Speed of Force or 'Transfer of Momentum'

so is it a no or a yes to my question?

 

Log in or Sign up to hide all adverts.

weird the same question was asked on other forums

this answer was given on one,
physforum.com

This is (roughly) an elastic collision in 1 dimension. Lets ignore rolling effects.

Density of iron is ρ = 7874 kg/m^3 and you are assuming the objects are sphere where V = (4/3) π r^3 -- so m = ρ V = (4/3) π ρ r^3 or r = ∛((3 m)/(4 π ρ))

m_A = 20 kg
r_A = ∛((60)/(31496 π)) m ≈ 0.085 m
m_B = 30 kg
r_A = ∛((90)/(31496 π)) m ≈ 0.097 m

A head-on collision is where they have opposite directions, thus:

v_A = -8 m/s
v_B = +15 m/s

Because momentum is conserved, total momentum before and after is the same.

m_A v_A + m_B v_B = m_A u_A + m_B u_B = 290 kg m/s

Because this is presumed to be elastic, with little energy lost to heating or converted to deformation or sound, twice the kinetic energy is conserved.

m_A v_A^2 + m_B v_B^2 = m_A u_A^2 + m_B u_B^2 = 8030 kg m^2/s^2

Solving for u_B in terms of u_A, we have:

u_B = (m_A/m_B) v_A + v_B - (m_A/m_B) u_A

Substituting this expression into the second of the former equations we have:

m_A v_A^2 + m_B v_B^2 = m_A u_A^2 + m_B ( (m_A/m_B) v_A + v_B - (m_A/m_B) u_A )^2 = m_A u_A^2 + (m_A^2/m_B) v_A^2 + m_B v_B^2 + (m_A^2/m_B) u_A^2 + 2 m_A v_A v_B - 2 (m_A^2/m_B) v_A u_A - 2 m_A v_B u_A

or
(m_A + m_A^2/m_B) u_A^2 + (- 2 (m_A^2/m_B) v_A - 2 m_A v_B ) u_A + ( (m_A^2/m_B - m_A) v_A^2 + 2 m_A v_A v_B ) = 0

or
(100/3 kg) u_A^2 + ( -1160/3 kg m/s) u_A + ( -15680/3 kg m^2/s^2 ) = 0

or
(5) u_A^2 + ( -58 m/s) u_A + ( -784 m^2/s^2 ) = 0

or
u_A = (58 m/s ± 138 m/s )/10

The two solutions are u_A = - 8 m/s = v_A which happens before the collision and
u_A = 19.6 m/s which happens after the collision -- lets keep that.
Then u_B = (m_A/m_B) v_A + v_B - (m_A/m_B) u_A = (-16/3) m/s + 15 m/s - (2/3) 19.6 m/s = (-160 + 450 - 392)/30 m/s = -3.4 m/s

So both balls changed direction.

Does the momentum afterwards check?
m_A u_A + m_B u_B = 392 kg m/s - 102 kg m/s = 290 k m/s Check
Does twice the kinetic energy afterwards check?
m_A u_A^2 + m_B u_B^2 = 7683.2 kg m^2/s^2 + 346.8 kg m^2/s^2 = 8030 kg m^2/s^2 Check

---
How much momentum was transferred?
m_A ( u_A - v_A ) = 20 * ( 19.6 + 8 ) = 552 kg m / s

How long did this take? About the same time for the sound to travel from the backend of one ball to the backend of the other. The speed of sound in iron is about 5130 m/s. The distance the sound (a wave that carries momentum) travels is about 0.364 m. So the average force is estimated to be about

( 552 kg m / s ) ( 5130 m/s ) / ( 0.364 m ) ≈ 7.8 million Newtons.

 

Log in or Sign up to hide all adverts.

That's not a complete sentence, but I answered it already: they are one event viewed from different directions.

 

Log in or Sign up to hide all adverts.

sorry, there was a copy/paste error there. I was saying "no" to your infinite jerk statement.

 

Motor Daddy said, "how does a mass apply a force to another mass in zero elapsed time?"

So I told him that it was infinite jerk. As to whether infinite jerk can exist, I made a thread about it last year, which was argued till kingdom come in typical Sf fashion.

