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Rubber Tube Contraction Velocity

11/25/2014 7:02 PM

Assume that you have 2 rubber tubes,of equal diameter and wall thickness,made of

the same material,natural rubber.

They have the same stretch force characteristics: A 50% stretch will require 50

pounds of pull,regardless of the length.

One tube is twice as long as the other,say 12 inches,and it is stretched to 18 inches,a

50% stretch,requiring 50 pounds of force to stretch it to 18 inches.

The second tube is 24 inches long,and it is stretched to 36 inches, also a 50%

stretch,and requires 50 pounds of force to stretch it to 36 inches.

If a projectile is placed in a pocket at the end of each tube,and released at the exact

same time, will there be a difference in the velocity of the projectiles?

Will there be a difference in the "time to target"?

It would seem to me that the shorter tube would accelerate the ball faster,due to the

force applied over a shorter distance,and arrive at the target sooner,even though the

maximum velocity achieved by the projectiles would be the same.

The shorter tube would get the advantage in the "hole shot".

The projectiles are of equal dimensions and material,and are spherical in shape.

Any ideas or opinions on this?

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#1

Re: rubber tube contraction velocity

11/25/2014 8:01 PM

What are you smoking?

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#2

Re: rubber tube contraction velocity

11/25/2014 8:34 PM

How do you propel the projectile again? Is the pocket ejecting the projectile? How big is the pocket? Is it ambient temperature?

Target is what? Where?

Give up smoking before it is too late!

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#3

Re: rubber tube contraction velocity

11/25/2014 8:50 PM

Energy input minus losses equals stored energy. 50# in both cases.

Energy Imparted into projectile minus losses equals distance traveled.

If both cases are equal.

Can you PM some inspiration my way?

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#4

Re: rubber tube contraction velocity

11/25/2014 8:51 PM

Energy = force x distance. So the longer one has the same force acting over twice the distance so has twice as much energy stored up. If it transfers this energy to the payload, the larger one imparts twice as much energy.

Energy = 1/2 m v^2, so if the projectile has twice as much energy, it will have sqrt(2) times the velocity.

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#6
In reply to #4

Re: rubber tube contraction velocity

11/25/2014 9:50 PM

Correct. GA

Actually, this would be correct if the tubing was weightless. There is more tubing to accelerate in the longer one.

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#7
In reply to #6

Re: rubber tube contraction velocity

11/25/2014 10:20 PM

Agreed. I was going to add the other energy loss of natural rubber not really being very elastic but the tubing mass difference will probably be the greater burden.

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#5

Re: rubber tube contraction velocity

11/25/2014 8:55 PM

Calculate the potential energy from the work done on each tube.

For a given projectile mass, if the potential energy is the same in every case, so will be the projectile's 'muzzle' velocity.

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#19
In reply to #5

Re: rubber tube contraction velocity

11/26/2014 11:04 PM

Rixter is correct. Energy = Force x distance, but the force changes as the rubber tube contracts. If we assume force/distance is linear, the average force over the given distance is 25 lbs for both cases. The potential energy of the longer one is twice as large as the potential energy of the shorter one when fully stretched since the distance is twice as much and the average force is the same. (If it's not linear, you have to integrate f(x)dx.) Assuming all of the potential energy is converted to kinetic energy, the ball from the long one will have twice the kinetic energy (0.5 mv^2) when it is released than the short one. They have the same mass, so the velocity of the faster one is sqrt(2) x velocity of the slower one.

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#8

Re: rubber tube contraction velocity

11/25/2014 10:55 PM

The longer the pull the more energy is stored, the more energy the faster the velocity...

http://slingshotforum.com/blog/11/entry-235-power-modelling-slingshot-band-velocity-and-energy-melchior-menzels-paper-2006/

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#11
In reply to #8

Re: rubber tube contraction velocity

11/25/2014 11:10 PM

I can easily see the info in the chart,but I think it is referring to the same

bands,pulled to different lengths, not to 2 bands of different lengths at rest,with the

same pull weight at the point of release.

The info in the chart is common sense;if you pull the band further,the projectile will

go further,but that is not exactly the situation I am referring to.

The pull rate will decrease with decreasing length,so it does not maintain the same

thrust for the entire stroke.

Thanks for the good link though.

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#22
In reply to #11

Re: rubber tube contraction velocity

11/27/2014 1:44 AM

In another lifetime, I made several spear-guns for scuba fishing, using such tubes.

I recall the grade being called 'surgical tubing'.

Given that the projectile will immediately tend to succumb to gravity when it is released, it stands tio reason that the longer the contact and/ push of the tubing, the further the projectile will travel. I am not saying it will travel faster...only further.

Anyhow, it all gets distorted under water, so maybe I'm just blowing bubbles here!

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#9

Re: rubber tube contraction velocity

11/25/2014 11:02 PM

I am looking at it like this:

The shorter tube expends all of it's energy(50 pounds) in 6 inches,the longer tube

expends all of it's energy(50 pounds) in 12 inches.

The force decreases with every inch of travel.

The shorter tube would impart a faster rate of acceleration to the projectile,thus

actually leaving the pocket of the tube sooner and arriving at the target sooner.

The maximum speed should be the same,but the shorter tube should get the

projectile to the target sooner,having accelerated the projectile at a faster rate.

Am I looking at this all wrong?

Or have I had too much "Georgia Moon"?

("Less than 30 days old" 100+proof.)

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#10
In reply to #9

Re: rubber tube contraction velocity

11/25/2014 11:07 PM

Finish that glass and get a good rest.

In the morning look up Hooke's law.

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#21
In reply to #10

Re: rubber tube contraction velocity

11/26/2014 11:42 PM

Sorry - Hooke's law won't help you with rubber. So, finish that glass, re-frame the question with steel springs, then look up Hooke's law...

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#12
In reply to #9

Re: rubber tube contraction velocity

11/25/2014 11:31 PM
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#23
In reply to #12

Re: rubber tube contraction velocity

11/27/2014 9:26 AM

I believe I recognize that flowchart in the background, one of my fellow programmers posted it in the shop in 1981. It might be a collectors item.

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#76
In reply to #9

Re: rubber tube contraction velocity

12/02/2014 9:15 AM

Wrong. The stored energy is not 50 pounds; it is 50 pounds times the length. Double the length = double the energy.

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#13

Re: rubber tube contraction velocity

11/25/2014 11:37 PM

Try a slingshot with 2 inches of tube length, and see what you get.

