Gravitational Potential Energy (1 Viewer)

[weirdguy99]

Could someone please help with this 2007 Physics HSC multiple choice question.

3. The gravitational potential energy of a given mass is known at both Earth’s surface and at a fixed distance above Earth.

What CANNOT be determined by comparing these two values of gravitational potential energy?

(A) The mass of Earth
(B) The speed of rotation of Earth
(C) The escape velocity of a satellite from Earth
(D) The work done in moving between the two points

I know the answer is B, but I want to know how to determine A, C and D.

Thanks in advanced.

 

[Pwnage101]

so you know GPE1 - GPE @ surface and GPE2 - GPE @ fixed distance.

we know GPE = -GMm/r ---> the only thing that changes from GPE1 and GPE2 is the value 'r' takes.

so:

GPE1=-GMm/r1
GPE2=-GMm/(r1+d)

so we know GPE1/GPE2 = (r1+d)/r1 [so in essence we know r1 now [we were given d since it is fixed]].

then M=GPE1*r1/(-Gm) ---> so A can be found

Vesc is only dependednt on M, G and r1, which we know ---> so C can be found

We know a changed in GPE is directly related to work done, so D can be found, and is simply |GPE1-GPE2|

 

[weirdguy99]

For D, how come its |GPE1-GPE2| instead of |GPE2-GPE1|??

 

[Pwnage101]

For D, how come its |GPE1-GPE2| instead of |GPE2-GPE1|??

They are the same.

Here is an example that might help:

|5-3|=|3-5|=2.

 

[weirdguy99]

Oh right, those were absolute values. I thought they were just brackets haha.