GPE HSC question (1 Viewer)

[doggian]

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 X	Model 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]

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]

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 X	Model 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]

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 .)