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#14

Re: Rubber Tube Contraction Velocity

11/26/2014 11:12 AM

Sorry, I am poor and dull at English units, fractions and irregular proportions are crazy stuff and quite labor intensive to precious neurons.

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#15

Re: Rubber Tube Contraction Velocity

11/26/2014 11:55 AM

The fog is lifting now from last night's binge.

That was a silly simple question.

Note to self:

Never mix corn whiskey with engineering forum.

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#16
In reply to #15

Re: Rubber Tube Contraction Velocity

11/26/2014 12:41 PM

I can't say anything about other members but I, for one, have been just as fogged on this forum before. My choice of beverages were aged a little longer than your latest choice but everyone is entitled to their choice of poison.

Happy Holiday.

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#18
In reply to #16

Re: Rubber Tube Contraction Velocity

11/26/2014 2:12 PM

This particular poison was very good,even though of a young age.

The worst moonshine I ever drank was about 50 years ago when I was hitch hiking.

An old battered rust bucket of a truck pulled over,and an old man asked where I was going.

"South",I said.

"Do you drink,son?"

"A little now and then" I replied.

"Get that jar out of the glove box"

I did,and he said"Take a drink of that"

When I opened the lid on the Mason jar an aroma hit me that had hints of swamp

water,overtures of frog urine,and a subtle bouquet of algae slime,and slight but

pungent odor of sulphur or rotten eggs.

I knew I did not want any of that,but he said"Take a drink,son"

"No thanks" I said.

The old man reaches beside the door and seat and pulls a pistol on me.

"Take a drink,I said".

So I took a small sip.

"I said take a drink- a big drink!"

So I did,and it was all I could do to suppress the gag reflex.

"That's better.Now hand it to me" he said.

He took the jar,and handed the pistol to me.

"Now,hold the pistol on me so I can take a drink"

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#17
In reply to #15

Re: Rubber Tube Contraction Velocity

11/26/2014 1:16 PM

Are these tubes vented or are both ends sealed?

Can these rubber tubes be used for distillation?

*Hic*

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#20

Re: Rubber Tube Contraction Velocity

11/26/2014 11:36 PM

Down of the farm, if we put 50# of force into any two objects and got twice as much energy out of one of them than we did the other, just because it was longer, we would have called it a miracle.

Maybe I should never have left there for the big city.

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#24
In reply to #20

Re: Rubber Tube Contraction Velocity

11/27/2014 1:03 PM

Your reasoning is flawed. Force is not energy.

You need 50 lbs of force to lift a 50 lb rock to a height of ten feet. You also need 50 lbs of force to lift another 50 lb rock to a height of 20 feet. Which one has the most stored potential energy? When they are dropped, essentially all of the potential energy becomes kinetic energy.

Convervation of energy:

(mgh + 0.5mv^2) at the top equals (mgh + 0.5 mv^2) at the bottom. (i.e., total energy at the top equals total energy at the bottom)

The same principle applies with rubber bands, except potential energy is force x distance. Force is variable with a rubber band. Gravitational force is essentially constant.

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#25
In reply to #24

Re: Rubber Tube Contraction Velocity

11/27/2014 1:54 PM

This may call for a practical experiment.

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#28
In reply to #24

Re: Rubber Tube Contraction Velocity

11/27/2014 2:48 PM

Nope. One cannot raise a 50 lb rock to any height with only 50 lbs of force. You need more.

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#29
In reply to #28

Re: Rubber Tube Contraction Velocity

11/27/2014 3:38 PM

Now, we're confusing work with force.

This may force me to buy some rubber tubing and work this out for myself.

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#79
In reply to #28

Re: Rubber Tube Contraction Velocity

12/02/2014 11:24 AM

OK, 50lb. (wt) rock, 50lb 1oz. forceto lift. Everyone is basically hitting right near the nail.

W=∫F·ds (where d represents in the infinitesimal and s represents displacement.

We have case 1 where (short one, assume l0=10 "), is drawn with an approximate force equation of F=ks where by definition, s= l-l0, and s(max)= 0.5(10")=5", so that W1=∫05ksds =1/2k(5)2. We have that k=50/5=10#/". Thus W1= 125 in.-lb.

In case 2, we have a similar integral to evaluate for work input: (in this case I0=20"), so that s(max)=10", and with k=50/10, or 5#/". W2 = 0.5(5)(100)=250 in.-lb.

100% conversion of Potential to Kinetic energy will be 0.5mv2. and

v1 =(125/0.5m)1/2, while v2 =(250/0.5m)1/2

(the same mass projectile is used in each case), and the velocity ratio becomes

v2/v1 = (2)1/2 by cancellation of factors. The long tube wins hands down.

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#80
In reply to #79

Re: Rubber Tube Contraction Velocity

12/02/2014 11:50 AM

GA.

The stupid system here tells me that I have voted this option too often, even though I have done it only once today so far.

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#26

Re: Rubber Tube Contraction Velocity

11/27/2014 2:17 PM

The maximum velocity of the projectile will be achieved when it is released and loses

contact with the cup.

The cup will be slowed by wind resistance,and thus will not follow or propel the

projectile for the entire length.

Any remaining travel of the cup has no effect on the

projectile,it is merely follow through,and since the contraction force is becoming

smaller as the tube becomes shorter this will also tend to make the cup lag behind

the projectile.

So it appears to be that all of the instantaneous energy is delivered to the projectile

in a very short portion of the stroke.The rest of the energy is wasted.

A super high speed video of both scenarios would be nice, but I do not have access to one.

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#27

Re: Rubber Tube Contraction Velocity

11/27/2014 2:35 PM

HTRN,

You are too old for homework, so what gives?

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#30
In reply to #27

Re: Rubber Tube Contraction Velocity

11/27/2014 4:28 PM

Curiosity.

I realize a bow and arrow are different, the arrow stays in contact for the full length

of the arrow,or a rifle where the expanding gas pushes the bullet for the entire length

of the barrel.

Position the release from the same point,so as not to give the shorter tube an

advantage by being closer to the target.

If you have a tube 1 meter long, in the relaxed state,stretched to 1.5 meters,with an

applied pull force of 50 pounds,versus a 2 meter tube,in the relaxed state, stretched

to 3 meters,with the same applied force, it will take twice as long for the long tube to

fully contract,(1 meter,vs 1/2 meter)thus requiring twice the time to deliver the full

energy that was put into it.

That means the projectile will accelerate at a slower rate than the shorter

tube,although they may reach the same velocity when leaving the pouch, but the

projectile in the longer tube will leave the pouch later.

