Checking energy to accelerate a body is TWICE what you get back from that object

[lenfromkits]

E= 1/2mv²

Since "for every action there is an equal and opposite reaction", I can only accelerate one object by pushing away from another, meaning both accelerate in opposite directions. If both weigh the same, then my energy that I spent will be divided into 2, meaning each half will only contain half the energy (in kinetic energy) that it takes to accelerate them. RELATIVE TO THE GROUND - NOT TO AN OBJECT.------------------------
It means that, (totally making up numbers here), if when my car is traveling at 100km/hr, it has 1000 joules of kinetic energy, and if one litre of gas has exactly 1000 joules of energy, then I will need to burn TWO litres of gas to get my car going 100km/hr.

And this is because my car has basically moved 'forward' while the Earth has moved backward - each absorbing half of the energy burned from the gas.

 

[FoxCommander]

Lets begin by saying we are in deep space. No gravity nothing. You push off from a rock the same mass as you. You exert a force of 100N for .1meters. You have done 10 Joules of work. Now let's look at the after math. The Rock has also done 10 Joules but in the opposite direction. To make things simple let's say you and the rock have a mass of 50 Killograms. You both will have whatever the same velocity is. How much work have YOU done? You have done 10 joules, how much work has the rock done? 10 joules. So if you invest 10 joules of work in one direction you will produce 10 joules of work in another. You will not however do 20 joules of work. Because you have only pushed 100N for .1meters.

In the case of the larger object, same thing applies. You push 100N one direction the asteroid whos mass>>your mass, It will also push 100N no more no less BUT in the opposite direction. So you are not losing half of your energy to moving an yourself. It is just how the math plays out, don't let the 1/2 in the KE=1/2mv^2 confuse you.

The 1/2 comes from the deriviation of the Principle of Work and Energy Which i can show you if you want. Its basically how the 1/2 comes out if you integrate xdx you will get 1/2x^2

As far as your formula for acceleration? not sure what you mean. But it is not correct because technically you are pushing a rock away, so you are causin the rock to accelerate over a distance of .1meters while the rock is in turn causing you to accelerate over a distance of .1meters, because something must push you in order for you to move. So you are not doing twice the work. You the pusher are only pushing on the rock not the rock and you. If you want to think about the car you need to push on the Earth hard enough and long enough till its pushing back causes you to reach a velocity of 100km/hr

Hope it makes sense,
Fox

 

[bp_psy]

E= 1/2mv²
But, what happens if one body is much larger than the other, so that it has almost no movement? There will of course be a microscopic amount of movement on the larger object as it pushes away from the smaller one, but does it still absorb half the invested energy?

The kinetic energy will no be the same.in you scenario the total momentum of the system is conserved that is the amplitude of the momentum of both objects will be the same.Use this to find the ratio of their velocity after the push using (1/2)mv² and you will not find the same energy on both objects.

And is this basically where the "1/2" comes from in this formula?

No the (1/2) comes from the definition of work done by a force over some distance $$\int Fds=\int m\frac{dv}{dt}ds=\int m\frac{ds}{dt}dv=\frac{1}{2}mv^2$$ it is always that.

And so the formula for acceleration (from a stationary 3rd party point of view) of a body is actually E = mv² since you basically have to waste half of it on some other backwards moving object? As in I better buy twice as much gas for my car to get it up to 100km/hr than I thought by looking at the 1/2mv² formula - since I'll be wasting half of it on trying to spin the Earth away from me?
Am I roughly on the right track?

Not really.

 

[Cleonis]

E= 1/2mv²

And so the formula for acceleration (from a stationary 3rd party point of view) of a body is actually E = mv² since you basically have to waste half of it on some other backwards moving object?

Am I roughly on the right track?

No. Unfortunately you have sidetracked yourself badly.

The 1/2 in the expression for the kinetic energy arises for the same reason as the 1/2 in the following expression for position as a function of time:

$$s(t) = \frac{1}{2}at^2$$


We have that in the case of a uniform force acceleration is uniform, and velocity of an object as a function of time is given by:

$$v(t) = at$$

Which is of course graphed as a straight line.

