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Author Topic: Where does the energy go when travelling in a circle?  (Read 5608 times)

Offline Steve

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Steve asked the Naked Scientists:
   
A spacecraft is travelling in a cirle at a constant angular velocity. It is expending energy (i.e. accelerating) in order to travel in a circle, and yet its kinetic energy is not changing.

Where is the energy going?

What do you think?
« Last Edit: 08/05/2010 22:30:04 by _system »


 

Offline GlentoranMark

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Where does the energy go when travelling in a circle?
« Reply #1 on: 08/05/2010 23:15:11 »
I think the question requires a closed system?
 

Offline Geezer

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Where does the energy go when travelling in a circle?
« Reply #2 on: 09/05/2010 05:38:07 »
I think GM is on the right track.

One way to look at it is that the spacecraft is continuously trading kinetic energy against potential energy, so there is no net change in its energy.

It's not so different from a pendulum. It's fairly obvious that a pendulum alternately "swaps" kinetic energy for potential energy. If a pendulum had no losses due to atmospheric or mechanical friction, it would go on for ever, so there would be change in energy.

In the case of an orbiting body, the "swapping" is continuous, and less obvious.
 

Offline Bored chemist

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Where does the energy go when travelling in a circle?
« Reply #3 on: 09/05/2010 18:33:58 »
I presume that you mean a ship orbiting a planet.
It isn't expending energy.
It's accelerating towards the planet (so there's a force), but it doesn't move towards the planet. Because the force moves through no distance no work is done.
 

Offline Geezer

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Where does the energy go when travelling in a circle?
« Reply #4 on: 09/05/2010 19:53:17 »

It's accelerating towards the planet (so there's a force), but it doesn't move towards the planet.


Hang on a minute! How can it accelerate towards the planet without getting closer to it?
 

Offline syhprum

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Where does the energy go when travelling in a circle?
« Reply #5 on: 09/05/2010 20:40:40 »
The case is simple if it is orbiting another body but what about when it is doing it remote from any other bodies ?
 

Offline Geezer

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Where does the energy go when travelling in a circle?
« Reply #6 on: 09/05/2010 20:48:42 »
The case is simple if it is orbiting another body but what about when it is doing it remote from any other bodies ?

Ah! Good point. Well, I suppose it would be consuming energy to maintain its kinetic energy, and the spent energy would be dissipated into space.
 

Offline syhprum

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Where does the energy go when travelling in a circle?
« Reply #7 on: 10/05/2010 11:04:56 »
I can but assume that it is radiating energy albeit at very low power as a gravity wave (gravitons ?) that leaves it at light velocity.
 

Offline Geezer

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Where does the energy go when travelling in a circle?
« Reply #8 on: 10/05/2010 18:36:46 »
I can but assume that it is radiating energy albeit at very low power as a gravity wave (gravitons ?) that leaves it at light velocity.

Isn't it dumping mass which has a lot of kinetic energy into space?
 

Offline Soul Surfer

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Where does the energy go when travelling in a circle?
« Reply #9 on: 10/05/2010 22:02:37 »
To return to the original question.  in the absence of a gravitational or electrical field an object cannot travel in a circle without continuously expending energy to produce the acceleration as the questioner points out. From newtons laws energy always has to be expended to change the direction of an objects motion. travelling in a circle like this is a very unnnatural and unlikely choice of motion.

Now if the object is in a circular orbit around a gravitating body the required continuous acceleration can be provided by a gravitational field.  The other important property that the body has is its angular momentum this is its velocity around the orbit and the centrifugal force exactly balances the attractive force represented by the acceleration of the body towards the planet so all the energy and force components are balanced.

it is interesting to note that although rockets start off by going upwards the most important part is the acceleration to get the horizontal velocity up to the 18,000 or so miles per hour to achieve orbital speed.
 

Offline JP

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Where does the energy go when travelling in a circle?
« Reply #10 on: 11/05/2010 03:09:57 »
This has to do with conservative vs. non-conservative forces right?  For a conservative force, the change in energy of an object depends only on the object's initial and final positions, not its path.  If you're in an orbit caused by a conservative force (gravity, for example), and you return to the same point, your energy hasn't changed. 

I can but assume that it is radiating energy albeit at very low power as a gravity wave (gravitons ?) that leaves it at light velocity.
Technically, I think you're right.  It's such a minor effect that for most purposes you can disregard it.
 

Offline Steve

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Where does the energy go when travelling in a circle?
« Reply #11 on: 11/05/2010 23:11:51 »
Can I just say that none of the above answers constitutes a serious scientific answer. Forget about planets, space, closed systems etc. The reason for placing the question in space away from other objects was to prevent simplistic answers around centridepal and centrifugal forces. The fact is we have a body in motion that is constantly maintaining its energy state by traveling in a circle, but needing to expend energy to maintain that state. Where is the energy going.
 

Offline JP

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Where does the energy go when travelling in a circle?
« Reply #12 on: 12/05/2010 03:10:29 »
Can I just say that none of the above answers constitutes a serious scientific answer.
Perhaps it would help if you asked a precise scientific question?  It's impossible to answer the question precisely unless you specify what is providing the force to keep the object moving in a circle. 

Even without that, Soul Surfer provided a very nice scientific explanation here: http://www.thenakedscientists.com/forum/index.php?topic=31452.msg309064#msg309064
 

Offline Geezer

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Where does the energy go when travelling in a circle?
« Reply #13 on: 12/05/2010 05:22:53 »
Can I just say that none of the above answers constitutes a serious scientific answer. Forget about planets, space, closed systems etc. The reason for placing the question in space away from other objects was to prevent simplistic answers around centridepal and centrifugal forces. The fact is we have a body in motion that is constantly maintaining its energy state by traveling in a circle, but needing to expend energy to maintain that state. Where is the energy going.
Well, if it's not orbiting something, it must be accelerating matter and ejecting it from the spacefraft to produce a reaction force. The energy leaves in the kinetic energy of the accelerated matter.
 

Offline syhprum

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Where does the energy go when travelling in a circle?
« Reply #14 on: 12/05/2010 17:05:35 »
Shakespear sends Puck in orbit around the Earth in 40 minutes whereas a normal orbital time at ground level would be 84 (Puck being a supernatual being is not concerned with air resistance), how much energy per Kg would be required to maintain this orbit ?
 

Offline graham.d

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Where does the energy go when travelling in a circle?
« Reply #15 on: 12/05/2010 17:29:21 »
I think Geezer has answered the original question correctly.
 

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Where does the energy go when travelling in a circle?
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