IMHO,but of course,as always, I could be wrong.

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#32
In reply to #30

Re: Rubber Tube Contraction Velocity

11/27/2014 11:03 PM

No. You are wrong. Newton's second law of motion very simply states F=ma. By your two given conditions, both tubes are pulled back to an identical force and the objects to be accelerated have the same mass the initial acceleration must be the same. The shorter slingshot will accelerate for less time making for a slower a release velocity.

This is getting embarrassing.

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#31

Re: Rubber Tube Contraction Velocity

11/27/2014 9:31 PM

Force x Distance = Work

If the force is applied against gravity or a spring or a rubber band, the work is stored up as potential energy. (Work done against frictional force is not stored as potential energy. It's converted to heat energy and lost forever. But I digress...)

For a rubber band,

Force x Distance = Potential Energy

If you double the distance with the same force... you double the potential energy.

It's that simple.

Potential energy is converted to kinetic energy when the object is dropped or the tension on the spring or rubber band is released.

If you don't believe me, dust off your Physics 101 book and read the chapter on Conservation of Energy.

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#33
In reply to #31

Re: Rubber Tube Contraction Velocity

11/27/2014 11:18 PM

1. I assume you are talking to me.

2. I never had a Physics 101 book.

3. I remember something about kinetic energy, but I thought they were talking about the state of Connecticut not the state of the energy.

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#34
In reply to #31

Re: Rubber Tube Contraction Velocity

11/28/2014 9:15 AM

Total work is greater with the long tube,I will not dispute that fact,but the total work

is not delivered to the projectile,and the applied force is not constant throughout the

whole stroke,it is decreasing as the tube becomes shorter,and the pouch is losing

acceleration.The projectile speed is also decreasing,but at a slower rate.

It is no longer in contact with the pouch.

The maximum acceleration is delivered at the instant of release,and the pouch lags

behind the projectile after this point,unable to impart any more energy into the

projectile.This energy is wasted.

Just as it requires more and more energy input into the band to stretch it

further, conversely,less and less energy is output as it contracts.

The shorter tube contracts to a relaxed state quicker,having only half the distance to

travel,thus imparting a greater "A" to the projectile at the instant of release.

A=the rate of change of velocity per unit of time.

If you were stretching the same relaxed length of tube twice as far,it would be a

different situation.

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#35
In reply to #34

Re: Rubber Tube Contraction Velocity

11/28/2014 9:37 AM

F = ma... The projectile is being accelerated the entire time it is in contact with the pouch because the pouch is exerting a positive force on the projectile the entire time. The force decreases as the stretch decreases, but it's still pushing the projectile forward. It's still accelerating the projectile forward.

The maximun acceleration is NOT delivered at the instant of release. The maximum acceleration is delivered when the force is at its maximum. The velocity is at its maximum the instant of release, because all of the acvailable potential energy has been converted to kinetic energy at this point. Once contact is lost acceleration ends. The projectile becomes a free-falling object with a positive velocity in whatever direction the slingshot pushed it.

More energy input = more energy output. Essentially all of the potential energy imparted to the projectile during the stretch is converted to kinetic energy dcuring the contraction.

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#56
In reply to #35

Re: Rubber Tube Contraction Velocity

12/01/2014 2:10 AM

This makes sense to me, at least.

Where is Del ? This scenario is akin to a bow string pull, but the archer is absent...

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#57
In reply to #35

Re: Rubber Tube Contraction Velocity

12/01/2014 1:23 PM

Ok.As you stated,the velocity is at it's maximum at the instant(or shortly thereafter),of release.

Now my question is:How does the pouch maintain contact with the projectile when the velocity of the pouch is decreasing at a faster rate than the projectile.

Wind resistance on the pouch surely is more than wind resistance on the projectile,

add to this the decreasing force (and decreasing velocity) from the contraction of the bands,and pouch lags far behind the projectile.

It cannot impart any more energy to the projectile.

IF the projectile has enough mass,(Say a bowling ball) it could absorb all of the energy from the full contraction of the bands.

In that case,I would agree with you answer.

Technically,I should have stated the mass of the projectile.

MY bad.

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#58
In reply to #57

Re: Rubber Tube Contraction Velocity

12/01/2014 1:30 PM

Inertia. You really need a refresher in Newtonian kinematics.

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#60
In reply to #58

Re: Rubber Tube Contraction Velocity

12/01/2014 3:01 PM

Inertia is a measure of mass.So where is you argument?

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#62
In reply to #60

Re: Rubber Tube Contraction Velocity

12/01/2014 3:11 PM

No, inertia is not mass. Mass is a scalar attribute. Inertia is a vector attribute. Inertia and energy (aka mass) must both be conserved. You really need some kinematics training.

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#61
In reply to #58

Re: Rubber Tube Contraction Velocity

12/01/2014 3:02 PM

Inertia is a resistance to change in acceleration.

Mass affects inertia,and effectively,are inseparable.

Semantics for the sake of argument have no value.

https://www.youtube.com/watch?v=fFFgWl6t-6c

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#65
In reply to #61

Re: Rubber Tube Contraction Velocity

12/01/2014 5:41 PM

View the link and get back to me on this.

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#36
In reply to #34

Re: Rubber Tube Contraction Velocity

11/28/2014 9:39 AM

Now you're saying that the draw back length is the same with different tubes?

Fine, whatever.

Please get your scenario straight that you want answered.

I may or may not be back to this chaotic thread.

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#37
In reply to #36

Re: Rubber Tube Contraction Velocity

11/29/2014 8:35 AM

No,that is not what I am saying.

I said in the original post,that each of the tubes were

stretched 50% of their relaxed length to get the same force at the end of the pull

stroke.

The pull force is not constant, but increases with length when pulled,and decreases

with length when released .

This means that the maximum force is applied to the projectile at the instant of

release,and decreases thereafter as the tube contracts.

Since the force is decreasing,and the projectile has already received the maximum

velocity at the instant of release,the projectile is free to leave the pouch and

continue on it's way,while the pouch lags behind as it decelerates due to friction in

the tubes and wind resistance,etc.

This energy is wasted and not delivered to the projectile.

Of course,the heavier the projectile the longer it takes to accelerate to max

speed,and the more energy it can absorb.

A shorter tube will return to the relaxed state quicker,because it has only half the

distance to travel from full stretch length.

Therefor,with the projectiles of the same weight,the shorter tube will deliver a faster

acceleration to the projectile( a greater A).

