How does momentum affect the motion of objects in a friction-less environment?

[marosa4]

What would the theoretical maximum possible speed be for a platform on a horizontal air-bearing (friction-less), if the only propulsion was a spring powered machine gun with unlimited steel balls? The balls go one way, the platform moves proportionally in the opposite direction. Ignore inertia and mass of the platform and the mass of all the steel balls. Ignore wind resistance. The gun fires the balls at 100kph. Assume the first ball causes the platform to accelerate to 1 kph. What speed would we attain after 10,000 balls?

 

[A.T.]

The balls go one way, the platform moves proportionally in the opposite direction. Ignore inertia and mass of the platform and the mass of all the steel balls. Ignore wind resistance.

Zero propulsion and zero mass to accelerate makes the problem indeterminate.

 

[marosa4]

Add whatever you need to provide an answer then. Basically it's not a math issue. The question boils down to 'Can projectiles with a 100kph velocity have a additive effect if enough of them are used, so that the platform's speed eventually exceeds 100kph.?

 

[jbriggs444]

Add whatever you need to provide an answer then. Basically it's not a math issue. The question boils down to 'Can projectiles with a 100kph velocity have a additive effect if enough of them are used, so that the platform's speed eventually exceeds 100kph.?

Consider that the first ball you fire has to result not only in the acceleration of the platform but in the entire pile of remaining balls.

You can write down an equation for conservation of momentum. Include the mass of a ball, the mass of the platform, the number of balls in the pile and the velocity with which one ball is ejected. Write it down. How much velocity does the platform and pile gain if one ball is fired when the pile size is n balls?

 

[Dale]

Can projectiles with a 100kph velocity have a additive effect if enough of them are used, so that the platform's speed eventually exceeds 100kph.?

Yes. The same is true with rockets. The maximum speed of a rocket is not limited to the speed of the exhaust. What you are describing is a rocket, so all of the usual rocket equations work.

 

[marosa4]

I understand what the theory is, but it still seems implausible. Logically, an equal reaction assuming the equal mass of projectile and platform, when the projectile is fired off at 100kph, the result must be that each would appear to be doing 50 in opposite directions, from a stationary point of view. So I can't see how the platform could ever go faster than the speed that it is being pushed. Surely it can only ever go 50kph. Has this ever been demonstrated on Earth? Is there an example of this effect on a machine in use today? (on earth)

 

[jbriggs444]

I understand what the theory is, but it still seems implausible. Logically, an equal reaction assuming the equal mass of projectile and platform, when the projectile is fired off at 100kph, the result must be that each would appear to be doing 50 in opposite directions, from a stationary point of view. So I can't see how the platform could ever go faster than the speed that it is being pushed. Surely it can only ever go 50kph. Has this ever been demonstrated on Earth? Is there an example of this effect on a machine in use today? (on earth)

This is the first time you have mentioned an equal mass projectile.

Say you have a 1 kilogram cart with a 128 kilogram projectile, a 64 kilogram projectile, a 32 kilogram projectile, a 16 kilogram projectile, an 8 kilogram projectile, a 4 kilogram projectile, a 2 kilogram projectile and a 1 kilogram projectile stacked on top in an inverted pyramid.

You shoot off the 128 kilogram projectile and gain 50 kph.
You shoot off the 64 kilogram projectile and gain another 50 kph
You shoot off the 32 kilogram projectile and gain another 50 kph
You shoot off the 16 kilogram projectile and gain another 50 kph
You shoot off the 8 kilogram projectile and gain another 50 kph
You shoot off the 4 kilogram projectile and gain another 50 kph
You shoot off the 2 kilogram projectile and gain another 50 kph
You shoot off the final 1 kilogram projectile and gain a final 50 kph.

Total 400 kph. See the Tsiolkovsky rocket equation for the case where the fuel is used continuously rather than in discrete shots.

 

[marosa4]

Yep, I get that. I'm having trouble visualizing how 100kph push can add up to be greater than 100. So is there any device or experiment on Earth that demonstrates this effect? I can't go to space to check, and I want proof of concept.

 

[jbriggs444]

Yep, I get that. I'm having trouble visualizing how 100kph push can add up to be greater than 100. So is there any device or experiment on Earth that demonstrates this effect? I can't go to space to check, and I want proof of concept.

How about shooting a rubber band forward (or eastward!) on a moving bus? It will go faster than 60 miles per hour (or faster than 700 miles per hour).

Edit: Or do it at midnight to pick up an extra 30 kilometers per second.

