Physics Halp! (1 Viewer)

[ohexploitable]

From the Dot Point book:

Satellite X has its orbit around Earth changed from an altitude of 10 000 km to an altitude of 20 000 km. Satellite Y has its orbit around Earth changed from an altitude of 20 000 km to an altitude of 30 000 km. Both satellites have a mass of 500 kg.

(a) Predict the amount of work done on X compared to the amount done in Y and explain your reasoning.

(b) Calculate the amount of work done on each satellite to see if your prediction was correct.

Their answer:

(a) Your prediction could be anything - less for X, less for Y, same for each. The most logical is the same for each based on the fact that they both have their orbit increased by the same amount.

(b) Calculations show the initial E_p of X is -3.119*10¹⁰ J and final is -3.114*10¹⁰ J for an increase of 5*10⁷ J. The initial E_p of Y is -3.114*10¹⁰ J and final is -3.109*10¹⁰ J also for an increase of 5*10⁷ J.

They're wrong, right?

 

[ohexploitable]

 

[khorne]

moar like they are both right...

Also it does...the minus sign is just directional (like all things in physics) the magnitude is still larger. Remember that it's moving from a point infinitely far away to a point near a mass

 

[spakfilla]

a) If we consider infinity as our zero level (I.E Ep @ infinity=0) then the further we travel from infinity the the lower the Ep becomes (cbf going into too much detail). Therefore Ep @ initial X is lower than the Ep @ initial Y and same for final X and final Y. (cbf going into too much detail)
If we look at the Ep when they are @ the same altitude everything would be constant except for the mass, therefore Ep of M1 > Ep of M2. Since the masses are the same they would have the same Ep @ 20 000Km

I believe you went wrong when you changed the sign because you multiplied by a negative, mathematical correct however if we choose infinity as our zero level the formula already has the negative sign.

b) Work em out post what u get and then i'll see if we get the same...cbf doing them

 

[ohexploitable]

moar like they are both right...

But if you do the calculations they are different from the answers,

Work done on X = 4.63*10⁹ http://www.wolframalpha.com/input/?....67*10^-11*((500*6*10^24)/(6378000+10000000))
Work done on Y = 2.09*10⁹ http://www.wolframalpha.com/input/?....67*10^-11*((500*6*10^24)/(6378000+20000000))

 

[khorne]

when spakfilla says lower, he means a larger value, only negative.

 

[ohexploitable]

the minus sign is just directional (like all things in physics) the magnitude is still larger

But work is a scalar quantity...

 

[ohexploitable]

My answer was:

Satellite X is closer to the Earth so there is a greater force acting upon it, hence, more work needs to be done to move it.

 

[ohexploitable]

If we use W=mgh, the value of 'g' at X is greater than at Y, since 'm' and 'h' remain constant, 'W' is directly proportional to 'g', so more work needs to be done to move satellite X.

 

[khorne]

Actual legit reply time:

just model it...have the distance @ lets say...1:10:000 and C = -Gm1m2 since it's constant for both yeah?

so W = fd so obviously, since distance is the same etc, more work has been done on the first one.

initial Gp = C
end Gp = C/2

Initial Gp = C/2
End Gp = c/3

so end - initial

-(c - c/2) = -c/2

and -(c/3 - c/2) = -c/6 for the other one

so yeah, it'd have different

 

[spakfilla]

why are u adding...makes no sense
However if u work out initial and final Ep their answers are wrong!!!!!!!!!!!!!!!!

 

[ohexploitable]

Also it does...the minus sign is just directional (like all things in physics) the magnitude is still larger. Remember that it's moving from a point infinitely far away to a point near a mass

But smaller magnitudes correspond to greater E_p?

 

[ohexploitable]

why are u adding...makes no sense
However if u work out initial and final Ep their answers are wrong!!!!!!!!!!!!!!!!

Final E_p - inital E_p, the two minuses make a plus.

 

[khorne]

yeah never mind, you're right with the calcs.

 

[ohexploitable]

he seems to be adding radius of earth (wrong) and the distance in S.I units, but fucked it

Are you referring to me (being wrong)?

 

[spakfilla]

What exactly don't you understand
It all depends on what you take as your zero level. If you choose infinity as the zero level you would find the further away the lower your Ep only by sign as khorne said, but the work done increase as you move from infinity (greater magnitude).

Initial work done for X > Initial Y however... Initial Ep for X < Y
Finial work done for X > final Y however....final Ep for X<Y

Therefore Total work done for X = Final - Initial
>Y as you calculations proved

 

[Omnipotence]