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Author Topic: Where does the energy go?  (Read 9302 times)

Offline jartza

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Where does the energy go?
« on: 27/10/2010 23:43:07 »
When I am climbing a ladder in a gravity field, my chemical energy is turning  into potential energy.

When I am climbing a ladder in a accelerating rocket, what energy is my chemical energy turning  into?



 

Offline JP

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Where does the energy go?
« Reply #1 on: 28/10/2010 04:46:22 »
Kinetic energy.

If the rocket stopped accelerating and you kept climbing, you'd accelerate ahead of the rocket.  The problem is that the rocket is burning fuel and gaining kinetic energy from that burn at a faster rate than you can due to your climbing, so it catches up with you every time you push off the ladder.

Disclaimer:  You could complicate matters by bringing up general relativity.  General relativity would have a much more complicated answer, since energy of a gravitational field is a murkier concept...
 

Offline jartza

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« Reply #2 on: 28/10/2010 09:39:57 »
Oh yes kinetic energy.

But what if two identical rockets are accelerating and one astronaut in one rocket is climbing a ladder, while another astronaut in another rocket is staying at the floor. Then the astronaut stops climbing and the rockets stop accelerating. Now everything is moving at the same speed in the two rockets. Where did the climbing energy go?
 
 

Offline Bill S

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« Reply #3 on: 28/10/2010 10:54:47 »
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one astronaut in one rocket is climbing a ladder,

How about the climbing astronaut radiates more heat?
 

Offline jartza

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Where does the energy go?
« Reply #4 on: 29/10/2010 06:26:37 »
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one astronaut in one rocket is climbing a ladder,

How about the climbing astronaut radiates more heat?

Yes but he also does the climbing work, in addition to the heating work.
 

Offline jartza

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« Reply #5 on: 29/10/2010 06:31:30 »
Oh yes the kinetic energy difference between climbing astronaut and the other astronaut increases all the time. When the climber stops quite large kinetic energy is transferred from the astronaut to the rocket.
 

Offline Vereava

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Where does the energy go?
« Reply #6 on: 01/11/2010 19:21:25 »
Where did the climbing energy go?
 

I believe the energy went back to it's former potential state. Are your rockets in a frictionless, gravity free state? Or are they climbing out of orbit?
 

SteveFish

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Where does the energy go?
« Reply #7 on: 01/11/2010 21:55:24 »
With two identical rockets and the astronaut climbing in one and not in the other, I think that when they run out of fuel their centers of gravity will be at the same height, while the one with the climber will have its center of gravity moved toward the nose cone a little.

In terms of understanding this sort of puzzle, it might be instructive to consider where the energy goes if two identical rockets are positioned nose to nose (no gravity field or on two rail cars) and turned on. They wouldn't move, so where did the energy go? I think Bill S nailed it.
 

Offline Vereava

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« Reply #8 on: 02/11/2010 02:37:49 »
Excuse me if this is a stupid question, but...

If one's chemical energy is being converted into kinetic energy, and that's helping you move up the ladder in the rocket that you're moving at the same speed as, is your kinetic energy (which is coming from chemical energy, being converted to body heat, as bill s. said) really going to change the center of gravity of a rocket that ways tons and tons more than you?
 

SteveFish

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« Reply #9 on: 02/11/2010 14:37:32 »
Vereava:

As I see it, you should consider to what extent the climbing astronaut actually moved up the ladder and the amount the climb pushed the rocket down. Keep in mind that the effect of the relative weights of the astronaut and the rocket is a ratio, so the change in the center of gravity would be small.

Steve
 

Offline jartza

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Where does the energy go?
« Reply #10 on: 03/11/2010 00:55:16 »
The muscles of the climbing astronaut do NOT cause the astronaut to gain more speed.
BUT the muscles of the climbing astronaut cause the astronaut to gain more SPEED ENERGY. (also known as kinetic energy)

Here is a table, on the left is the speed of the rocket, and on the right is the speed of the climber, all speeds are relative to inertial observer, an observer that is not in a rocket:

10   11
20   21
30   31
40   41


Now here are kinetic energies corresponding to those speeds: (the astronaut has mass 2 kg, and so does the rocket)

100   121
400   441
900   961
1600  1681


Here is the difference table, where we can see that the climber is gaining extra kinetic energy at constant rate:

21
41
61
81

 

Offline TylerDurden4

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« Reply #11 on: 24/11/2010 20:12:10 »
You are forgetting that with every action, there is an equal and opposite reaction. Every step on the ladder you take is stealing kinetic energy from the rocket and giving it to you. It might be easier to visualize this if you imagine standing on the nose of your rocket and jumping. The rocket would slow down and you would speed up. Climbing the ladder would have the same effect, though the KE of the rocket as a whole system (you included) would remain the same. Thus it would require the same amount of energy to stop both rockets no matter what you are doing inside.