 

[russ_watters]

Yep, I get that. I'm having trouble visualizing how 100kph push can add up to be greater than 100. So is there any device or experiment on Earth that demonstrates this effect? I can't go to space to check, and I want proof of concept.

Each speed boost is from zero and independent of all other speed boosts; The ball and "rocket" start off stationary with respect to each other. So when you fire a ball backwards, you propel the platform in the opposite direction. Your speed change then gets added to the cumulative speed with respect to the ground that you have gained.

 

[sophiecentaur]

Logically,

The most 'logical' thing to do is to accept that it's right and then learn why. Intuition is notoriously bad at getting Science 'right'.
You say that you understand what the theory is but, if you did, then you would believe the 'accepted' answer. Applying Momentum Conservation (one of the most steadfast Laws that we have ever found) to each 'ejection', you get the answer that the platform can go faster and faster and the ejection speed is not the limit. Do the sums.
But first, get your initial model right. How can you ever have unlimited steel balls? That would imply that your initial mass was infinite. Assume an initial mass of M+nm where M is the basic mass of the platform and that you have n balls of mass m. Put in some numbers if you can't stand algebra but that is nothing like as good.
There is no magic involved with this so the Maths can be totally relied upon. And if you don't believe in maths, why are you using a computer to communicate with PF? The whole internet system is based on Maths which Works.

 

[marosa4]

That does not demonstrate the effect of Newtons third law. Now if the rubber band could be shot out the back window, and the bus speed up, that would be something. Assuming that the bus was already doing same speed that the rubberband would be "fired". So I repeat the question, "Is there an Earth bound experiment demonstrating this effect?"

 

[marosa4]

Each speed boost is from zero and independent of all other speed boosts; The ball and "rocket" start off stationary with respect to each other. So when you fire a ball backwards, you propel the platform in the opposite direction. Your speed change then gets added to the cumulative speed with respect to the ground that you have gained.

But from my point of view, (the earth) the rocket is NOT stationary, and the gas stream as I measure it is say 10,000kph, and the rocket is somewhat less, say 3,000kph. So from my stationary point of view and measuring system, using reliable scientific principals, (Newtonian) once the rocket reaches the theoritical maximum velocity of 5,000kph, there is no way it can go any faster. So I still would like to see an Earth bound experiment that demonstrates this effect of incremental velocity increase from a lesser velocity reaction.

 

[marosa4]

hysical

The most 'logical' thing to do is to accept that it's right and then learn why. Intuition is notoriously bad at getting Science 'right'.
You say that you understand what the theory is but, if you did, then you would believe the 'accepted' answer. Applying Momentum Conservation (one of the most steadfast Laws that we have ever found) to each 'ejection', you get the answer that the platform can go faster and faster and the ejection speed is not the limit. Do the sums.
But first, get your initial model right. How can you ever have unlimited steel balls? That would imply that your initial mass was infinite. Assume an initial mass of M+nm where M is the basic mass of the platform and that you have n balls of mass m. Put in some numbers if you can't stand algebra but that is nothing like as good.
There is no magic involved with this so the Maths can be totally relied upon. And if you don't believe in maths, why are you using a computer to communicate with PF? The whole internet system is based on Maths which Works.

So can I assume then, that its never been shown to work in a real physical experiment?

Maths is not proof of concept. Demonstration and observation is. Maths equations relly on postulates or assumptions that you have the correct equation in the first instance. So they can be misleading.

 

[marosa4]

Consider that the first ball you fire has to result not only in the acceleration of the platform but in the entire pile of remaining balls.

You can write down an equation for conservation of momentum. Include the mass of a ball, the mass of the platform, the number of balls in the pile and the velocity with which one ball is ejected. Write it down. How much velocity does the platform and pile gain if one ball is fired when the pile size is n balls?

OK, as a thought experiment then, another vehicle is keeping pace alongside the "platform" in question. The support vehicle has a bunch of balls, and it places one ball at a time as needed, on to the platform so it can be fired off at 100kph. Now we have no mass problem for the platform. One ball fired at 100kph from the initially stationary platform results in say a 10kph velocity of the platform as a reaction according to Newton's third law. So then we give another ball to the platform and repeat the firing. Platform increases speed to 20kph... Repeat... Can the platform ever exceed 50kph? I am measuring the speeds of platform and the projectiles from my stationary observatory. What will happen, and what will I measure?

