A 65-kg hiker climbs to the second base camp on Nanga Parbat...

A $65-\mathrm{kg}$ hiker climbs to the second base camp on Nanga Parbat in Pakistan, at an altitude of $3900 \mathrm{~m}$, starting from the first base camp at $2200 \mathrm{~m}$. The climb is made in $5.0 \mathrm{~h}$. Calculate (a) the work done against gravity, (b) the average power output, and (c) the rate of energy input required, assuming the energy conversion efficiency of the human body is $15 \%$

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is calculated using the expression mgh, where m is the mass, g is the acceleration due to gravity, and h is the height difference. This concept is fundamental when analyzing problems involving elevation changes against gravity.

Work Done Against Gravity

Work done against gravity is the energy required to raise an object to a certain height and is equivalent to the change in gravitational potential energy. When an object is lifted, the work performed is given by mgh, making it an essential concept in understanding energy expenditure in vertical movements.

Average Power

Average power is defined as the amount of work done or energy transferred per unit time. It is calculated by dividing the total work done by the time taken to perform that work. This concept is crucial in determining the rate at which energy is expended or transformed in any physical process.

Energy Conversion Efficiency

Energy conversion efficiency refers to the effectiveness with which an input energy source is converted into useful output energy, such as mechanical work. In the context of human performance, it represents the fraction of metabolic energy that is transformed into mechanical energy, with the remainder being lost as heat or other forms of non-useful energy. This concept is key to analyzing the real energy requirements beyond the mechanical work performed.

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