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GPE HSC question (2 Viewers)

doggian

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I don't really understand the answer to this question (26 a) from the 2015 Physics HSC. It reads as follows: Consider the following two models used to calculate the work done when a 300 kg satellite is taken from Earth's surface to an altitude of 200 km. You may assume that the calculations are correct.
Model XModel Y
Data: g=9.8ms-2
m = 300 kg
delta h = 200 km

W=Fs
=mgh
=3x102x9.8.2.105
=5.9x108
Data: G = 6.67x10-11Nm2kg-2
rEarth = 6.38x106
rorbitx10 = 6.58x106m
M = 6.0x1024
m = 300 kg
W = delta Ep

delta Ep= Ep final - Ep initial
=-(GMm)/rorbit - (GMm)/rEarth
=1.824x1010 - (-1.881x1010)
=5.7x108J
a) What assumptions are made about Earth's gravitational field in models X and Y that lead to the different results shown?

I have a photo of the question in case the table doesn't work
 

doggian

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Sorry, forgot to say: the model answer is that the assumption in X is that g is constant (which I understand) and the assumption in Y is that g changes with height. This doesn't seem to make sense however since Y doesn't even include g as a constant or variable, the only thing's it assumes are constant are the masses, radii and universal gravitational constant
 

InteGrand

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I don't really understand the answer to this question (26 a) from the 2015 Physics HSC. It reads as follows: Consider the following two models used to calculate the work done when a 300 kg satellite is taken from Earth's surface to an altitude of 200 km. You may assume that the calculations are correct.
Model XModel Y
Data: g=9.8ms-2
m = 300 kg
delta h = 200 km

W=Fs
=mgh
=3x102x9.8.2.105
=5.9x108
Data: G = 6.67x10-11Nm2kg-2
rEarth = 6.38x106
rorbitx10 = 6.58x106m
M = 6.0x1024
m = 300 kg
W = delta Ep

delta Ep= Ep final - Ep initial
=-(GMm)/rorbit - (GMm)/rEarth
=1.824x1010 - (-1.881x1010)
=5.7x108J
a) What assumptions are made about Earth's gravitational field in models X and Y that lead to the different results shown?

I have a photo of the question in case the table doesn't work
The model X is assuming constant gravity, whilst Y takes into account changing gravity.
 

InteGrand

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Sorry, forgot to say: the model answer is that the assumption in X is that g is constant (which I understand) and the assumption in Y is that g changes with height. This doesn't seem to make sense however since Y doesn't even include g as a constant or variable, the only thing's it assumes are constant are the masses, radii and universal gravitational constant
Y uses the -GMm/r formula for E_p, which is a result of assuming gravity is varying (namely GM/r^2 at radial distance r).



(To recall the mathematical definition of potential energy and how it results in -GMm/r, see: http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html#gpt .)
 
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