A hiker with mass 70 ,kg climbs from sea level to the summit of a mountain that is…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A hiker with mass 70\,kg climbs from sea level to the summit of a mountain that is 1.20\,km above sea level. Assume the Earth is a perfect sphere of radius

R_{\!E}=6.37\times10^{6}\,\text{m}

and mass

M_{\!E}=5.97\times10^{24}\,\text{kg}

. Neglect air resistance and any motion of the Earth during the climb. (a) Calculate the magnitude of the local gravitational field

g_{\text{summit}}

at the mountain summit using universal gravitation. (b) Determine the hiker’s weight at the summit and the percent difference between this value and the hiker’s weight at sea level, where

g_{0}=9.80\,\text{N\,kg}^{-1}

. (c) The hiker’s equipment manual states that any weight measurement within 1.0\% of the true value is considered acceptable. Based on your calculation in part (b), evaluate whether taking

g=9.80\,\text{N\,kg}^{-1}

for all altitudes up to 1.20\,km satisfies this criterion, and justify your answer.

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