Weight On Mount Everest

Classical Mechanics Level 3

While your mass is the same everywhere, your weight , which is the gravitational force you feel as a result of your mass, depends on where you are.

How much lighter are you on the top of Mount Everest than at sea level? Express your answer as the ratio of your weight on Mount Everest to your weight at sea level, to 3 decimal places.

Assume the radius of Earth at sea level is $6.371 \times 10^6 \text{ m}$ and the height of Mt. Everest is $8.8 \times 10^3 \text{ m}$ .

The answer is 0.997.

1 solution

Adam Strandberg
Feb 23, 2016

Since gravity is proportional to $\dfrac{1}{r^2}$ , the ratio of your weight on Everest to your weight at sea level will be

$\frac{F_\text{Everest}}{F_\text{sea}} = \frac{r_\text{sea}^2}{r_\text{Everest}^2} = \left(\frac{6.371 \times 10^{6} \text{ m}}{6.380 \times10^{6} \text{ m}}\right)^2 = 0.997$

P.S. : I would not recommend going to high altitudes as a weight loss plan. The weight all comes back the moment you quit.

Weight On Mount Everest

The answer is 0.997.

1 solution

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