Given this expression, how much distance does the object travel in t units of time? Well, the distance covered is proportional to the area underneath that graph. The area underneath that graph is a triangle with base t and height a*t. The area of that triangle is $\frac{1}{2}at^2$

We have that when an object is accelerated by a force, then the amount of energy gained is F*d (d = distance traveled)
That allows you to derive an expression for energy as a function of velocity, which comes out as: $\frac{1}{2}mv^2$

The factor 1/2 is unrelated to the physics of action-reaction.

 

[lenfromkits]

Lets begin by saying we are in deep space. No gravity nothing. You push off from a rock the same mass as you. You exert a force of 100N for .1meters. You have done 10 Joules of work. Now let's look at the after math. The Rock has also done 10 Joules but in the opposite direction. To make things simple let's say you and the rock have a mass of 50 Killograms. You both will have whatever the same velocity is. How much work have YOU done? You have done 10 joules, how much work has the rock done? 10 joules. So if you invest 10 joules of work in one direction you will produce 10 joules of work in another. You will not however do 20 joules of work. Because you have only pushed 100N for .1meters.

In the case of the larger object, same thing applies. You push 100N one direction the asteroid whos mass>>your mass, It will also push 100N no more no less BUT in the opposite direction. So you are not losing half of your energy to moving an yourself. It is just how the math plays out, don't let the 1/2 in the KE=1/2mv^2 confuse you.

The 1/2 comes from the deriviation of the Principle of Work and Energy Which i can show you if you want. Its basically how the 1/2 comes out if you integrate xdx you will get 1/2x^2

As far as your formula for acceleration? not sure what you mean. But it is not correct because technically you are pushing a rock away, so you are causin the rock to accelerate over a distance of .1meters while the rock is in turn causing you to accelerate over a distance of .1meters, because something must push you in order for you to move. So you are not doing twice the work. You the pusher are only pushing on the rock not the rock and you. If you want to think about the car you need to push on the Earth hard enough and long enough till its pushing back causes you to reach a velocity of 100km/hr

Hope it makes sense,
Fox

Hi, thanks. I'm still stuck. Your explanation was very thoughtful, thank you - but it didn't quite address my example because I'm looking at everything from a THIRD point of view (ie, the earth) - not from one of the two objects in space.

So, if we just imagine me in a boat pushing away from you in your boat. Relative to the water, each boat is moving. Each has its own separate kinetic energy. The total kinetic energy of that system is now my boat plus your boat (relative to the water). The total energy of the system is TWICE the energy of just my boat. My boat only contains HALF of the energy I invested (since yours contains the other half) - relative to the water. (I understand that one boat relative to the other boat is a different story and that since one can just regard the other as stationary, it can regard itself as containing all the kinetic energy, but I am relating everything to the water, since that's really what we do when we talk about a moving object - relate it to the earth).

 

[FoxCommander]

The kinetic energy will no be the same.in you scenario the total momentum of the system is conserved that is the amplitude of the momentum of both objects will be the same.Use this to find the ratio of their velocity after the push using (1/2)mv² and you will not find the same energy on both objects.

Actually it might depend on how you push off. When you push off like i explained earlier as in 100N for .1 meters you will have the same kinetic energy for both but you will have different momentums. At least that is what i calculated out and the physics seems to check out.


Fox

 

[bp_psy]

How much work have YOU done? You have done 10 joules, how much work has the rock done? 10 joules. So if you invest 10 joules of work in one direction you will produce 10 joules of work in another. You will not however do 20 joules of work. Because you have only pushed 100N for .1meters.

The rock does not push your whole body over the same distance.Therefore using F*Deltax does not work.

Actually it might depend on how you push off. When you push off like i explained earlier as in 100N for .1 meters you will have the same kinetic energy for both but you will have different momentums. At least that is what i calculated out and the physics seems to check out.

In this case momentum is conserved (it remains 0) the energy is not.