The longer tube may deliver the same final speed,but if released at the same instant,

the shorter tube will arrive at the target sooner for two reasons:

1. Faster acceleration,and

2. It is closer to the target if the fixed point of the tubes are the same.

Even if the release points are the same, the shorter tube will launch the projectile

first.

It only has to travel 1/2 the distance to deliver the full amount of power required to

launch the projectile.

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#38
In reply to #37

Re: Rubber Tube Contraction Velocity

11/29/2014 9:38 AM

You are mixing kinematic terms and concepts.

Since the force is decreasing,and the projectile has already received the maximumvelocity at the instant of release, NO! The acceleration is at a maximum at the moment of release. The velocity is at a minimum at the moment of release. The velocity is at a maximum when it leaves the slingshot. The acceleration is at a minimum immediately after leaving the slingshot. The velocity of a bullet is highest when it leaves the muzzle.

There are secondary concerns like; spring mass, spring efficiency, tensile strength of the water balloon, coefficient of friction through air, alignment of force and center of mass that should be considered once one grasps the fundamentals but you are confusing velocity and acceleration. These are the most fundamental terms of kinematics.

Be careful with that Georgia Moon. It appears to have a lingering effect.

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#39
In reply to #38

Re: Rubber Tube Contraction Velocity

11/29/2014 10:57 AM

Ok.I should have said " the instant (undefined time interval) after release when the projectile leaves the pouch." instead of "at the instant of release.

I just presumed that my intent was clear,but sometimes I am not too good at

explaining what I am seeing in my mind.

I am seeing the projectile leaving the pouch after the maximum acceleration an instant(undefined time interval)after release.

If you break down the time instant small enough, you will see that for a VERY short

instant, the projectile does not move at all after release.

The pouch deforms slightly as it accelerates due to the inertia of the projectile.

As the energy is transferred to the projectile from contact with the pouch,it begins to

accelerate until it reaches maximum velocity,and the velocity from this instant is

decreasing,but the pouch is falling behind due to frictional and other losses,which are

greater than the losses of the projectile.

The projectile cannot accelerate after it leaves the pouch,obviously.

At this point in time, it has not passed the anchor point of the tube ,however.

The point being that the shorter tube will launch the projectile sooner than the longer

tube,due to a quicker contraction of the short tube than the longer tube.(hic!)

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#40
In reply to #39

Re: Rubber Tube Contraction Velocity

11/29/2014 11:27 AM

Now you're just messing with me. You bring up the crux of the matter and then misapply it. The projectile in the short tube releases the projectile in less time than the long tube. The long tube projectile is accelerated for a longer period of time than the short tube. Longer acceleration time results in more velocity. Δv=a*Δt

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#41
In reply to #40

Re: Rubber Tube Contraction Velocity

11/29/2014 12:28 PM

Peak velocity may be greater with the longer tube, but by the time the projectile leaves

the pouch of the longer tube, the shorter one is already closer to the target while the

longer tube projectile is still in the pouch.

The longer tube has to contract twice as far to deliver full power,and if the tubes have

the same contraction velocity,it will take twice as long,and the projectile will feel less

initial "G" force after release,it will have a longer time to accelerate to the same speed.

Remember,they are starting with the same amount of pull force,and the contraction

velocity is the same for both tubes.

The longer tube does not have twice the pull force or twice the speed of the shorter

tube.

Once the projectile loses contact with the pouch, the acceleration is over,and I don't

think it is in contact for the full stroke because the force is decreasing(slowing down)

as it contracts.

It would be interesting to see a high speed video of both cases.(hi hi hic!)

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#42
In reply to #41

Re: Rubber Tube Contraction Velocity

11/29/2014 1:34 PM

On my phone.

You've made a lot of assumptions.

But, the short tube projectile will begin deceleration sooner the long tube projectile.

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#43
In reply to #42

Re: Rubber Tube Contraction Velocity

11/29/2014 2:18 PM

I am sure you have seen a 1/4 mile race,where the faster car lost to the slower one because of the "hole shot",or faster reaction time from the start.

Higher final speed,but longer Elapsed Time.

I think this case may be similar.

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#44
In reply to #43

Re: Rubber Tube Contraction Velocity

11/29/2014 4:51 PM

Take that analogy a step further.

I get a 6 inch hole shot on you off the line, but my motor blows up 6 inches sooner than yours.

Now, what we haven't established............................. is the distance to the finish line.

Nor the actual advantage you have with a longer engine life.

Care to nail down all the variables, before we go on?

Remember, on the strip, we start at the same place.

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#45
In reply to #44

Re: Rubber Tube Contraction Velocity

11/29/2014 6:24 PM

What about the time dilation from the change in G due to the desires of the Cthulu riding a tachyon burst into a molting blackhole? Can this be compensated by a thiotimoline trigger mechanism on the turboencabulator?

Waaaa!!! What can I say about this fabulous elixir!

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#46
In reply to #45

Re: Rubber Tube Contraction Velocity

11/29/2014 7:12 PM

Yes, but not yet.

First, I'll have to get:

1/4-Inch Surgical Tubing, Amber, 3-Feet

There's an outdoor outfitters store down the street who sells this.

Much work to be done, such as determination of pull back force required to achieve 50% elongation.

Some calibration of equipment, (fish scale) and the decision to use two tubes vs one for ease of launch. Mechanism for release of projectile, etc.

I don't expect results until after the first of the year.

I'm cleaning out my lab and making room for this experiment after completing work on the last cold fusion project. The results of that trial were not conclusive, but there's all this slime on the floor that I'll have to clean up.

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#48
In reply to #46

Re: Rubber Tube Contraction Velocity

11/29/2014 7:50 PM

I was using Thera-Band therapy tubing for this discussion,and regular surgical tubing may not give the same results.

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#47
In reply to #44

Re: Rubber Tube Contraction Velocity

11/29/2014 7:36 PM

Finish line is 6 inches from the start.!!

If you both have the same top speed potential you can never catch the hole-shot guy.

Seriously,the farther it is to the finish line, the more the separation distance.

A 1 second advantage at 60 mph is only 88 feet,but at 120 mph, it is twice that.

Let us assume a 200 fps velocity,which is common for a bean shooter,measured at the exit side of fork of the bean shooter.

In 1/400th of a second,the shorter tube projectile is 6 inches from the point of release, and has reached maximum speed of 200 fps.

In the same time interval, the longer tube has only reached 100 fps,assuming a linear power delivery.

In the next 400th of a second, the shorter projectile travels another 6 inches and is now 1 foot from release point.