 

[russ_watters]

But from my point of view, (the earth) the rocket is NOT stationary, and the gas stream as I measure it is say 10,000kph, and the rocket is somewhat less, say 3,000kph. So from my stationary point of view and measuring system, using reliable scientific principals, (Newtonian) once the rocket reaches the theoritical maximum velocity of 5,000kph, there is no way it can go any faster.

Newton's "reliable scientific principal" is called "the principal of relativity":
https://en.wikipedia.org/wiki/Principle_of_relativity

It's what we're trying to explain to you.

So I still would like to see an Earth bound experiment that demonstrates this effect of incremental velocity increase from a lesser velocity reaction.

Stand up and walk across the room. Due to Earth's rotation you were just walking at roughly 900 miles per hour. Given that you are not Superman, your ability to increase your speed is clearly not impacted by the speed you already had.

 

[marosa4]

Newton's "reliable scientific principal" is called "the principal of relativity":
https://en.wikipedia.org/wiki/Principle_of_relativity

It's what we're trying to explain to you.

Stand up and walk across the room. Due to Earth's rotation you were just walking at roughly 900 miles per hour. Given that you are not Superman, your ability to increase your speed is clearly not impacted by the speed you already had.

So that is the best experiment you have? Me walking across the room and the planet rotating under foot? Hardly something I can measure. Can you think of something more practical to show the effect please? Newtons application of Relativity results in the fact that the platform can not move faster than the speed of the projectile. I'm measuring it from a stationary position. The Newton's math is correct. So I'm still insisting on simple experiment please. No experimental evidence, then the claim is still just an hypothesis.

 

[marosa4]

The most 'logical' thing to do is to accept that it's right and then learn why. Intuition is notoriously bad at getting Science 'right'.
You say that you understand what the theory is but, if you did, then you would believe the 'accepted' answer. Applying Momentum Conservation (one of the most steadfast Laws that we have ever found) to each 'ejection', you get the answer that the platform can go faster and faster and the ejection speed is not the limit. Do the sums.
But first, get your initial model right. How can you ever have unlimited steel balls? That would imply that your initial mass was infinite. Assume an initial mass of M+nm where M is the basic mass of the platform and that you have n balls of mass m. Put in some numbers if you can't stand algebra but that is nothing like as good.
There is no magic involved with this so the Maths can be totally relied upon. And if you don't believe in maths, why are you using a computer to communicate with PF? The whole internet system is based on Maths which Works.

You can back up your experimental evidence with Maths if you want. But to begin just show me what experiments have been conducted please.

 

[russ_watters]

So that is the best experiment you have? Me walking across the room and the planet rotating under foot?

Yes. It demonstrates the effect you are investigating and is easy to do.

Hardly something I can measure...

Well that's an interesting take. In order for a measurement to be useful, you need to predict what you will measure and then see if the measurement matches the experiment. Do you have any prediction you can calculate here? See: the Principle of Relativity says there is nothing to calculate...or, rather, that all calculations produce the same answer: 0.

Can you think of something more practical to show the effect please?

...So I'm still insisting on simple experiment please.

There can be nothing more simple and practical than an experiment you can do right now, yourself. Can you explain differently what kind of experiment you want? Based on the Principle of Relativity, literally any experiment involving motion will demonstrate it.

Newtons application of Relativity results in the fact that the platform can not move faster than the speed of the projectile.

It most certainly says nothing of the sort.

The Newton's math is correct.

Please show us the math you are referring to.

 

[marosa4]

Yes. It demonstrates the effect you are investigating and is easy to do.

Well that's an interesting take. In order for a measurement to be useful, you need to predict what you will measure and then see if the measurement matches the experiment. Do you have any prediction you can calculate here? See: the Principle of Relativity says there is nothing to calculate...or, rather, that all calculations produce the same answer: 0.

There can be nothing more simple and practical than an experiment you can do right now, yourself. Can you explain differently what kind of experiment you want? Based on the Principle of Relativity, literally any experiment involving motion will demonstrate it.

It most certainly says nothing of the sort.

Please show us the math you are referring to.

Newtons law says and equal and opposite reaction, not any provision for multiplication of the velocity on one side.

Let me put this another way. If YOU were teaching a class of young people about this claimed effect, and you wanted to perform an experiment to show how a slow speed, re applied to an object can increase its speed to be greater than the input speed, how would you do it?

 

[jbriggs444]

Newtons law says and equal and opposite reaction,

Momentum added to projectile in one direction = momentum added to vehicle in the opposite. No mention of how fast the pair is moving prior to the event. You always get the addition of momentum as per Newton, regardless.

 

[russ_watters]

Newtons law says and equal and opposite reaction, not any provision for multiplication of the velocity on one side.