 

[FoxCommander]

Ahhhhh See now i understand what you want me to answer,
Your boat will yes have half of the energy of the SYSTEM but not on what you have invested. If you concsider a coordinate system where your forward is positive and your backwards is negative, The you push on my boat in the negative direction and i push back(equal and opposite) in the positive direction. There fore we have canceled each others work. So from a third party perspective we have both pushed on each other and both invested energy in the system making the total energy twice of what you individually added. Make sense?

Another thing is that you are not pushing both boats so you have not invested any energy in your own boat. Only in mine, and i have inturn provided the same investment in your boat. This is the basic principle of Newtons law. Yes you have stumped me even thinking about it but in the end it makes if you think about it in terms of both of us pushing on each other.

Another thing is that the Total energy is still Zero... How? well you must also take in direction. Your positive kinetic energy +my NEgative kinetic energy=0 since we both have the same. But that might be a bit confusing so disregard it if you don't understand.

Fox

 

[bp_psy]

Another thing is that the Total energy is still Zero... How? well you must also take in direction. Your positive kinetic energy +my NEgative kinetic energy=0 since we both have the same. But that might be a bit confusing so disregard it if you don't understand.

Fox

Energy is a scalar quantity you do not take into count any direction.

 

[lenfromkits]

Ahhhhh See now i understand what you want me to answer,
Your boat will yes have half of the energy of the SYSTEM but not on what you have invested. If you concsider a coordinate system where your forward is positive and your backwards is negative, The you push on my boat in the negative direction and i push back(equal and opposite) in the positive direction. There fore we have canceled each others work. So from a third party perspective we have both pushed on each other and both invested energy in the system making the total energy twice of what you individually added. Make sense?

Another thing is that you are not pushing both boats so you have not invested any energy in your own boat. Only in mine, and i have inturn provided the same investment in your boat. This is the basic principle of Newtons law. Yes you have stumped me even thinking about it but in the end it makes if you think about it in terms of both of us pushing on each other.

Another thing is that the Total energy is still Zero... How? well you must also take in direction. Your positive kinetic energy +my NEgative kinetic energy=0 since we both have the same. But that might be a bit confusing so disregard it if you don't understand.

Fox

Thanks.

Re: "zero net energy": But I invested energy. Where did it go. I hope you're not going to make suggestions to me one what to do with my money! Haha. :) I'm just kidding.

Re: me pushing on you and you pushing on me. This is true - BUT, regardless, I'm only counting the 'energy' invested which is the total of us pushing on each other's boat.

Re: net energy is zero. I don't think they actually cancel each other out and that they are based on direction like that. I see what you mean but theoretically I can capture back the energy from each of those boats into the same repository, increasing it each time. For instance, each could ram into a lever that lifts a weight up off the ground - but by way of pulleys, they lift the same rock.

 

[FoxCommander]

This is true... Hmmm i knew a way to explain how the total energy comes out to zero... but i don't remember... Does anyone know?

 

[bp_psy]

This is true... Hmmm i knew a way to explain how the total energy comes out to zero... but i don't remember... Does anyone know?

Stop trolling.

 

[lenfromkits]

This is true... Hmmm i knew a way to explain how the total energy comes out to zero... but i don't remember... Does anyone know?

Net energy gain/loss is zero. I started in my case with a bowl of cornflakes I ate for breakfast and used that to push the boats apart. In the end, that energy from the cornflakes still exists in the same amount in the kinetic energy of our boats.

But, just to reflect. My main question then is, in this case (relative to the water) a person would have to say that the kinetic energy in my boat is only HALF of the energy I invested to get it moving at that speed. So since we ALWAYS push away from another moveable object, the energy to accelerate an object up to velocity=V is always twice the energy we can get back from that object. To recoup the full energy, we have to also find the object that was pushed 'away from.'

This is still how I see it so far. The key point here is all this is "relative to the water" - not to one of the boats.

