A 65 -kg hiker climbs to the top of a 4200 -m-high mountain....

A 65 -kg hiker climbs to the top of a 4200 -m-high mountain. The climb is made in 5.0 h starting at an elevation of 2800 m. Calculate $(a)$ the work done by the hiker against gravity, $(b)$ the average power output in watts and in horsepower, and $(c)$ assuming the body is 15$\%$ efficient, what rate of energy input was required.

A 65 -kg hiker climbs to the top of a 4200 -m-high mountain. The climb is made in 5.0 h starting at an elevation of 2800 m. Calculate $(a)$ the work done by the hiker against
gravity, $(b)$ the average power output in watts and in horsepower, and $(c)$ assuming the body is 15$\%$ efficient, what rate of energy input was required.

Key Concepts

Unit Conversion

Unit conversion is the process of changing a measurement from one unit system to another, such as converting watts to horsepower. This is essential for comparing and understanding the magnitude of physical quantities in different contexts or regions where different measurement systems are used.

Average Power

Average power is defined as the amount of work done or energy transferred divided by the time during which the work is done. It provides a metric for the rate at which energy is expended or converted and is useful when comparing different processes that may take varying amounts of time.

Efficiency

Efficiency in this context is the ratio of useful work output to the total energy input, expressed as a percentage. It illustrates how effectively the input energy is converted into the desired work, and inefficiencies often appear as losses in the form of heat or other forms of energy not contributing to the work.

Work Against Gravity

This concept refers to the energy expended to overcome the force of gravity when raising an object to a higher elevation. It is calculated by multiplying the weight of the object with the change in height, and it is a specific case of the more general idea of work done by a force acting over a distance.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object as a result of its position within a gravitational field. It is given by the product of an object's mass, the acceleration due to gravity, and its height above a reference point, and it quantifies the amount of work needed to elevate the object to that height.

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