Rope Tension When Lifting a Mass

Newton's second law on a hoisted load reads T − mg = ma, so the rope carries T = m(g + a). Lift a 50 kg crate while accelerating upward at 2 m/s² and the rope feels 50 × (9.80665 + 2) ≈ 590 N, about 20% more than the 490 N it holds at rest or at constant speed. Decelerate on the way up — or accelerate downward — and a goes negative, easing the tension; at a = −g the rope goes completely slack and the load is in free fall.

This is exactly why you feel heavy as an elevator starts up and light as it starts down: the floor is the "rope", and the scale under your feet reads m(g + a). Rigging engineers turn the same relation into a dynamic load factor, sizing slings and hooks for the accelerating case rather than the static weight — snatching a load, or an emergency stop, can spike the tension well past the crane's nameplate figure.