 

[FoxCommander]

Okay first: I know i was thinking the same thing with the investments hahaha.
Your so called investment which is the total work by pushing you did went into my boat moving. While when you were pushing on my boat the boat was pushing back and so my boats investment went into your body which is attached to your boat etc. Makes sense?
Second: True So yes there will be 20 joules of energy in the system being us and our boats. Not sure what else you mean by this statement
Third: Ya i don't knwo where i was going by that but you are also tru that you could harvest this energy BUT you cannot increase it. If you rammed both into a lever then yes the energy would be transferred to the rock therefore it will have 20joules of energy but then that's it youwill have 20 joules stored. Unlessyou pushed again you can not have more energy. If you could you should sell that idea becaus you have just invented something that creates energy from nothing and you would be a trilionare hahaha.

 

[FoxCommander]

The energy you are investing is 10 joules correct? That is to say that you pushed 100N for .1meters. That is how much you have personally invested. You have now pushed the boat which has 10 joules of energy. Your boat will also have 10 joules of energy. So you will invest 10 joules, your boat will have 10 joules. So you have not invested anymore than you have. This is what i can observe from the water. I see that your speed is x and your mass is m so your KE will be 10 joules. And i know that you did 10 joules of work.

 

[lenfromkits]

Okay first: I know i was thinking the same thing with the investments hahaha.
Your so called investment which is the total work by pushing you did went into my boat moving. While when you were pushing on my boat the boat was pushing back and so my boats investment went into your body which is attached to your boat etc. Makes sense?
Second: True So yes there will be 20 joules of energy in the system being us and our boats. Not sure what else you mean by this statement
Third: Ya i don't knwo where i was going by that but you are also tru that you could harvest this energy BUT you cannot increase it. If you rammed both into a lever then yes the energy would be transferred to the rock therefore it will have 20joules of energy but then that's it youwill have 20 joules stored. Unlessyou pushed again you can not have more energy. If you could you should sell that idea becaus you have just invented something that creates energy from nothing and you would be a trilionare hahaha.

Well. If I invest 20 joules of energy into this system of moving boats, then that system contains 20. since your boat is now moving the same speed as my boat (relative to the water), each must contain 10 joules of energy. There is no other way that this can add up.

Therefore, if I invested 20 joules into the system just to get my boat up to this speed (ignoring your boat), then it took 20 joules for me to get my boat up to a speed that has only 10 joules of energy. It means that an object that has 1/2mv₂ would always require 2 * (1/2mv₂) of energy to get it there.

 

[FoxCommander]

see but you did not invest 20 joules. Us two pushing on each other added up to 20 joules. If you pushed 100N for .1meters then the you have invested 10 joules there, for you to invest 20 you would have to double either your distance you pushed or the force you pushed

 

[lenfromkits]

see but you did not invest 20 joules. Us two pushing on each other added up to 20 joules. If you pushed 100N for .1meters then the you have invested 10 joules there, for you to invest 20 you would have to double either your distance you pushed or the force you pushed

No, but YOU aren't pushing. Just me. I do all the pushing and I invest 20 joules of energy doing it. Assume that as the opening statement.

After the boats move apart, we now have TWO boats moving (not just one as you described a couple of messages ago). The total energy of this new moving system is the sum of your energy plus my energy. The total of this system MUST equal the energy I invested - which is 20 joules.

So if the total of energy in two boats is 20 joules (same mass/same speed), then each has 10 joules.

 

[FoxCommander]

You do? What happened to Newtons law? Did it fly out the window? haha You must remember that when you apply a force on an object it pushes back on you. This is the part that i see you must have trouble with. The object(whatever it is boat rock) will always push back. Therefore doing work on you. So where does the work from the object go? It doesn't disapear it goes into your motion as yours goes into the object.

I know you say you invested 20 because you are the one pushing but if the other object didnt push back you wouldn't move you would just stay stationary while the other boat moves away.

And you yes the system has 20 joules but YOU have only pushed 100N for .1Meters which is 10 joules, So you must ask yourself where did the other 10 come from? its obviously not from you because you have finished pushing and you didnt push twice so you must assume that its from the object applying a force on you simultaneously.