In the same interval,the longer projectile has reached it's maximum speed of 200

fps,but it is 1 foot behind the shorter one.

Add to this the extra six inches that it is starting from behind the shorter tube.

Since they both have the same maximum speed,the second one cannot catch the

first one,because the same forces will be acting on it as on the shorter one,

decelerating at the same rate,subject to the same friction,assuming the friction is a

result of the distance traveled through the air.The wind resistance to the pouch is

also greater, on the longer tube,having traveled twice as far.

And remember,the long tube is also starting 6 inches behind the short tube,(we are not on a drag strip).

and the internal friction of the tube contracting twice as far has to be considered.

Time starts when tube is released.

Time interval to target is quicker with the short tube.(hic)

Please correct me if I have my math or logic wrong.

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#49
In reply to #47

Re: Rubber Tube Contraction Velocity

11/29/2014 7:50 PM

Correct you?

You've hole shot me and overwhelmed me with fast talk.

I'll think more about this after I've had a nap.

If you can't dazzle 'em with brilliance......................................................

#48<reply>

Another variable???????????????????????????????????????????????????????????

Can you PM a sample to me?

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#50
In reply to #49

Re: Rubber Tube Contraction Velocity

11/29/2014 7:52 PM

Do not be baffled by my bull sh-t.

It is the Georgia Moon talkin'.

(Just got another refill from Uncle Bill's still on the hill!)

I noticed a couple of buzzards dropping out of the sky above the still,too drunk to fly.

If I am talking too fast,read slower.

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#51
In reply to #50

Re: Rubber Tube Contraction Velocity

11/29/2014 9:32 PM

"buzzards dropping out of the sky"

And, that's just from the smell.

Remember, I grew up in Arkansas. My cousin hauled shine in his '55 chevy.

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#52
In reply to #51

Re: Rubber Tube Contraction Velocity

11/30/2014 8:23 AM

I am an old Smokey Mountain Hillbilly.Come from a long line of hillbillies.

Liquid corn was the best and sometimes only way to make money in the hills.

Runners up there preferred the old Hudsons with a souped up motor and suspension.

Back then,the feds were called Revenuers or G-Men.

Officially,it was ATU, (Alcohol Tax Unit),not ATF:

They didn't have anything to do with firearms.

The high tech of the time was sticking their head out of the window and sniffing for

the brew,then following their nose.

The home made moon was also used for medicine.

Add some Camphor to it,and it would cure just about anything that ailed you.

I used to sneak some of that "cough syrup" from grandma's place,and almost got

hooked on it.

She noticed a lot of it was disappearing,and put a stop to it.

Caught me red handed,and red faced.

I still remember the lashing I got for that.

And I still remember the taste and sometimes get the cravin',even now,almost 60

years later.POTENT stuff!

I used to go with grandpa to an old abandoned mica mine.

It had been abandoned because it was not commercially profitable,but grandpa knew

where an unwworked vein was,and we took out big sheets of it and hauled it home in a mule and wagon.

He kept it stacked on a stone table and used it for barter in town.

At the time it was very valuable.

Some of the women also would pick Galax leaves and sell them to florists who would take all they could get.

This provided a small legal cash flow.

Times were hard,but I wouldn't trade them for a soft life.

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#53
In reply to #52

Re: Rubber Tube Contraction Velocity

11/30/2014 5:58 PM

I went to high school with a guy whose father got rich making shine.

He bought the kid a Chevy dealership with the money. The kid did build it up into a successful multi-dealership operation.

My parents didn't drink and never broke the law. I lead a sheltered life.

Like everybody else for miles around we were poor but ate well were dressed well and didn't know any other life style.

I have to bite my tongue when my wife opens the fridge and leaves it open "too" long.

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#54
In reply to #53

Re: Rubber Tube Contraction Velocity

11/30/2014 6:37 PM

Grandpa figured he was doing the right thing.

He payed taxes on the seed corn,the fertilizer,the sugar,the yeast,and reported the

income from the "moon" as income from selling the corn.

He figured they were trying to tax his labor and that was not right.

And it is HARD work making moon.

Try walking a mile or more thru the thick brush with a 100 lb cylinder of LP gas on your shoulder.

The tare weight of the cylinder added another 73 pounds.

His load weighed more than he did.He only weighed about 145lb.

If you were lucky,you could find a cylinder with a 71 pound tare weight,but these were rare.

2 pounds makes a BIG difference over a long distance.

Then there was all of the other hardware to get in there also:kettle,thump keg,piping,tubing,etc.

Another several hundred pounds,all by manual labor.

The local church was built with "moon" money,and he tithed every Sunday.

So the money was put to good use in more than one way.

The Lord works in mysterious ways,and seemed to protect him from the revenuers for many years.

He made it up till the last year of his life,and had no regrets.

No more being made in the woods.High tech infrared cameras on planes make it

impossible to hide a heat source now.

You can buy Georgia Moon in the liquor stores now,at least around here,anyway.

It is not nearly as good as the old home made though.

Grandpa's was as smooth as cream,and had a delicious corn malt flavor that is

lacking in the store bought variety.

He made his own malt and did not use much sugar,but he still got 100 proof after tempering.

It is an acquired taste,like many fine things.

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#55
In reply to #54

Re: Rubber Tube Contraction Velocity

11/30/2014 10:02 PM

Do people that break the law by evading the FTA or INS for decades produce high quality offspring? Yes, they both can produce exceptional people. IMHO I find that they more often produce spoiled brats on the edge of society.

Should an illegal shiner be allowed to claim paying all taxes because they were fully paid for another use, no. If you evade the law, you should either pay the price or accept when others skirt the law for a similar good reason.

I despise two faced zealots more that confidence men!

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#59
In reply to #55

Re: Rubber Tube Contraction Velocity

12/01/2014 2:45 PM

"We hang the petty thieves,and elect the great ones to office."=Aesop

Look at the Kennedy family,and their history during prohibition.

JFK was a great man, but without his father's illegal "moon" running,he would have

never been heard of.I don't think he was a spoiled brat on the fringe of society.

The prohibition laws were repealed eventually,because they were wrong,and

it was a bad law.

Some bad laws never get repealed.

I read a story of a young boy that was perpetually intoxicated.He was accused of

drinking liquor,but he denied it.

After many exasperated failed attempts to catch him nipping,he was given a total

physical examination.

There was a yeast culture in his stomach that converted food into alcohol,a

natural liquor still.

If you follow the letter of the law,he could have been charged a liquor tax

on the alcohol his body produced.