Going back to the ideas of some earlier posts: Couldn't a photon with even a miniscule mass explain dark energy? Wouldn't it cause the red shifting that we see from all distant objects that we use as the fundamental measurement of the relative speed of said object?
 

Offline jartza

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« Reply #12 on: 24/11/2010 20:51:40 »
You are forgetting that with every action, there is an equal and opposite reaction.

Who? Me? Am I really forgetting that?  ;D
By the way there is no reaction involved climbing up a ladder.  ;D
A 70 kg person standing on a ladder weighs 700N.
A 70 kg person climbing up a ladder weighs 700N.
See?  ;D

Welcome to the forum :)


« Last Edit: 24/11/2010 21:05:14 by jartza »
 

SteveFish

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« Reply #13 on: 25/11/2010 01:43:49 »
Jartza. You say--"there is no reaction involved climbing up a ladder." This is untrue and you can do the experiment yourself. Put a block of wood on a scale and stand on the scale next to it. Notice the weight registered. Step up onto the block and the measured weight will go up while you are pushing down on the block to raise yourself. Equal and opposite reaction. Steve
 

Offline jartza

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« Reply #14 on: 25/11/2010 06:46:15 »
Jartza. You say--"there is no reaction involved climbing up a ladder." This is untrue and you can do the experiment yourself. Put a block of wood on a scale and stand on the scale next to it. Notice the weight registered. Step up onto the block and the measured weight will go up while you are pushing down on the block to raise yourself. Equal and opposite reaction. Steve

Yes, but a guy climbing up a ladder in an accelerating rocket is just continuously shifting his weight from a step to another step, increase of weight on one step is canceled out by decrease of weight on another step.

Climber is not stealing energy from rocket.
It's more like climber is helping the rocket to accelerate, because in the end
climber's chemical energy has been turned into rocket's kinetic energy, when the climber has bumped on the ceiling, or otherwise stopped climbing.

« Last Edit: 25/11/2010 06:49:28 by jartza »
 

SteveFish

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« Reply #15 on: 25/11/2010 16:18:54 »
Jartza:

You are focused on the total mass of the rocket, including the climber. Just think it through and include the energy of the climbers leg thrusting down against the ladder, and thereby the rocket, to move himself up. Action and reaction. Each step acts against the rocket thrust by temporarily adding the force of the leg thrust to the mass of the climber.

Another way to look at this is to alter the forces involved. Suppose that the rocket was very small and could only lift a platform, a ladder, and a very large and strong ladder climbing expert that is more than half the overall mass of the whole contraption. As the rocket lifts slowly to one meter the climber races up the ladder thrusting it back to the ground.

Steve
 

Offline jartza

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Where does the energy go?
« Reply #16 on: 26/11/2010 02:49:28 »

Yes, but "OUR" climber uses his leg to push the ladder with a force that is the same as the climbers "weight".

 

Offline Geezer

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Where does the energy go?
« Reply #17 on: 26/11/2010 06:51:23 »

Yes, but "OUR" climber uses his leg to push the ladder with a force that is the same as the climbers "weight".



I don't think that is correct. If his leg only exerted sufficient force to support his weight, he would not be able to climb the ladder. He has to supply additional force to accelerate his mass.
 

Offline Airthumbs

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« Reply #18 on: 26/11/2010 09:27:36 »
Has anyone considered that it might be a little bit difficult to climb up a ladder while being subjected to 3-6g? The original question did state that the rocket was accelerating in a gravity field.  I am assuming however that this accelerating rocket is attempting to reach escape velocity of 11.2km/second.   ;D
 

Offline peppercorn

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Where does the energy go?
« Reply #19 on: 26/11/2010 10:57:43 »
Has anyone considered that it might be a little bit difficult to climb up a ladder while being subjected to 3-6g? The original question did state that the rocket was accelerating in a gravity field.  I am assuming however that this accelerating rocket is attempting to reach escape velocity of 11.2km/second.   ;D
Knowing the MO of the OP, I would say he is not interested in escape velocity w.r.t. this question.
It seems hard enough to explain the simplest concepts of free-space acceleration to the OP without the need to bring gravity or escape velocities into it.
 

Offline elfabyanos

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Where does the energy go?
« Reply #20 on: 26/11/2010 11:46:42 »
Jartza - force = mass x acceleration.

For the climber to go from one step to the other he must accelerate upwards, and this requires a force. This force is imparted downwards onto the step, and is in addition to the force of weight that is also imparted onto the step.

As the climber transfers his weight to the higher step the force imparted on it will only be his weight, as the kinetic energy gained by exerting a force downwards onto the previous step will have been transformed into potential energy, and there is no other force anywhere, until he steps up again.

Quote
Yes, but "OUR" climber uses his leg to push the ladder with a force that is the same as the climbers "weight".