 

[lenfromkits]

You do? What happened to Newtons law? Did it fly out the window? haha You must remember that when you apply a force on an object it pushes back on you. This is the part that i see you must have trouble with. The object(whatever it is boat rock) will always push back. Therefore doing work on you. So where does the work from the object go? It doesn't disapear it goes into your motion as yours goes into the object.

I know you say you invested 20 because you are the one pushing but if the other object didnt push back you wouldn't move you would just stay stationary while the other boat moves away.

And you yes the system has 20 joules but YOU have only pushed 100N for .1Meters which is 10 joules, So you must ask yourself where did the other 10 come from? its obviously not from you because you have finished pushing and you didnt push twice so you must assume that its from the object applying a force on you simultaneously.

That is not true. I'm sorry. Yes - a force of pushing on something has the effect of having a counter force pushing back. But that has nothing to do with this and it is best to put aside that for now...

Energy cannot be created or destroyed. Regardless of who is pushing on whom, if 20 joules of energy goes into a system then that system MUST contain 20 joules of energy. The object that is "pushing back" does not expend any energy - that is only the fictitious counter force of inertia. The 'reaction' that of Newton is the whole point here - it's YOUR boat moving away from mine.

On a floating log in between us I have, say, I jar of gasoline that has a potential energy of 20 joules that I used in a motor to push us apart. It pushes us apart. In the end, your boat is moving. My boat is moving. If there was only 20 joules worth of gasoline in that jar, then the total kinetic energy of my boat plus your boat MUST be 20 joules or the law of conservation of energy is broken.

I just want to empasize that that Newton's law doesn't state that things push back on you like that. It states that for every action, there is an equal and opposite reaction. So, the whole point of this whole thread is about recognizing that and embracing it and pointing out that give this law, whenever one object accelerates, it can only do so by causing ANOTHER object to move in the opposite direction - therefore taking away half of the energy invested.

 

[FoxCommander]

So what you are saying is that yes you push/apply a force on the boat. The boat logically moves away. If the boat doesn't push back how is your boat moving? In your terms there has been no force on your boat. There for there should not be any change in your velocity. There for your boat should be stationary and thus the other boat will be the only thing moving. Correct?

If that is correct then you pushed the boat away for .1 meters at 100N and so your kinetic energy(which is zero since you haven't moved) plus the boats will be 10 joules.

Newton's law is set in stone. There is no fictious force, it is an actual force. Something must push back on you for you to be moving. Some force must be applied to your boat for it to be moving.

 

[lenfromkits]

So what you are saying is that yes you push/apply a force on the boat. The boat logically moves away. If the boat doesn't push back how is your boat moving? In your terms there has been no force on your boat. There for there should not be any change in your velocity. There for your boat should be stationary and thus the other boat will be the only thing moving. Correct?

If that is correct then you pushed the boat away for .1 meters at 100N and so your kinetic energy(which is zero since you haven't moved) plus the boats will be 10 joules.

Newton's law is set in stone. There is no fictious force, it is an actual force. Something must push back on you for you to be moving. Some force must be applied to your boat for it to be moving.

The forces don't matter! Sure, go with that. Fine. It's not relevant.

You are disregarding the law of conservation of energy - which is set in stone.

20 joules into the system = 20 joules in the system.

 

[FoxCommander]

I never debated that. I am debating the fact that you just said Newtons Law, which is where the law of conservation of energy comes from, is wrong. And you do have to take into acount the forces because that's what makes everything move.

Okay. Let's go step by step. You stationary on the boat. with another boat next to you.
Im watching from the shore. You push the boat. Now both you and the boat are now moving. What caused you to move? What caused the boat to move?

 

[lenfromkits]

Wow. I never said anywhere in this forum that Newton was wrong. If you feel that way, then I can see where some of the confusion is coming from.

The actual forces are not relevant. If you insist on saying they are, then you are not addressing the question I set out. I am discussing energy. You are talking about something different.

