The weight of bodies may change somewhat from one location...

The weight of bodies may change somewhat from one location to another as a result of the variation of the gravitational acceleration $g$ with elevation. Accounting for this variation using the relation in Prob. 1-9, determine the weight of an 80-kg person at sea level $(z=0)$, in Denver $(z=1610 \mathrm{~m})$, and on the top of Mount Everest $(z=8848 \mathrm{~m})$.

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Key Concepts

Newton's Law of Universal Gravitation

This law describes how every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It forms the basis for understanding the gravitational interactions that determine the acceleration due to gravity at a given location.

Gravitational Acceleration Variation with Altitude

The acceleration due to gravity (g) is not constant but decreases with increasing altitude. This variation is typically modeled by an inverse-square law, where g is proportional to 1/(R + z)² (with R being Earth’s radius and z the elevation). This relationship explains why objects weigh slightly less at higher elevations.

Weight as a Measure of Gravitational Force

Weight is defined as the gravitational force acting on an object, calculated by multiplying the mass of the object by the local acceleration due to gravity. Changes in the value of g with altitude lead to changes in weight, even though the mass remains constant.

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