 

How convenient that the one case we have found where something travels greater than c, it results in the one situation that allows for travel faster than c. So what great scientist was it that ran these test and discovered that one end of an object only reacts at the speed of sound again?

 

Nothing is traveling faster than light.

I don't know. If this is important to you why not look it up?

 

A reasonably good approximation of a ball hitting a wall has the wall being fixed and infinitely hard and the ball is modeled as a mass with a spring sticking out. In this case, the jerk is constant and the acceleration and force both increase linearly over time.

The instant the ball touches the wall, the force and acceleration are still zero. Then the force begins to rise with time under the equation f=kt. Jerk is constant at k.

I haven't seen the thread in question, but this is a pretty simple Newtonian mechanics problem that should not be controversial.

 

That is NOT what I said. Being ignorant is bad enough. Choosing ignorance (and actually fighting against learning!) because it is more aesthetically pleasing is crack pottery.

This is such a trivial issue, it is never studied on its own. Anyone who understands what sound is should get it. Btw, if you haven't read the wiki on the speed of sound, please do: it describes the first accurate measurement of the speed of sound in air as well as the basics of the methodology I gave you for the experiment in a rod. I gave several examples of fields that require this understanding in a previous post (if you don't understand the examples, ask specific questions about them), but if you want to see the experiment done and can't be bothered to do it yourself, you might try suggesting it to a kid for an 8th grade science fair project.

If you do have an interest in learning, but a stubbornness against taking other peoples' word for it, then do the experiment yourself. If there is something about the setup/method that you don't understand, I'll explain it to you. Heck, if you show me you are serious, I'll even duplicate the experiment with you. Worst case scenario, you blow a Saturday afternoon and all you get out of it is learning something and showing a few strangers on the internet there is more to you than you are showing in this thread.

 

The important issue is whether we can really approximate the ball-wall system like that. For that I'm really not sure.

Here's the thread in question: sciforums - dot - com/showthread.php?115721-Is-it-possible-to-have-Infinite-Jerk


^Did that to avoid my post requiring approval due to Sf links.

 

From my readings from sources that I trust, I only found that the galaxies on the edge of the visable universe only travel close to the speed of light. I thought the notion of space allowing for FTL travel actually comes from the Big Bang Theory or the fact that galaxies outside of the visable universe would then have to travel FTL given their predicted rate of expansion even though they cannot be seen.

I don't care to waste my time looking it up because the only reason why I mention it is because every actual scientific discovery is also mentioned who has made the discovery. It just proves that it is not real science, that nobody knows who discovered it. For all we know, it could have been discovered by some crank troll on the internet. The point here is that there was no great scientist that discovered this by experiment.

 

If it only works in one specific situation then it is not science. A scientific principle must be able to be repeated in a number of situations.

 

@Russ_Watters just don't to reply Prof. Layman anymore. It's never gonna work

Please Register or Log in to view the hidden image!

 

I guess there is at least one sane person here.

 

It is a more complicated function because of the shape of the ball, but the important part of the illustration - that jerk is finite - is the same.

 

Right. The laws of aerodynamics make a plane fly but can't make my car fly so they must be wrong too.

Please Register or Log in to view the hidden image!

Translation: "My ignorance is more comfortable to me, so I prefer to stay ignorant."

 

He's one hard-headed crackpot, that's for sure.

 

It was a simple question for clarification from you.

You did not give any specific/precise answer in terms of 'yes' or 'no'.

What is your 'definition' of an 'event'?

How do you distinguish between two events?

Considering there is only one observer viewing the event, how there are different directions of view for a single event?

 

I'm not a grammar nazi, I only said that because the grammar errors made for more than one possible interpretation of your question and I didn't want to be blamed for picking the wrong one.

??? The very first word of the response was "no". That's your precise/concise answer.

Hopefully, you're not still confused by my quote error...

From the dictionary: "a thing that happens".

If one thing happens, that's one event. If two things happen that's two events.

There is not just one observer, there are three. Or if you prefer, since this is a thought experiment, one observer capable of imagining himself in three different places.

 

I think this is not a proper definition of an 'event' in Physics, to define any 'physical event' as it happens.

Better definition of the term 'event' can be: "a thing that happens in a particular time and at a particular location".