As far as 'what caused the boat to move' - it doesn't matter. Could be an explosion. Could be an elastic band. Could be a big fish splashing.

The boats move apart. Period. But, the question only states that if it took, say 1,000,000 joules of energy to separate those boats, then that new moving system - MUST have 1,000,000 joules of energy in the system. The question then states that this thefore means that each boat must have a separate kinetic energy of 500,000 joules based on each's movement. Period. It can't add up otherwise. If each boat has 1,000,000 joules of kinetic energy then that doubles the energy - which is impossible. If you say only ONE boat has 1,000,000 joules, then that ignores that BOTH are moving. It's really quite simple.

So the question finally asks for confirmation that, given that two objects are always involved (ACCORDING TO NEWTON), and in our case it takes 1,000,000 joules to get MY boat up to a kinetic energy of 500,000 joules, then the ratio there is 2:1. That's all. It means it always takes twice as much energy to accelerate an object as you can get back out of it - UNLESS you go find the 'other' object and get the other half from it as well.

I have to go, I'm hoping some other people can respond as well. Thanks for your attempts to help, but think we are not on the same wavelength as far as communicating goes so not talking about the same things.

 

[FoxCommander]

I have finally understood you. I will discuss the forces later on. To start you have said "The BoatS move apart" That is to say two boats. The explosion that creats 1million J is used to move those TWO boats not one. There fore they will both have 500k J. So you have spent 1 million J to move TWO boats both at 500k J. Energy is conserved and the ratio of energy to boats KE is one to one ie 2*(KE of boat)500k J/1 million J is 1:1

Concider you and a wall(walls don't move) So you on a skateboard between same explosion and wall. Explosion goes off. Wall's after velocity is 0. Your velocity? whatever it would be. All energy is going into you. You now have 1 million joules of energy. the amount of energy spent is 1 million Joules. 1:1

Now the forces. Here it is. why i have emphasised it. When you have an explosion you have ONE source of energy. One source to move 2 boats. Therefore energy of EACH boat to total spent is yes 1:2. In the case of the wall, ONe source ONE object. therefore 1:1.

When you push the boat, where is the energy coming from? Both of you! You pushing on the boat and the boat pushing on you. TWO sources TWO objects 1:1.

I can't make this any clearer. I am sorry to confuse you and frustrate you. If this last one dosent do it for you I would sugest talking to a physics professor.


Fox

 

[lenfromkits]

I have finally understood you. I will discuss the forces later on. To start you have said "The BoatS move apart" That is to say two boats. The explosion that creats 1million J is used to move those TWO boats not one. There fore they will both have 500k J. So you have spent 1 million J to move TWO boats both at 500k J. Energy is conserved and the ratio of energy to boats KE is one to one ie 2*(KE of boat)500k J/1 million J is 1:1

Concider you and a wall(walls don't move) So you on a skateboard between same explosion and wall. Explosion goes off. Wall's after velocity is 0. Your velocity? whatever it would be. All energy is going into you. You now have 1 million joules of energy. the amount of energy spent is 1 million Joules. 1:1

Now the forces. Here it is. why i have emphasised it. When you have an explosion you have ONE source of energy. One source to move 2 boats. Therefore energy of EACH boat to total spent is yes 1:2. In the case of the wall, ONe source ONE object. therefore 1:1.

When you push the boat, where is the energy coming from? Both of you! You pushing on the boat and the boat pushing on you. TWO sources TWO objects 1:1.

I can't make this any clearer. I am sorry to confuse you and frustrate you. If this last one dosent do it for you I would sugest talking to a physics professor.


Fox

Walls do move. How much each moves depends on the total centre of gravity of the two masses involved. Since the walls are attached to the Earth, one body is me on the skateboard while the other is the earth. If I push away from the Earth, the centre of gravity between me and the Earth is "almost" exactly at the centre of the Earth - so it barely moves. But since physics and movement are perfect, it DOES move - just a very very small amount.

