How does gravitational variation affect kinetic energy calculations?

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Homework Help Overview

The discussion revolves around the kinetic energy calculations of a 1600 kg object falling from an altitude of 400 km to 100 km above the Earth's surface, while generating a significant amount of heat energy during its descent. Participants are exploring the implications of gravitational variation at high altitudes on these calculations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants attempt to calculate potential energy and kinetic energy, questioning the accuracy of their results. There is a focus on understanding the implications of using the formula PE = mgh at high altitudes where gravity may not be constant.

Discussion Status

Some participants have provided hints regarding the assumptions made in the calculations, particularly about the constancy of gravity at high altitudes. There is an ongoing exploration of alternative formulas for potential energy that account for varying gravitational force.

Contextual Notes

Participants express uncertainty about the terminology used in the discussion and the implications of altitude on gravitational calculations. The original poster's calculations yield results that differ from expected values, prompting further inquiry into the assumptions made.

d4nk1337sauce
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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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