There is nothing morally wrong with making moonshine, man has been doing it

for centuries.

It only became illegal when the government wanted to collect taxes on it and

had to control it to make sure they were not losing any revenue.

IF you buy a load of building materials and let it sit in a pile and decay into dust,you

will not pay any more taxes than you paid when you bought it.

Now,if you take that same load of material,and build a house with your own

hands and sweat,you will pay taxes for as long as it exists.

Is that right? To tax a man's blood,sweat and tears?

I personally think not,but what I think does not matter in the long run.

Everything that is right is not legal,and everything that is illegal is not

wrong,in a moral sense.

I guarantee you if there was a reliable method of determining how many Johns

a prostitute had serviced in a night, so that the government could tax it,it

would be legal and it would be taxed.

Then eventually,they would tax married people based on a how many times they

had sex.
Sounds preposterous,but it is closer to the truth than anyone would like to

Admit.

Government never gets enough money.

They could take every cent that every worker makes and still be in the hole.

It reminds me of an old movie:The Blob.

The more it ate,the bigger it got,the bigger it got, the more it ate.

That is a good analogy for government everywhere.

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#63

Re: Rubber Tube Contraction Velocity

12/01/2014 4:58 PM

This is not entirely elementary: Impulse is what actually leads to final velocity,

J=∫F dt, and since F=ma, we have also F=dp/dt, thus J = ∫dp = mΔv, and since v(initial) = 0 (at rest, maximum draw), we have J = mv. However, the integral is over time. If the time for case 1 (half-length tube 50% elongation) is half the time for case 2 (full length tube 50% elongation), then very simply mv1<mv2. I am having brain lock all of a sudden. I must defer to those familiar with actual data on rubber tube draw - such as, if F=kd/d0 (modified Hooke's law) is obeyed, then it will be possible to solve rather easily, but if F= f(d), then not so easy?

Assumption: F=kd, thus a =kd/d0m, thusly we know that at draw back we have equilibrium of kd/d0 = 50# (weight, not mass). 50# weight is a force of 9.80*50/2.2 in Kg-m/sec2. 222.7 to be precise. and we know that at drawback in both instances, d/d0 = 1.5. Upon release from hold, the forces are no longer in equilibrium, and d/d0 →1.0 as time increases, and F drops off also. we need the time to travel back to d/d0=1.0, but somehow I believe this to be the same. Is this not why bows are specified by pull weight more than the length of the draw?

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#64
In reply to #63

Re: Rubber Tube Contraction Velocity

12/01/2014 5:38 PM

You can do it that way if you prefer:

mΔV = FΔt

ΔV = Δt(F/m)

The masses (m) of the projectiles are equal.

The force (F) needed to stretch the long rubber band to 150% of its original length is equal to the force needed to stretch the short rubber band to 150% of its original length.

The time required for the long rubber band to contract (Δt) is greater than the time required for the short rubber band to contract.

Therefore, the change in velocity (ΔV) is greater for the long rubber band than the short one.

I think it's easier to use the Conservation of Energy method:

The Potential Energy stored in the projectile by the stretched rubber band = Fd

The Kinetic Energy of the projectile after the release = (1/2)mV²

Potential Energy is converted to Kinetic Energy:

The longer rubber band provides greater Fd, which results in greater (1/2)mV²

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#68
In reply to #64

Re: Rubber Tube Contraction Velocity

12/01/2014 6:37 PM

IF the projectile was attached to the pouch,it would deliver all of the energy to the

projectile,but since it is free to leave the pouch,it will leave when the pouch begins to

slow down.

If the maximum velocity of the pouch is reached very soon after the release,then it is

slowing down from that time on,and has lost contact with the projectile.

Therefor a lot of the input energy is wasted propelling an empty pouch.

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#69
In reply to #68

Rubber Tube Contraption

12/01/2014 7:05 PM

Since this is a hypothetical problem, can't we assume that the pouch has no weight and no cross section?

And, if the projectile was attached to the pouch, it would put your eye out when it came back at your head.

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#74
In reply to #69

Re: Rubber Tube Contraption

12/02/2014 8:29 AM

I do not hold the sling shot like a rifle,at eye level.

I hold it at chest level,with the sternum as a reference point.

Like shooting from the hip with a rifle.

I can get a long pull from stronger tubes this way.

I can put a 3/8 ball into a 2 inch bird house hole at 35 yards.

Not great,but not too bad. Good enough for rabbits,squirrels,and snakes.

I thought I was pretty good 'til I saw a video of a guy shooting a marble in the air

with another marble.

I can hit a skeet about 50% of the time, but not a marble!

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#75
In reply to #74

Re: Rubber Tube Contraption

12/02/2014 9:04 AM

OK, this is my final comment here. Experimental data trumps all theory. Why not set up an experiment with two sling shots with different tubing lengths and test.

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#78
In reply to #75

Re: Rubber Tube Contraption

12/02/2014 11:24 AM

I agree with Redfred. This isn't rocket science. It's classic Physics 101. If you want to verify or disprove the theory, make two or three slingshots of varying length and do an experiment. To really illustrate the concept, build one ridiculously long and see what happens.

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#70
In reply to #68

Re: Rubber Tube Contraction Velocity

12/01/2014 9:28 PM

So long as any tension at all remains in the tube, the pouch will continue to accelerate.

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#71
In reply to #70

Re: Rubber Tube Contraption

12/01/2014 9:41 PM

But at some point, the projectile will leave the pouch even though the pouch is still traveling forward.

It has already received sufficient kinetic energy to "set it free" from the pouch.

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#72
In reply to #71

Re: Rubber Tube Contraption

12/01/2014 11:10 PM

Wrong; not until the pouch stops accelerating, i.e., no remaining tension.

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#73
In reply to #72

Re: Rubber Tube Contraption

12/02/2014 8:16 AM

Ok,so you are saying that the longer tubes can contract faster than the short tubes?

From 50% stretch on each one, with 50 pounds of pull on each one?

Equal pull,twice the length will travel faster than 1/2 the length with same pull?

In effect,you are saying that the longer tube can contract a 1 foot distance faster

than the shorter tube can contract 6 inches?

The heart of the matter is where does the pouch reach maximum velocity?

I am not speaking of stretching the same tube twice the length;that would have an

obvious answer.

This situation is not as obvious at it appears at first glance.

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#66

Re: Rubber Tube Contraction Velocity

12/01/2014 5:53 PM

If you stretch a dead horse to 150% of its original length, how many pieces will you have?