And how do you apply that to a real scenario?

Let me put this another way. If YOU were teaching a class of young people about this claimed effect, and you wanted to perform an experiment to show how a slow speed, re applied to an object can increase its speed to be greater than the input speed, how would you do it?

I would call a student up to the front of the class and ask them to walk back in forth. Then I'd ask if they felt it was harder to walk one way than the other. And why not.

I'll put some math to it. Let's say I burn energy at a rate of 100 Watts when running at 10 mph (about as fast as I can run these days). If this is directly proportional to my speed, then in order to walk east, I would need to expend 9,000 Watts. That level of exertion would definitely be noticeable in walking.

One other issue in solved by the principle of relativity is that 900mph isn't your only speed right now. You also have a speed due to the Earth's orbit around the sun, the sun's orbit around the center of the galaxy, etc. You have, in fact, an infinite number of frames of reference to choose from, there would be an infinite number of answers to any motion question, making calculations impossible.

 

[Dale]

Has this ever been demonstrated on Earth?

It has been demonstrated in space. There is a lot of air resistance on earth.

 

[marosa4]

Momentum added to projectile in one direction = momentum added to vehicle in the opposite. No mention of how fast the pair is moving prior to the event. You always get the addition of momentum as per Newton, regardless.

OK, Jet aeroplanes exhaust velocity is always much larger velocity than the plane's velocity, even when the famous Blackbird spy plane SR71flew at extremely high altitude in a rarefied atmosphere, it did not even equal the velocity of the exhaust gas. So there is one experiment that we have data on that does NOT show that a lesser velocity can add up to create a higher velocity. Surely there is just one decent experiment to prove this claim?

And how do you apply that to a real scenario?

I would call a student up to the front of the class and ask them to walk back in forth. Then I'd ask if they felt it was harder to walk one way than the other. And why not.

I'll put some math to it. Let's say I burn energy at a rate of 100 Watts when running at 10 mph (about as fast as I can run these days). If this is directly proportional to my speed, then in order to walk east, I would need to expend 9,000 Watts. That level of exertion would definitely be noticeable in walking.

One other issue in solved by the principle of relativity is that 900mph isn't your only speed right now. You also have a speed due to the Earth's orbit around the sun, the sun's orbit around the centre of the galaxy, etc. You have, in fact, an infinite number of frames of reference to choose from, there would be an infinite number of answers to any motion question, making calculations impossible.

That's only going to confuse the student. That is no way explains how a lower

It has been demonstrated in space. There is a lot of air resistance on earth.

Sorry, not good enough. You nor I can perform a test in space. Surely there is a simple experiment to demonstrate even a SMALL increase in velocity from a low input velocity. For instance, I spin a merry go round on a frictionless bearing in a vacuum chamber, it won't spin one bit faster than the speed of the input device. So there is one test where the rocket velocity principal is NOT demonstrated. (not disproved, but just not able to demonstrate it.) However, this test perhaps SHOULD have been suitable to show how a fixed, small velocity can combine to result in a higher velocity. Why does it fail? And what test can you or some Physics professor dream up that will show this effect? Actually, flywheels do run in a vacuum housing on air bearings, powered by high-speed gas. They do not ever rotate faster than the gas velocity, don't even approach that speed. Why can't they show the expected velocity increase you are claiming?

 

[Dale]

Sorry, not good enough. You nor I can perform a test in space.

No, that is not an acceptable position to take on this forum. The experiment has been done and it is perfectly valid. You don’t get to cherry pick what evidence is admissible and what is not. That is the role of the peer review system.

If you are interested there is plenty of information on telemetry and rocket design. You can go over it in as much detail as you like, but you don’t get to just neglect it.

 

[jbriggs444]

OK, Jet aeroplanes exhaust velocity is always much larger velocity than the plane's velocity, even when the famous Blackbird spy plane SR71flew at extremely high altitude in a rarefied atmosphere, it did not even equal the velocity of the exhaust gas.

But the exhaust gas exceeded the velocity of the plane. Something you claim is impossible.

 

[marosa4]

No, that is not an acceptable position to take on this forum. The experiment has been done and it is perfectly valid. You don’t get to cherry pick what evidence is admissible and what is not. That is the role of the peer review system.

So it's impossible to prove this effect of what should be standard physics, unless I go into space. Impossible on Earth regardless of the conditions.? So if I think the space experiment is flawed, and want to check the concept, and reproduce the experiment, I can not do any test on Earth? This is a problem that should not exist for such a simple theory.