The point is that it therefore does absorb some of the energy. That giant mass moving every-so-slightly should absorb 500,000 joules of the energy, which was part of my question needing confirmation - is it still 50/50 or does it skew. Regardless, there is an amount.

As far as your idea of energy coming from both sides, it does not. force - yes, energy no. Energy needs a source. Just because I am burning gas to create a force does not mean you are in reverse. You are only experiencing the equivalent FORCE in reverse - not the equivalent expenditure of energy.

 

[Doc Al]

I just want to empasize that that Newton's law doesn't state that things push back on you like that. It states that for every action, there is an equal and opposite reaction. So, the whole point of this whole thread is about recognizing that and embracing it and pointing out that give this law, whenever one object accelerates, it can only do so by causing ANOTHER object to move in the opposite direction - therefore taking away half of the energy invested.

Only in certain cases will the division of energy be 1:1.

The boats move apart. Period. But, the question only states that if it took, say 1,000,000 joules of energy to separate those boats, then that new moving system - MUST have 1,000,000 joules of energy in the system. The question then states that this thefore means that each boat must have a separate kinetic energy of 500,000 joules based on each's movement. Period. It can't add up otherwise. If each boat has 1,000,000 joules of kinetic energy then that doubles the energy - which is impossible. If you say only ONE boat has 1,000,000 joules, then that ignores that BOTH are moving. It's really quite simple.

So the question finally asks for confirmation that, given that two objects are always involved (ACCORDING TO NEWTON), and in our case it takes 1,000,000 joules to get MY boat up to a kinetic energy of 500,000 joules, then the ratio there is 2:1. That's all. It means it always takes twice as much energy to accelerate an object as you can get back out of it - UNLESS you go find the 'other' object and get the other half from it as well.

Assume for the moment that no energy is lost to heat, noise, and so on, so that we can assume that all of the 1,000,000 joules used to separate the boats goes into the mechanical energy of the boats.

In addition to energy being conserved, you must also conserve momentum. So if the two boats start from rest and have the same mass, then they each end up with half the total energy. (We assume no other forces act on the boats.) But if one boat has twice the mass of the other, it will end up with only 1/3 of the total kinetic energy. If one boat has 100X the mass of the other, the smaller boat will end up with 100X the kinetic energy of the big boat--99% of the total energy goes into the smaller boat.

Walls do move. How much each moves depends on the total centre of gravity of the two masses involved. Since the walls are attached to the Earth, one body is me on the skateboard while the other is the earth. If I push away from the Earth, the centre of gravity between me and the Earth is "almost" exactly at the centre of the Earth - so it barely moves. But since physics and movement are perfect, it DOES move - just a very very small amount.

The point is that it therefore does absorb some of the energy. That giant mass moving every-so-slightly should absorb 500,000 joules of the energy, which was part of my question needing confirmation - is it still 50/50 or does it skew. Regardless, there is an amount.

If you push against the wall, sure it and the Earth moves (since momentum is conserved)--but just a teeny bit that you'll never be able to measure. But the main thing is that the giant mass would absorb a negligible amount of energy. For all practical purposes, all the energy goes to you and your skateboard.

 

[sophiecentaur]

Only in certain cases will the division of energy be 1:1.Assume for the moment that no energy is lost to heat, noise, and so on, so that we can assume that all of the 1,000,000 joules used to separate the boats goes into the mechanical energy of the boats.

In addition to energy being conserved, you must also conserve momentum. So if the two boats start from rest and have the same mass, then they each end up with half the total energy. (We assume no other forces act on the boats.) But if one boat has twice the mass of the other, it will end up with only 1/3 of the total kinetic energy. If one boat has 100X the mass of the other, the smaller boat will end up with 100X the kinetic energy of the big boat--99% of the total energy goes into the smaller boat. If you push against the wall, sure it and the Earth moves (since momentum is conserved)--but just a teeny bit that you'll never be able to measure. But the main thing is that the giant mass would absorb a negligible amount of energy. For all practical purposes, all the energy goes to you and your skateboard.

