Hey I have a few Space questions that I was hoping to get some help with
1. Would a planet rotating quicker or slower increase the gravitational acceleration according to
2. How is an object's GPE and Work related (on Earth)? So for expressions: GPE = mgh and W = Fs
Hi,
Not sure if you need to know for HSC but
1. The centripetal (rotational force) = mv
2/r, so as v increases, the centripetal force increases
When a planet rotates, the centripetal force = gravitational force
So if the velocity is increased, the centripetal force increases and therefore so must the gravitational force, and as Fg = GMm/r
2, r decreases.
Basically, it rotates faster when it's closer to the centre of the earth, and if it's closer then g is more.
Extra:
mv
2/r = GMm/r
2v
2=GM/r
GM (constant for a particular planet) = v
2r
So as velocity increases, r decreases
2. Work is like a transfer of energy.
Work = Fd = ma*d.
gpe = mgh
You can do work on an object vertically to give it more gpe, as the change in work = change in gpe (as a of object= g)
So you can increase an object's gpe by doing work on it (vertically). It's like a transfer of energy, if done vertically the work is converted into gpe
Horizontally, the work is converted into ke (gpe unaffected horizontally)
Don't know if this will help but hope so
With your notes :
- Yes when g = 9.8 but g=GM/r
2 so can be different. To accurately find gpe you'd need a graph showing the change in g for long distances where this value would change
- gpe isn't really calculated in space, just know that it's higher further away. gpe is mostly used for changes in energy, so change in (∆) gpe = mg∆h
Not sure about that last question, don't recall learning it