 

[marosa4]

But the exhaust gas exceeded the velocity of the plane. Something you claim is impossible.

No, The exhaust gas is ALWAYS much faster than the rocket or plane. I never said otherwise. What you are claiming is that somehow the plane or rocket can go faster than the exhaust gas from its own engine.

 

[marosa4]

No, that is not an acceptable position to take on this forum. The experiment has been done and it is perfectly valid. You don’t get to cherry pick what evidence is admissible and what is not. That is the role of the peer review system.

If you are interested there is plenty of information on telemetry and rocket design. You can go over it in as much detail as you like, but you don’t get to just neglect it.

Once upon a time, the "peers" said the Earth was flat. Experiments and results can have different conclusion as to the meaning, depending on one's assumptions to begin with.

 

[Dale]

Once upon a time, the "peers" said the Earth was flat. Experiments and results can have different conclusion as to the meaning, depending on one's assumptions to begin with.

Totally irrelevant. I am not assigning any meaning here. You asked if a specific effect had ever been observed, and it has, conclusively. It is demonstrably possible for a reaction engine velocity to exceed the exhaust velocity.

 

[marosa4]

Totally irrelevant. I am not assigning any meaning here. You asked if a specific effect had ever been observed, and it has, conclusively. It is demonstrably possible for a reaction engine velocity to exceed the exhaust velocity.

Never been observed by anyone other than NASA then is the answer you have for me.
Never observed on earth, and cannot be for some unexplained reason.
They claim to be able to measure Gravitational Waves, and curved spacetime, from earth, but can't demonstrate a simple chemical rocket working like they claim. Why is this unbelievable?

 

[Dale]

Never observed on earth, and cannot be for some unexplained reason.

I explained it already: air resistance.

but can't demonstrate a simple chemical rocket working like they claim.

They have demonstrated it multiple times. The delta v to the space station is about 9 kps and the space shuttle’s exhaust velocity is only about 4 kps. Do you really want to claim that no space shuttle ever made it to the space station?

So it's impossible to prove this effect of what should be standard physics, unless I go into space. So if I think the space experiment is flawed, and want to check the concept, and reproduce the experiment, I can not do any test on Earth?

No, it is not impossible. It is just pointless and expensive, so it hasn’t been done to my knowledge. You can certainly do the test, all you have to do is pay for it. I doubt that you will be able to convince anyone else to chip in.

 

[Dale]

This is the first time you have mentioned an equal mass projectile.

Say you have a 1 kilogram cart with a 128 kilogram projectile, a 64 kilogram projectile, a 32 kilogram projectile, a 16 kilogram projectile, an 8 kilogram projectile, a 4 kilogram projectile, a 2 kilogram projectile and a 1 kilogram projectile stacked on top in an inverted pyramid.

You shoot off the 128 kilogram projectile and gain 50 kph.
You shoot off the 64 kilogram projectile and gain another 50 kph
You shoot off the 32 kilogram projectile and gain another 50 kph
You shoot off the 16 kilogram projectile and gain another 50 kph
You shoot off the 8 kilogram projectile and gain another 50 kph
You shoot off the 4 kilogram projectile and gain another 50 kph
You shoot off the 2 kilogram projectile and gain another 50 kph
You shoot off the final 1 kilogram projectile and gain a final 50 kph.

Total 400 kph. See the Tsiolkovsky rocket equation for the case where the fuel is used continuously rather than in discrete shots.

This would be relatively inexpensive, and if you kept the speeds low enough and the times short enough then air resistance could be minimal. You would only need three stages to prove the point. First stage gets it up to half the “exhaust” velocity, second stage gets it to “exhaust” velocity, and the third stage pushes it past “exhaust” velocity.

 

[weirdoguy]

Once upon a time, the "peers" said the Earth was flat.

I think that you really should read up on how modern empirical sciences work. Bringing up times where science (in a modern sense, with its modern rigour) barely existed shows only that you don't know much about the things you're trying to talk about... Thus your attitude is a little bit inappropriate.

 

[cjl]

No, The exhaust gas is ALWAYS much faster than the rocket or plane. I never said otherwise. What you are claiming is that somehow the plane or rocket can go faster than the exhaust gas from its own engine.

Actually, this is incorrect for every single orbital rocket. A solid fuel rocket motor has an exhaust velocity of around 2.5km/s, and liquid fuel ranges from 2.5-5 km/s. Orbital velocity is in excess of 7 km/s, so every rocket launched to orbit or escape ends up traveling faster (relative to its launch pad) than the exhaust velocity.