Mechanics help needed !! (1 Viewer)

[cssftw]

Hi guys, here's a question from Cambridge 4U EX 7.1 Q9. It is Q9 part (b) where I can not understand what to do.









Now part (a) I was able to complete --> the answer is:

But I just don't know how to do part (b) -- can someone please explain the theory? E.g. how do you do it, and the reasoning for why you did what you did. Sorry I don't have a physics background, so I don't really understand what the particle needs to do to escape the force of attraction.

Thanks guys

 

[thoth1]

this is wat i got:
particle will escape earth's influence as x approaches infinity. as x approaches infinity v = . but for particle to escape earths velocity v > 0. therefore u^2 > 2gr.

this was confirmed correct by the worked solutions i hav 4 cambridge.

 

[thoth1]

4U worked solutions posted by spiral in this thread:

http://community.boredofstudies.org/showthread.php?t=253736&page=1

 

[cssftw]

particle will escape earth's influence as x approaches infinity..... but for particle to escape earths velocity v > 0

Sorry about this, I'm a little dim-witted in this area -- could you please explain this further if possible (e.g. what do you mean by earth's velocity)?

 

[thoth1]

Sorry about this, I'm a little dim-witted in this area -- could you please explain this further if possible (e.g. what do you mean by earth's velocity)?

sorry i meant the earth's gravitational field (ie the gravitational force between particle and centre of earth).

as u can see in question f = mgr^2/x^2. therefore as x approaches infinity. the gravitational force will approach zero.
this makes sense bcuz as the particle moves further and further away the force pulling it towards the earth's centre will weaken.

 

[cssftw]

sorry i meant the earth's gravitational field (ie the gravitational force between particle and centre of earth).

as u can see in question f = mgr^2/x^2. therefore as x approaches infinity. the gravitational force will approach zero.
this makes sense bcuz as the particle moves further and further away the force pulling it towards the earth's centre will weaken.

ahh okay so that explains why x--> infinity, but why does v need to approach 0? i.e. v-->0?

 

[thoth1]

ahh okay so that explains why x--> infinity, but why does v need to approach 0? i.e. v-->0?

v doesnt approach zero. i said v > 0. since to escape earth's field particle has to be continuously moving away. hence v > 0. if v < 0, particle would be moving bak towards earth.