At last someone has injected some sense into this thread. Dalespam has said all that's necessary about the topic. N3 rules as ever.

Why do people jump in with both feet and try to rubbish stuff like Newton's laws and how the laws apply? If they think they have found a 'way round' something as basic as N3 then they really should think that they are Wrong and that they really need to find the flaw in Their argument and not in Newton's. Only after a vast amount of work on their part should they even consider that they may be even a teeny bit right. I know about the 'spirit of enquiry' and all that but there is a saying involving rushing in where angels fear to tread.

 

[mrspeedybob]

There are 2 factors at play here...

Conservation of energy
Conservation of momentum

In an action and reaction scenario momentum is going to be conserved, in other words both boats will leave with the same momentum away from the interaction point. Momentum is M*V but energy is 1/2*M*V^2 so both objects will not leave with the same kinetic energy. Let's consider 2 scenarios

You are in a boat weighing 1000 kg I am in a dingy weighing 100 kg. You push off with a force that results in you going 1 m/s since my momentum must be equal I must be going 10 m/s. You have 500 joules of kinetic energy and I have 5000 joules of K.E. so 5500 joules of work has been done.

Now suppose instead of a 100kg dingy I am in a 10000 kg yacht. If you give the same push now I wind up with 500 joules of K.E., moving about 0.32 m/s, you would leave with 5000 joules of K.E. at a speed of 3.2 m/s.

As you can see momentum is conserved in both instances but in the second case you leave with a much greater velocity for the same energy input. This is why cars are so much more efficient then rockets. In a car your reaction mass is the entire earth, it is very large compared to the car and so the car ends up with the vast majority of the kinetic energy. In a rocket the reaction mass is small compared to the vehicle and so most of the energy gets carried away by the fuel and only a small part is added to the vehicles kinetic energy. The perfect scenario would be for the reaction mass to be infinite, in which case all of the energy would be added to the vehicle. Wheel driven vehicles such as cars or trains are very close to this.

This is also why you can shoot a pistol without blowing your hand off. The mass of the gun is large compared to the mass of the bullet. The same momentum is added to each when the explosive detonates but the bullet carries the vast majority of the energy.

 

[lenfromkits]

There are 2 factors at play here...

Conservation of energy
Conservation of momentum

In an action and reaction scenario momentum is going to be conserved, in other words both boats will leave with the same momentum away from the interaction point. Momentum is M*V but energy is 1/2*M*V^2 so both objects will not leave with the same kinetic energy. Let's consider 2 scenarios

You are in a boat weighing 1000 kg I am in a dingy weighing 100 kg. You push off with a force that results in you going 1 m/s since my momentum must be equal I must be going 10 m/s. You have 500 joules of kinetic energy and I have 5000 joules of K.E. so 5500 joules of work has been done.

Now suppose instead of a 100kg dingy I am in a 10000 kg yacht. If you give the same push now I wind up with 500 joules of K.E., moving about 0.32 m/s, you would leave with 5000 joules of K.E. at a speed of 3.2 m/s.

As you can see momentum is conserved in both instances but in the second case you leave with a much greater velocity for the same energy input. This is why cars are so much more efficient then rockets. In a car your reaction mass is the entire earth, it is very large compared to the car and so the car ends up with the vast majority of the kinetic energy. In a rocket the reaction mass is small compared to the vehicle and so most of the energy gets carried away by the fuel and only a small part is added to the vehicles kinetic energy. The perfect scenario would be for the reaction mass to be infinite, in which case all of the energy would be added to the vehicle. Wheel driven vehicles such as cars or trains are very close to this.

This is also why you can shoot a pistol without blowing your hand off. The mass of the gun is large compared to the mass of the bullet. The same momentum is added to each when the explosive detonates but the bullet carries the vast majority of the energy.

? Who is this guy? :). Thanks! That is a really great and thoroughly put explanation. I really appreciate all the effort. I get it now. The momentum is equal. I can also see now that the momentum formula in this case is linear, whereas the energy formula is nonlinear, so they increase at different rates.

Thanks for the help.
Len