Mount Everest is approx. 9km high. Calculate how much less a mountaineer of mass 100kg(with a back pack would weigh at its summit, compares to her weight at sea level.

Question

anonymous · Answer

we will first find the gravitational force by F=GM/r^2, the use that to find the weight, w=mg
right?

jamesj · Answer

Use Newton's Universal Law of Gravity as you did in your last question.  You'll need
M = mass of earth
R = radius of earth at sea level
m = her weight = 100 kg

Then her weight at sea level is
$$Weight_{sea \ level} =  F_{gravity \ @ \ sea \ level} = \frac{GMm}{R^2} $$
while atop Everest her weight is
$$ Weight_{Everest} = F_{gravity \ atop \ Everest} = \frac{GMm}{(R + 9)^2} $$

jamesj · Answer

actually, you should measure distance in meters, so you need R in meters, and then atop Everest, the force due to gravity is
$$ \frac{GMm}{(R+9000)^2} $$

anonymous · Answer

the equation I wrote should be g=GM/r2 
Isn't it more simpler to use this equation than GMm/r2?

jamesj · Answer

As weight, W = mg, you're doing exactly the same thing.  Just breaking up the calculation into two pieces.

anonymous · Answer

true :)