we add the inertia force (ma) to the FBD then we can solve it using dynamic equilibrium (all forces balance).

Edit: This method is D’Alembert’s principle.

Since he is accelerating downward, there is an inertia force F = ma upward (opposite the direction of acceleration). The only other two forces acting on the fireman are the rope tension upward and his weight = mg downward.