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# Gravitational Potential Question watch

1. Hi guys,

So for question 12c part ii, my initial thought was to use conservation of energy, so the loss of potential energy of the satellite would equal to the gain of KE

However, the mark scheme has equated the centripetal and gravitational forces to work out the change in kinetic energy. I understand what they have done.

My question is why do the two methods yield two different results. Can i assume that half the change in potential energy is wasted? Or is there something that I am overlooking.

2. (Original post by Shaanv)
Hi guys,

So for question 12c part ii, my initial thought was to use conservation of energy, so the loss of potential energy of the satellite would equal to the gain of KE

However, the mark scheme has equated the centripetal and gravitational forces to work out the change in kinetic energy. I understand what they have done.

My question is why do the two methods yield two different results. Can i assume that half the change in potential energy is wasted? Or is there something that I am overlooking.

I agree that this a slightly weird question if you try to approach it from the angle of reduced potential. But i think for these types of questions we must just try and form an equation where Ek (i.e 1/2 mv2 = something) and the easiest way to do this would be to equate centripetal force to the force due to gravity.

On that link i posted, someone talks of only half the energy being converted back to kinetic energy, but i am not so sure how correct that is, if we throw a ball in the air and it comes back down, it has the same kinetic energy (almost)..
3. (Original post by BDunlop)

I agree that this a slightly weird question if you try to approach it from the angle of reduced potential. But i think for these types of questions we must just try and form an equation where Ek (i.e 1/2 mv2 = something) and the easiest way to do this would be to equate centripetal force to the force due to gravity.

On that link i posted, someone talks of only half the energy being converted back to kinetic energy, but i am not so sure how correct that is, if we throw a ball in the air and it comes back down, it has the same kinetic energy (almost)..
So if the orbit is elliptical then my method was correct, however as we are assuming the orbit is circular then the mark scheme was correct.

IRL am i right in thinking that the orbits are elliptical?
4. (Original post by Shaanv)
So if the orbit is elliptical then my method was correct, however as we are assuming the orbit is circular then the mark scheme was correct.

IRL am i right in thinking that the orbits are elliptical?
Yes, IRL all orbitals are elliptical (i'm pretty sure). I don't fully understand why it doesn't work, but i guess for the exam we're just going to have to remember to use centripetal force .. (i hate just accepting things)
5. (Original post by BDunlop)
Yes, IRL all orbitals are elliptical (i'm pretty sure). I don't fully understand why it doesn't work, but i guess for the exam we're just going to have to remember to use centripetal force .. (i hate just accepting things)
I hate it too, are u doing a levels?
6. OK no, there is a subtlety here.

Firstly, this question only makes sense if you're talking about circular orbits. If you have an elliptical orbit, the radius and consequently the GPE and KE are constantly changing as it moves nearer/further from the earth.

Now, you have to realise that for a satellite of a given mass and height there is only one speed that will maintain a circular orbit, and we get this by comparing centripetal and gravitational forces. If you just reduced the height and put all the released energy into KE, the satelite would be moving too fast and would move into an elliptical orbit. So we're talking about moving a satellite from a circular orbit at one height to a circular orbit in another, and some work would need to be done to remove the excess energy and reduce the speed. This is why it's half the number you might expect.

This all said, I think it's a confusing and poorly worded question.
7. (Original post by Rinsed)
OK no, there is a subtlety here.

Firstly, this question only makes sense if you're talking about circular orbits. If you have an elliptical orbit, the radius and consequently the GPE and KE are constantly changing as it moves nearer/further from the earth.

Now, you have to realise that for a satellite of a given mass and height there is only one speed that will maintain a circular orbit, and we get this by comparing centripetal and gravitational forces. If you just reduced the height and put all the released energy into KE, the satelite would be moving too fast and would move into an elliptical orbit. So we're talking about moving a satellite from a circular orbit at one height to a circular orbit in another, and some work would need to be done to remove the excess energy and reduce the speed. This is why it's half the number you might expect.

This all said, I think it's a confusing and poorly worded question.
That makes sense, thanks for your input. The spec only focuses on circular orbits.

Glad i wasnt the only one who thought the question was a little dodgy.
8. (Original post by Shaanv)
Hi guys,
So for question 12c part ii, my initial thought was to use conservation of energy, so the loss of potential energy of the satellite would equal to the gain of KE

However, the mark scheme has equated the centripetal and gravitational forces to work out the change in kinetic energy. I understand what they have done.

My question is why do the two methods yield two different results. Can i assume that half the change in potential energy is wasted? Or is there something that I am overlooking.

(Original post by Shaanv)
That makes sense, thanks for your input. The spec only focuses on circular orbits.

Glad i wasnt the only one who thought the question was a little dodgy.
I don’t really think question is poorly worded or dodgy. I agree that there is subtlety in the question. I believe it is intended.

As OP (Shaanv) had pointed out the going through of the wrong path (using conservation of energy) to find the answer, this implies the occurrence of misconception.

If the satellite is moving in a circular motion about the Earth at a particular radius r, the total energy of a satellite-Earth system has only one total energy value. This means that at different orbits, the total energy will be different.

As a result, it should not be surprised that conservation of energy cannot be used to find the change in kinetic energy just as it is.

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Updated: April 8, 2018
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