Question

A 100-kg woman hikes from sea level to the top of Mt. Everest (elevation 8848 m). Assuming her mass remains the same, how much does her weight due to gravity change by? The radius of the earth is 6.38 × 10⁶ m.

Answer 1

Here we have given that,

Mass of women = 100-kg

total elevation h = 8848 m.

g = 9.805 m/s^2

radius of the earth is 6.38 × 106 m.

Now the only thing in this question we need to find is the value of gravity g' at that much height so that,

The formula for gravity will be as,

g' = g /(1+h/R)^2

On substitution of values we will get,

g' = 9.805 /(1 + 8848/6.38 ×10^6)^2 = 9.777 m/s2

So that her new weight will be,

W' = 100× 9.777 = 977.78 N

Hence her new weight due to gravity change will be 977.78 N

And her weight at the surface of earth will be,

We = 100 × 9.805 = 980.5

Hence the change in her weight due to gravity will be

Delta( W) = 980.5 - 977.78 = 2.72 N which is the required change.

And her new weight is 977.78 N