Suppose Earth were a nonrotating uniform sphere. As a reward for earning the hig

Question

Suppose Earth were a nonrotating uniform sphere. As a reward for earning the highest lab grade, your physics professor chooses your laboratory team to participate in a gravitational experiment at a deep mine on the equator. This mine has an elevator shaft going 16.0 km into the Earth. Before making the measurement, you are asked to predict the decrease in the weight of a team member, who weighs 1000 N at the surface of Earth, when she is at the bottom of the shaft.
What is her predicted decrease in weight?
N

The density of Earth's crust actually increases with depth. Is your prediction higher or lower than the actual experimental result?
higher
lower

Explanation / Answer

 The depth of the elevator d = 16.0 km = 16*10^3 m  The weigth of the person is w = 1000 N then mass of the person is m = 1000/9.8 = 102 kg So at depth d the weigth of the person is varies by g' = g ( 1 -d/R)            g' = (9.8 m/s^2) [ 1 - (16*10^3m)/ 6.38*10^6 m) ]               = g(0.9975)            Now the weigth of the person is              w' = mg' then w = mg - mg' = mg (1-0.9975)              = (0.0025)1000 N = 2.5 N Yes the density of the earth crust is increase The density of the earth  = MV = M(4/3)R^3 at depth d the density                    ' = M / (4/3)(R-d)^3 The density of the earth  = MV = M(4/3)R^3 at depth d the density                    ' = M / (4/3)(R-d)^3         

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