Physics

Problem

A surveying team sets up a portable gravimeter on the summit of Mount Kibo, which rises directly above the surrounding plains of Tanzania. The instrument records a vertical gravitational field magnitude of

9.72\,\text{N/kg}

. Take Earth’s mean radius to be

6.37\times10^{6}\,\text{m}

and the field magnitude at sea level at this latitude to be

9.80\,\text{N/kg}

. Neglect Earth’s rotation. (a) Determine the elevation of Mount Kibo’s summit above sea level implied by the gravimeter reading. (b) An equipment crate has a mass of

45\,\text{kg}

. Calculate the difference between the crate’s weight at sea level and at the summit, expressing your answer to two significant figures. (c) State one practical reason, other than a change in gravitational field strength, why field measurements at high elevations might differ from the ideal prediction, and briefly explain its effect on the measured value.

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