Potential energy of earth and gravity

[Bandarigoda]

Assume Earth's radius R and there is a mass m. We put that mass in height of R from the Earth's surface. I want to calculate it's potential energy.

I calculated it and got mgR/4 but my teacher said the answer is mgR/2 . Why my answer is wrong?

I just calculated the gravity in the height of R and applied it to e = mgh

 

[tiny-tim]

Hi Bandarigoda!

I calculated it and got mgR/4 but my teacher said the answer is mgR/2 . Why my answer is wrong?

I just calculated the gravity in the height of R and applied it to e = mgh

??

Show us your full calculations.

(and at that distance you can't treat gravity as constant)

 

[voko]

Either answer can be right or wrong, depending on where the potential energy is supposed to be zero. Unless you fix that, the discussion is meaningless.

 

[Bandarigoda]

Here

 

[Enigman]

You are assuming zero potential energy at the surface of Earth while your teacher's doing it at infinity. Both answers are correct but at these distances infinity is usually used.
Your teacher is using the formula:
$$U= \frac {Gm_1m_2}{R}$$ [edited]
Assuming U=0 at R=$\infty$

 

[tiny-tim]

ahhh now i understand …

you've correctly found the different values of g(r) (as a function of radial distance r),

but then you've used mgh (= mg(r - R)) for potential energy,

instead of -MmG/r

 

[Bandarigoda]

Oh thank you very much guys. I got it now.

 

[tiny-tim]

Your teacher is using the formula:
$$U= \frac {Gm_1m_2}{R^2}$$
Assuming U=0 at R=$\infty$

for the record: that should be

$U= -\frac {Gm_1m_2}{R}$ ​

 

[Enigman]

Uncaffeinated brain fart.