No not at all. The man's bone's exert a force downwards equal to the man's weight, and the ladder exerts an equal and opposite force upwards.

Only when the climber moves do the muscles exert force, and this is in addition to the weight.

OK, this is slightly simplified as our bones do not lock out fully and some muscle is need to maintain posture, but the principle is the same. To move more force must be put into the system.

Without a net force there is no acceleration. Newton's laws of physics. For the man to accelerate upwards the force on the step of the ladder must be larger than the weight of the man. The ONLY way this is possible is that this extra force comes from his muscles.

That is indeed the reason why we have muscles.  ;)

Quote
Yes, but a guy climbing up a ladder in an accelerating rocket is just continuously shifting his weight from a step to another step, increase of weight on one step is canceled out by decrease of weight on another step.

Wrong. I can climb up a ladder, and have one foot on one step and one foot on another. I can continually shift my weight from one to the other by changing my posture slightly without going anywhere. Just as I can shift my weight from side to side whilst standing with my legs together without going anywhere.

If there were no other forces apart from decreasing on one step cancelled out by another then the man cannot be moving. If he is, then there are. The force on the step will be larger than his weight so long as he is pushing on it to lift himself up.

Quote
Climber is not stealing energy from rocket.
It's more like climber is helping the rocket to accelerate, because in the end
climber's chemical energy has been turned into rocket's kinetic energy, when the climber has bumped on the ceiling, or otherwise stopped climbing.

No. If the climber goes from the bottom of the rocket to the top then he must have travelled faster than if if he had stayed at the bottom.

The total kintetic and potential energy of the man-rocket system is the same regardless of what the man does as long as he holds on. But if the man climbs up the rocket he gains more potential energy than he would otherwise, and the rocket gains less potential energy. The man will be 20 metres higher than if he didn't climb, the rocket will be a few centimetres lower.

The same applies in a boat. If the boat is accelerating, but you walk forward in the direction of travel the boat does not accelerate as much. This is because you are exerting a backwards force on the boat, to which it must equally respond. So the some of the boat's engine power goes into accelerating you and not the boat. But you give that power back as soon as you stop walking (unless you fall off the front of the boat).
« Last Edit: 26/11/2010 11:54:15 by elfabyanos »
 

Offline jartza

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Where does the energy go?
« Reply #21 on: 27/11/2010 04:17:19 »
All of you guys,
How come climbing energy is height times WEIGHT?

 

Anyone want to correct me on these statements:
A 70 kg person standing on a ladder weighs 700N.
A 70 kg person climbing up a ladder weighs 700N.
What are the real numbers?
« Last Edit: 27/11/2010 13:04:19 by jartza »
 

SteveFish

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« Reply #22 on: 27/11/2010 16:48:58 »
Jartza:

You are very confused. Newton is a unit of force. A ~70kg astronaut standing on a ladder in a rocket before lift off exerts 700N of force downward on the ladder. This is because his mass is being accelerated downward by the earth's 1g. If the rocket takes off and accelerates upward at 1g, thereby increasing the total acceleration downward for the rocket and its contents to 2g, the force on the ladder exerted by the astronaut increases to 1400N. If he then takes a step upward on the ladder with the acceleration of 1/7g the force he exerts on the ladder increases to 1500N while he is pushing down.

Steve
 

Offline jartza

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Where does the energy go?
« Reply #23 on: 28/11/2010 07:52:06 »
Jartza:

You are very confused. Newton is a unit of force. A ~70kg astronaut standing on a ladder in a rocket before lift off exerts 700N of force downward on the ladder. This is because his mass is being accelerated downward by the earth's 1g. If the rocket takes off and accelerates upward at 1g, thereby increasing the total acceleration downward for the rocket and its contents to 2g, the force on the ladder exerted by the astronaut increases to 1400N. If he then takes a step upward on the ladder with the acceleration of 1/7g the force he exerts on the ladder increases to 1500N while he is pushing down.

Steve


Well of course.


Oh yes, I guess I should tell you that unit of weight is Newton.

« Last Edit: 28/11/2010 08:21:00 by jartza »
 

Offline jartza

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Where does the energy go?
« Reply #24 on: 28/11/2010 08:11:42 »
Let's start again from the beginning.

There's an accelerating rocket in outer space, in the rocket there's Bob "climbing" a
ladder "upwards". Where does Bob's energy go?

Answer: The energy turns into kinetic energy of Bob.


Question 2: Bob stops climbing, where is Bob's energy now?
Obvious answer: Bob's kinetic energy is evenly spread into Bob-rocket system.


Advanced considerations: Bob starts climbing, climbs, and stops climbing. This has zero
effect on Bob-rocket system, probably. Where does Bob's energy go in this case?

Answer: The energy must be in the exhaust gases.

 

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