How does gravitational variation affect kinetic energy calculations?

AI Thread Summary
Gravitational variation significantly impacts kinetic energy calculations, especially at high altitudes where gravity is not constant. In the scenario of a 1600 kg object falling from 400 km to 100 km, the heat energy generated during descent is 8.3 x 10^8 J. The initial calculations using the standard potential energy formula (PE = mgh) yield a velocity of 2200 m/s, which is slightly off from the expected 2100 m/s. The discussion highlights the need to use more accurate formulas for potential energy that account for varying gravitational force at such altitudes. Understanding these variations is crucial for precise energy calculations in physics.
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Homework Statement



A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3 x10^8J of heat energy while descending to an altitude of 100 km.

Homework Equations


KE+PE+HEAT=KE+PE+HEAT


The Attempt at a Solution


i made PE at 100km above Earth and got 1600x9.81x300000=800V^2+8.3x10^2J
i got V=2200 but the answer should be 2100 about last 2 digits can be off by a bit I am not sure where i go wrong
 
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d4nk1337sauce said:

Homework Statement



A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3 x10^8J of heat energy while descending to an altitude of 100 km.

Homework Equations


KE+PE+HEAT=KE+PE+HEAT


The Attempt at a Solution


i made PE at 100km above Earth and got 1600x9.81x300000=800V^2+8.3x10^2J
i got V=2200 but the answer should be 2100 about last 2 digits can be off by a bit I am not sure where i go wrong

What do we need to find here ?
What is V? velocity?
 
Hint: Your altitude is lofty.
 
LawrenceC said:
Hint: Your altitude is lofty.

sorry for the late reply iv been working 8 hours everyday.

even after i made PE at 0km and subtracted mgh100km from 400km i got 2200 I am not sure what you mean any more hits? please lol?

honestly i guess i don't really know what lofty means haha
 
Last edited:
cupid.callin said:
What do we need to find here ?
What is V? velocity?

velocity yes sorry for late response iv have been working quite a bit
 
d4nk1337sauce said:
sorry for the late reply iv been working 8 hours everyday.

even after i made PE at 0km and subtracted mgh100km from 400km i got 2200 I am not sure what you mean any more hits? please lol?

honestly i guess i don't really know what lofty means haha

Hint: PE = mgh assumes gravity is constant. When you're talking about altitudes in the hundreds of kilometers, you can't necessarily make that assumption any more. Do you know any formulas for potential energy that don't assume constant gravity?
 
cjl said:
Hint: PE = mgh assumes gravity is constant. When you're talking about altitudes in the hundreds of kilometers, you can't necessarily make that assumption any more. Do you know any formulas for potential energy that don't assume constant gravity?

yeah i got it i was kinda suprised they would make us us m1m2G/r and i found out what lofty ment lol thanks for the help
 

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