Force of Gravity of Al on Mt. Everest

AI Thread Summary
To calculate the force of gravity acting on Al at the top of Mt. Everest, the formula F = GMm/r^2 is used, where G is the gravitational constant, M is the Earth's mass, m is Al's mass, and r is the distance from the Earth's center. The correct distance r is the sum of Mt. Everest's height (8,848 m) and Earth's radius (6.38e6 m). The calculation yields a force of approximately 569.385 N, which is consistent with Al's weight at sea level, though he would weigh slightly less at the summit. The values used in the calculation are deemed appropriate, confirming that the approach to finding r is correct. Overall, the calculations align with expected gravitational effects at high altitudes.
thelightsare
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Homework Statement


In this problem find the force of gravity of Al. Al is standing at the top of Mt. Everest at an elevation of 8,848 m. Al has a mass of 58 kg. The Earth has a mass of 5.97e24 and a radius of 6.38e6m. What is the force of gravity acting on Al?


Homework Equations



F = GMm/r^2

The Attempt at a Solution


the dist. used to find F is from Al to the Earth's center ?
so r = 8848+6.38e6 ?
then plug in values

F = G 58(5.97e24)/(8848+6.38e6)^2
F\approx569.385 N?

Is this right? I feel like I'm missing soemthing
 
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thelightsare said:

Homework Statement


In this problem find the force of gravity of Al. Al is standing at the top of Mt. Everest at an elevation of 8,848 m. Al has a mass of 58 kg. The Earth has a mass of 5.97e24 and a radius of 6.38e6m. What is the force of gravity acting on Al?


Homework Equations



F = GMm/r^2

The Attempt at a Solution


the dist. used to find F is from Al to the Earth's center ?
so r = 8848+6.38e6 ?
then plug in values

F = G 58(5.97e24)/(8848+6.38e6)^2
F\approx569.385 N?

Is this right? I feel like I'm missing soemthing
Hi, welcome to PF! Your equation is correct, but perhaps the values you are using are a bit off, since Al would weigh about 569 N at sea level, (more or less, depending on variabilities in Earth's radius, etc), then he should weigh a wee bit less atop the Mount. But in terms of significant figures, essentially, he weighs pretty much about the same on top as he does at the bottom.
 
Hi! Thanks you for the welcome and your help. And just for reassurance, for r was i right to add the two values together?
 
thelightsare said:
Hi! Thanks you for the welcome and your help. And just for reassurance, for r was i right to add the two values together?
Yes, the distance apart is measured to Earth's center.
 
Thanks so much!
 

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