If the escalator in Prob. 14-46 is not moving, determine the...

If the escalator in Prob. $14-46$ is not moving, determine the constant speed at which a man having a mass of $80 \mathrm{kg}$ must walk up the steps to generate $100 \mathrm{W}$ of power-the same amount that is needed to power a standard light bulb.

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Key Concepts

Work-Energy Principle

The work-energy principle connects the work done on an object to its change in kinetic or potential energy. It asserts that the work done against gravitational forces results in an equivalent increase in gravitational potential energy, linking the concepts of mechanical work, energy, and power in scenarios such as walking up stairs.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, calculated as m*g*h (mass times gravitational acceleration times height). When a person walks up a set of stairs, energy is expended to increase their gravitational potential energy, representing the work done against gravity.

Power

Power is the rate at which work is done or energy is transferred, typically measured in watts (W). In this context, raising a person's mass against gravity at a certain vertical speed converts energy at a rate given by the product m*g*v, with v being the vertical speed. This concept is essential for determining the required walking speed for a given power output.

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