According to my phys teacher 0.75MJ is right. Should I be worried that he did it in his head while he was on the phone?
Lockhart said:
Unless i've remembered the question horribly wrong, or I made a stupid mistake. Wasn't the quetsion asking for us to move something from the centre of the earth to 80000km away. In which case what puzzels me is how we are meant to calculate the poteintual energy of the obect is when it is in the centre as the distance in the equation is equal to zero the potientual energy become an negitive infinate number as it is -MmG/r.
From memory it said that the object was 10 000, then 20 000 then 80 000km above the surface of a planet, not necessarily Earth, so you can't sub in for M. (BTW it has to be from the surface because E
_{U}=GMm/r only when the object is above the Earth, but below it becomes more complicated because you can't consider the planet as a point mass with a nice centre of gravity.) Did anyone else do the satellite moving from 20 000km to 80 000km? Hopefully we'll get marks because the question was dodgy. If it was definitely 10 to 80 then I am screwed and my whole ans is wrong, but I might get a mark for the right concepts.
Lockhart said:
If that follows it requires an infinate amount of energy to move the object away from the centre. That really confuses me.
This comes from Newton's definition of a gravitational field: F
_{G} = GMm/r
^{2} so as r-->infinity, F-->0. What I think you're confused about is where the object is moving: at an infinite distance, there is no F
_{g} so E
_{U}=0 because grav. potential energy is provided by the field. As you move towards infinity, the satellite does work and some of the E
_{U} is converted to the E
_{U} which makes the satellite move. It would take an inifite amout of energy to move out of the gravitational field because you can't go the infinite distance required to get out of the field. You don't need an infinite amount of energy to get the satellite to the surface of the Earth from the centre or something.
Lockhart said:
In the end I think I said something like its 8 times the distance therefore 8 times the Ep because of a linear relationship.
It's
not linear as a function of r (but it is as a function of m, the satellite mass) because it's 1/r =
hyperbolic. Also it wants the change in E
_{U} as you go from 20 000km to 80 000, not the loss in E
_{U} from the surface. I'll stick my solution on lj and link it here.
Hopefully no-one else is confused now. If I do have something wrong, yell at me b/c I'll feel terrible misleading these ppl. (Only b/c there are no ends to justify it.
)