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#67
In reply to #66

Re: Rubber Tube Contraction Velocity

12/01/2014 6:17 PM

We don't stretch dead horses around here,I don't know about Arkansas.

But I have to give an Arkansas inventor credit for inventing the tooth brush.

Anywhere it it would be called a teeth brush.

And,I just recently read that Arkansas just passed a new law:If you divorce your

wife,she can still be your sister.

I will take all of the "Tar Heel" or Red Neck jokes you've got.

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#77

Re: Rubber Tube Contraction Velocity

12/02/2014 9:40 AM

In this thread, the Gran Patron and Georgia Moon aficionados seem actually to be drinking Pure Old Panther Piss, which is/was sold in Mason jars in some areas of the countryside.

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#81
In reply to #77

Re: Rubber Tube Contraction Velocity

12/02/2014 11:54 AM

I'm going to drink mine with some surgical tubing, after stretching it to twice its length.

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#82
In reply to #81

Re: Rubber Tube Contraction Velocity

12/02/2014 11:58 AM

Slam dunk! The best kind.

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#86
In reply to #77

Re: Rubber Tube Contraction Velocity

12/02/2014 1:16 PM

UMMM! PANTHER PISS GOOD! (in Homer Simpson voice)

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#83

Re: Rubber Tube Contraction Velocity

12/02/2014 12:21 PM

In conclusion,

  • Natural rubber tubes can be used for flippers.
  • Moonshine causes hallucinations.
  • Gas operated autoloaders have less muzzle velocity.
  • Don't leave rubber tubes laying around for junkies to use.
  • The tube ends can be open or closed without effect.
  • You can't kill a dead horse with a Wham-o to the touchhole.
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#84

Re: Rubber Tube Contraction Velocity

12/02/2014 12:34 PM

I did the calculations. My assumptions are listed below the table.

Case 1 - 12" rubber band stretched to 18" (0.5 feet stretch)

Case 2 - 24" rubber band stretched to 36" (1 ft stretch)

Case 3 - 4 ft rubber band stretched to 6 ft (2 ft stretch)

Case 1Case 2Case 3
massgrams1.05241.05241.0524
massKg0.00105240.00105240.0010524
maximum forcelbs505050
average forcelbs252525
stretch distancefeet0.512
Fdft-lbs12.52550
FdJoules16.933.967.8
½m(v^2)Joules16.933.967.8
Velocitymeters/sec179.5253.8358.9
Velocityfeet/sec5898331178

Assumptions:

mass of 1/4" steel ball bearing = 1.0524 grams

maximum force = 50 lbs

average force = 25 lbs

All of the potential energy (Fd) is converted to kinetic energy (½mv2)

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#85
In reply to #84

Re: Rubber Tube Contraction Velocity

12/02/2014 1:13 PM

This only works if the ball bearing remains in contact with the pouch and accelerates

for the full length of contraction.

Once the ball loses contact,energy input into the ball bearing ceases.

Any further movement of the pouch is wasted.

Also,what you are saying is that the longer the tube, the faster it can contract to the

relaxed state,even though it has twice the distance to go?

It does not begin at 50 pounds and maintain it for the full length,it decreases as it

contracts,from 50 to zero.

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#87
In reply to #85

Re: Rubber Tube Contraction Velocity

12/02/2014 1:45 PM

"This only works if the ball bearing remains in contact with the pouch and accelerates for the full length of contraction. Once the ball loses contact,energy input into the ball bearing ceases."

Correct. In case 1, the ball bearing is in contact with the pouch for 6 inches. It is only being accelerated during this 6 inch span. The force exerted on the ball at the beginning is 50 lbs. The force exerted at the end of the 6 inches is 0 lbs. That's where my assumption of 25 lbs average force came from. Likewise, in case 2 the ball bearing is accelerated forward only during the 12" contraction span. The average force during this 12" span is 25 lbs.

"Also,what you are saying is that the longer the tube, the faster it can contract to the relaxed state, even though it has twice the distance to go?"

No. The average force is the same, the distance is longer, the time to contract is longer. The time and distance the ball is being accelerated forward is longer.

"It does not begin at 50 pounds and maintain it for the full length, it decreases as it contracts, from 50 to zero."

Correct. That's where my average force of 25 lbs came from. I assumed the force per unit of stretch distance is linear. Probably not a bad assumption as long as you remain in the elastic range for the rubber band. Even if it's a bad assumption, the error is about the same for all 3 cases.

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#88
In reply to #87

Re: Rubber Tube Contraction Velocity

12/02/2014 2:34 PM

I agree with Lyn (for once or 200 times), that now is the time to put this to the mythbusters, lay it out on the line, put your money down, and apply the projectiles to the ballistic pendulum. I presume that HTR can hit a ballistic pendulum in the base with a butt fiddle, or was that butt with a base fiddle?

It looks like a challenge. If tribefan is right, those little 1 gram BB's are gonna smart at over 1000 fps! Practically, I do not believe natural rubber will contract that fast at all, ever. I think it gets in its own way.

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#90
In reply to #88

Re: Rubber Tube Contraction Velocity

12/02/2014 3:01 PM
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#91
In reply to #90

Re: Rubber Tube Contraction Velocity

12/02/2014 4:16 PM

HTR did specify natural rubber in the OP. or whatever is available at the local Ace Hardware. Hevea Brasiliensis it is. As to the design of the punkin' chunker, I don't care, and I really don't care if you have to "shoot" it from the hip to keep from putting your eye out. It's Christmas, of course you want a BB gun.

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#94
In reply to #90

Re: Rubber Tube Contraction Velocity

12/03/2014 11:04 AM

HTR needs to rejoin the conversation, and specify once again, the precise conditions of the test:

(1) actual lengths of tubing to be used

(2) mass of the projectiles (and shape if not spheres), density (matters)

(3) single band length with straight (more or less) draw, or double band as in slingshot?

(4)distance to target, target composition (prefer ballistic gel), and mass of target, along with suspension length for ballistic pendulum tests. (or high speed bullet chronometer specification).

(5)the number for emergency services for dummies who just shot their eye out right before Christmas

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#95
In reply to #94

Re: Rubber Tube Contraction Velocity

12/03/2014 12:32 PM

In the original post,I posed two questions:

One: Velocity of the projectile

Two:Time to target.

