The escalator steps move with a constant speed of 0.6 m / s . If the steps are 125 mm high and 2

step 1 problem we have an escalator that has a velocity of 0 .6 meters per second. I mean on that the h

The escalator steps move with a constant speed of 0.6 m / s...

The escalator steps move with a constant speed of $0.6 \mathrm{m} / \mathrm{s} .$ If the steps are $125 \mathrm{mm}$ high and $250 \mathrm{mm}$ in length, determine the power of a motor needed to lift an average mass of $150 \mathrm{kg}$ per step. There are 32 steps.

Key Concepts

Gravitational Potential Energy

This concept involves the energy required to lift a mass against the force of gravity. It is calculated as the product of mass, gravitational acceleration, and vertical displacement. In the context of the escalator, it quantifies the work done in raising the mass of each step by a certain height, which is integral to determining the energy input needed from the motor.

Mechanical Power

Mechanical power is defined as the rate at which work is done or energy is transferred. In this problem, it is used to determine the motor’s capacity to perform continuous work, specifically how quickly it can deliver the energy required to lift the steps. Power calculations link the work done (in terms of gravitational potential energy) to the constant speed at which the escalator moves.

Escalator Geometry and Vertical Displacement

The geometry of the escalator—particularly the height of each step—directly sets the vertical displacement that the mass must be lifted. This vertical movement is the key factor in calculating gravitational potential energy. Although the step's length is a geometric detail, the vertical height is the critical dimension used to compute the energy gain per step.

Unit Conversion and Dimensional Analysis

Accurate calculation requires consistent units throughout the computation process. Converting measurements such as millimeters to meters and ensuring that all physical quantities are expressed in compatible units is essential in applying the formulas for work and power correctly in engineering and physics contexts.

Transcript

Please give Ace some feedback