An escalator handles a steady load of 30 people per minute...

An escalator handles a steady load of 30 people per minute in elevating them from the first to the second floor through a vertical rise of 24 ft. The average person weighs 140 lb. If the motor which drives the unit delivers 4 hp, calculate the mechanical efficiency $e$ of the system.

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Key Concepts

Work and Energy in Lifting

This concept involves calculating the work done in lifting an object against gravity, which is given by the product of force (in this case the weight of the person) and the vertical distance. Understanding this calculation is essential when determining the energy required to move objects in vertical systems such as elevators or escalators.

Power and Energy Conversion

Power represents the rate at which work is done or energy is utilized. In mechanical systems, power may be provided in units like horsepower, which often needs to be converted into other units (such as foot-pounds per second) to compare against the work done. This conversion is critical when matching the energy output of a motor with the energy required to perform a task.

Mechanical Efficiency

Mechanical efficiency is a measure of how effectively a machine transforms input energy into useful work. It is defined as the ratio of the output work (energy transferred, such as elevating passengers against gravity) to the input energy (energy provided by the motor) over a given period, and it accounts for energy losses due to factors like friction and heat.

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