A cage carrying a miner descends straight down a deep vertical mine shaft

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

Problem

A cage carrying a

70\,\text{kg}

miner descends straight down a

1.2\,\text{km}

deep vertical mine shaft. At a certain instant the cage is

1.2\,\text{km}

below the surface and is accelerating downward at

2.0\,\text{m\,s}^{-2}

. Take

g

at the surface as

9.80\,\text{m\,s}^{-2}

and Earth’s radius

R = 6.4\times10^{6}\,\text{m}

. (i) Using a first-order approximation valid for depths much smaller than

R

, calculate the approximate value of

g

at this location in the shaft. (ii) Determine the reading shown by a bathroom scale on which the miner is standing at that instant.