Q.Why is electrical power required at all when the elevator is descending? Why should there be a limit on the number of passengers in this case?

Concept: Work-energy theorem and controlled motion under gravity.

When the elevator descends, gravity does positive work and would naturally accelerate it downward. To maintain a safe, constant speed (or decelerate when stopping), the motor must exert an upward force through the cable tension, doing negative work to oppose gravity. This requires electrical power.

The motor has a maximum power rating $P_{\max}$. For descent at constant velocity $v$, the required power is $P = T \cdot v$, where tension $T = Mg - Ma$ (with $a$ the controlled deceleration or zero for uniform motion). Even at constant speed, $T$ must support the load against gravity's excess. As passenger mass $M$ increases, the required tension and hence power increase. …

Why power is needed when descending

When an elevator descends, gravity does the work of moving it downward—so at first glance it seems no power should be required. The key insight is that an elevator must descend at constant, safe speed, not accelerate freely under gravity.

Without active control, a loaded elevator would simply fall, accelerating at $g$ until catastrophe. The motor must therefore exert an upward force to keep the descent smooth and controlled. Think of it as continuous braking: the motor opposes gravity just enough to maintain constant velocity.

Additionally, real elevators face friction—in the pulley bearings, along the guide rails, in the cable system. Even during descent, energy is continuously dissipated as heat through these resistive forces, and the motor must supply power to overcome them.

The physics of controlled descent

1. Force balance at constant speed For an elevator of mass $m$ descending at constant velocity, Newton's first law requires zero net force:

where $T$ is the upward cable tension (produced by the motor), $mg$ is the weight, and $f$ represents frictional forces. Rearranging: $T = mg + f$.

2. Power requirement Power is force times velocity. The motor must supply:

Even though gravity provides the downward motion, the motor does negative work (absorbs energy) to prevent acceleration. In practice, this energy is either dissipated in the motor's resistance or fed back into the electrical system (regenerative braking in modern elevators).

3. Effect of increasing passenger load More passengers means larger $m$, so:
   • The required braking tension $T = mg + f$ increases.
   • Friction $f$ often increases with load (more normal force on guide rails).
   • The motor must handle greater power: $P \propto m$.

Why passenger limits matter during descent …

Concept: Controlled Motion and Power Requirements

Even a "falling" elevator must be actively controlled to descend at a

safe, steady speed rather than accelerate freely under gravity — that

control is what needs electrical power.

Step 1: Why free fall is not acceptable

If the motor simply let go, the loaded elevator would accelerate downward

under gravity ($a=g$) without limit — unsafe. So the descent must happen at

a controlled, essentially constant speed.

Step 2: Force balance for constant-speed descent

For an elevator of mass $m$ (including passengers) descending at constant

velocity, Newton's first law requires zero net force:

where $T$ is the upward cable tension supplied by the motor and $f$ is the

friction in the pulleys/guide rails.

Step 3: Power needed to maintain this

Power delivered (or absorbed, in braking mode) is force times velocity:

The motor must supply this power continuously — either dissipating it as

heat or, in a regenerative system, feeding it back to the grid — purely to

prevent uncontrolled acceleration and to overcome friction.

Step 4: Effect of adding passengers

Increasing the number of passengers increases $m$, which:

• increases the required tension $T=mg+f$, …