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What is the energy/work required to turn something? 
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#1
Mar1408, 11:04 AM

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Normally one would think that the work required to move something in a circle is zero since the force is directed normal to the direction of movement and kinetic energy doesn't change. This is easy to understand using a spinning disk, where every particle has a cohort what is changing momentum in the opposite direction such that momentum is conserved.
But, take the case of so single particle, say a spaceship in deep space. It will tend to move in a straight line unless a force is applied to change its direction. Fire a rocket normal to the direction of travel and the spaceship will travel in a circle. Clearly, the energy required to do this is not zero. Wouldn't the same analysis apply to turning a car or bicycle or ourselves? How do we calculate the energy cost of turning a single moving particle in a circle knowing the mass, speed, and turning radius through an arc of x radians? 


#2
Mar1408, 11:36 AM

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#3
Mar1408, 01:10 PM

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#4
Mar1408, 01:21 PM

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What is the energy/work required to turn something?
A satellite orbits the earth, its momentum continually changing. Does it require energy to maintain its orbit? 


#5
Mar1408, 02:40 PM

P: 21

Further, it is not clear to me that satellites are not requiring energy to make their circles. The moon speeds up because its orbit is slower than the earth is spinning so energy is transferred between the two from the tidal influences. Other satellites that orbit faster than the earth slow down I suspect for the same reason. It is not obvious because the energy requirements are small compared to the energy they contain. The classical physics approach usually requires objects to be rigid, to simplify the solution. Rigid bodies do not exist in the real world. Anyhow, I don't think this is as straight forward as it is sometimes presented. I would like to understand what is going on whether it is straight forward or not. 


#6
Mar1408, 03:07 PM

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#7
Mar1408, 03:25 PM

P: 21

1. Even though we are not increasing the total energy of the spaceship in this maneuver, can we calculate from this how much energy the rocket is delivering to space (how much of its total available energy has it lost)? 2. Can we calculate from this what the turning radius of the spaceship would be? 


#8
Mar1408, 03:33 PM

P: 218

PS. Is there a better way to do dot product in latex? 


#9
Mar1408, 03:41 PM

P: 21

There has to be a way of calculating this, otherwise I don't see how NASA could have ever hit the moon. 


#10
Mar1408, 03:49 PM

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#11
Mar1408, 04:04 PM

P: 21

Since we can calculate the radius of the circle and we know the speed of the spaceship we can know the time that the rocket must fire to turn the spaceship around. From this can we calculate how much energy left the rocket during a 180º turn and, at the same time, the power of the rocket? 


#12
Mar1408, 04:33 PM

P: 218

What do mean by "how much energy left the rocket"? The rocket is what is being fired off of the spaceship right? The spaceship loses the kinetic energy it gave to the rocket, which depends on the rocket velocity. 


#13
Mar1408, 04:55 PM

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#14
Mar1408, 05:06 PM

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#15
Mar1408, 05:13 PM

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#16
Mar1408, 07:28 PM

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In the case of the rocket, we seem to be forgetting that the rocket turning in a circle via thrust from it's own engine is going to be accelerating spent fuel outwards, resulting in a large increase in kinetic energy of the spent fuel, and therefore work is being done.
If the rocket were captured by a frictionless circular track that was extremely massive (or otherwise virtually imobile), then the rocket would follow the circular track with no consumption of energy. 


#17
Mar1408, 07:57 PM

P: 21

It seems the only thing we know here is the thrust of the rocket. Does it matter how the thrust is generated as to what the energy spewed into space is (I assume different types of rockets have different efficiencies in this regards)? Is there some way thrust can be converted into energy? If there is no one to one correlation of thrust to energy is there a possibility of knowing what the "best case" scenario would be, a rocket with 100% efficiency perhaps? 


#18
Mar1408, 09:23 PM

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Efficiency for rocket engines, is rated at impulse per unit of fuel.
http://en.wikipedia.org/wiki/Rocket_engine The power produced by a rocket engine would require knowledge of the actual rate of kinetic energy of the spent fuel which would equal the spent fuels terminal velocity (relative to the rocket), times the rate of mass of spent fuel ejected from the engine (mass of spent fuel ejected per unit time). This link provides some "common" efffective exhaust velocities. http://en.wikipedia.org/wiki/Specific_impulse Another link, with an equation for calculating exhasust velocity: http://en.wikipedia.org/wiki/Rocket_engine_nozzle 


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