The material used is Thera Band-Gold Tubing

The specifications are listed on this link.

http://www.thera-band.com/faqs_consumer.php#faq_1

1.The test involves 2 tubes , like a slingshot

The different lengths of tube were arbitrary,used to simplify the math for the

question, the specifications on the link show that regardless of length, the same

percentage of stretch will give the same increase in pull force,and the pull strength

was rounded off for same reasons stated above.The actual lengths of tube do not

matters as long as the same ratios can be maintained The projectile is a 5/16 inch

steel ball, wt: 2.052GThe distance to targets is 10 feet from the front side,the anchor

point,of the sling shot .

Targets are two,each made of the same solid material, 3/4 inch

plywood is suggested, free to swing,and break a photocell at the slightest movement,

positioned below each target,and a timer configured to each photocell to determine

which beam broke first,and thus which target was struck first.The projectile launch

points will have a trigger mechanism mechanically attached to each one,configured

so that each projectile is released at the same time and will also include photocells to

detect when the trigger was pulled,and when the projectile has begun to move.Tests

should be conducted in a closed structure to eliminate any wind fluctuations.This

should provide all the information required to determine velocity and time to

target.

Any other information should be able to be calculated from this information,unless of

course,I have forgotten something.(likely).

And lastly,I do not put slingshot near eyes when shooting,but if you use that

method,goggles or safety glasses are recommended,of course.

Good luck!

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#93
In reply to #88

Re: Rubber Tube Contraction Velocity

12/03/2014 9:36 AM

I thought 1000 ft/sec seemed a little high, too. But the assumption was rubber tubing that would have 50 lbs of force after being stretched to 150% of its relaxed state. That seems pretty high, too. If anyone wants to measure the actual force and stretch distance for some tubing, give me the data and I will revise my table. Also, the 1000 ft/sec case was 4 feet long relaxed; 6 feet stretched. Pretty big slingshot. If the tubing gets in the way of the little ball during launch, all bets are off. We gotta design it somehow so the tubing doesn't get in the way.

This thread has gotten me interested in slingshots again. I had one many years ago and was a pretty good shot. Not as good as Redneck, but not bad. I'm going to build one this weekend! Ha! Ha!

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#89

Re: Rubber Tube Contraction Velocity

12/02/2014 2:52 PM

I think I have stretched this conversation out to the point where the pressure has

increased exponentially,so while you guys hash it out,I will,like the signifying

monkey,who started trouble between the lion and elephant,sit back and watch from a

distance.

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#92
In reply to #89

Re: Rubber Tube Contraction Velocity

12/02/2014 4:19 PM

Oh great launcher of metal spheres into tiny bird box holes, pray tell, why not participate in the launchery? Or better still - further specify the design of the launcher. I have a few suggestions for the ballistic pendulum.

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#96

Re: Rubber Tube Contraction Velocity

12/03/2014 2:19 PM

Revised calculations:

Case 1: 6" tubes stretched to 12" (100% elongation)

Case 2: 12" tubes stretched to 24"

Case 3: 24" tubes stretched to 48"

Case 1Case 2Case 3
massgrams2.05202.05202.0520
massKg0.00205200.00205200.0020520
maximum forcelbs28.428.428.4
average forcelbs14.214.214.2
stretch distancefeet0.512
Fdft-lbs7.114.228.4
FdJoules9.619.338.5
½mv

2

Joules9.619.338.5
Velocitymeters/sec96.9137.0193.7
Velocityfeet/sec318449636
Accelerationfeet/sec

2

100987100987100987
Time in slingshotsec0.003150.004450.00629
Time to targetsec0.031470.022250.01573
Total time (release to target)sec0.034610.026700.02203

Assumptions:

14.2 lbs force at 100% elongation for each rubber tube

distance to target is ten feet

ammo = 2.052 grams

It's going to be hard to measure such short elapsed times accurately. We might want to consider shooting each slingshot into the air at a specified angle and measure the distance traveled.

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#99
In reply to #96

Re: Rubber Tube Contraction Velocity

12/03/2014 5:55 PM
Theraband Gold tubing provides for :
tubing Atubing B14.2lbs pull at 100% elongationFds=dW
length1224inches63.16475Newtons forcekg-m/s

2

Fds=dW
0.30480.6096m2.052g ball weightF=ks
2.05E-03Kg projectileat s=dF=ks
elongation 50%, s0.15240.3048m 5/16ball diameterF=kdat s=d
7.9375mm ball(ignores air resistance)k=F(100)/dF=kd
extended length:0.45720.9144m49.48315mm

2 cross-section

k=F(100)/d
4.95E-05m

2 cross-section

W=(k/2)s

2|0d

=kd

2/2

k=F(100%)/s(50%)414.4668207.23342N/mW=(k/2)s

2|0d

=kd

2/2

10ft to targetD=D(0)+v(0)t+0.5at

2

W (input)4.8131549.6263074N-m304.8cm to targetD(0)=0D=D(0)+v(0)t+0.5at

2

3.048m to targetv(0)=0D(0)=0
!00% W->K.E.4.8131549.6263074N-mD=dv(0)=0
t=sqrt(d*2/a)D=d
velocity at release68.4996.86m/sect=sqrt(d*2/a)
acceleration30782.030782.0m/sec

2

a, ft/sec

2

100991100991ft/sec

2

time loose to free:0.0044500.006293s
time free to target:0.0445010.031467s
total0.0489520.037761s

I applied a 50% elongation as stated in the initial post.

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#103
In reply to #99

Re: Rubber Tube Contraction Velocity

12/04/2014 11:12 AM

Great chart!

The only problem I see is that you are considering the 50 pounds of force to be

constant from end to end of the tubing,.

It is really decreasing at a linear rate.

At 50% elongation, there will be 50 pounds of force at time of release,thereafter,it

will be less until the relaxed state.

If you look at the force per inch of tubing,the shorter tubing has the same force

concentrated into a shorter length,therefor the "energy density" so to speak, of the

tubing is twice that of the longer tubing.

It should contract quicker,delivering the same amount of thrust at a faster rate,thus

faster Acceleration.

Add to this the 1 foot further from the target In case 2) of the longer tube

(remember,the timing starts when the projectile clears the anchor point of the

tube,which is the same distance from the target for all tubes. )

About a 5% longer distance to target, in case 1, 10% in case 2, and about 33% in

case 3.

The longer tube cannot contract as quickly as the shorter tube,but it applies a gentler

force over a longer distance, end result is same total energy input into the projectile.

Time-to-target should be quicker with the shorter tube.

Where am I going wrong with this train of thought?

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#105
In reply to #103

Re: Rubber Tube Contraction Velocity

12/04/2014 11:47 AM

Since the % elongation is the same for the long one and the short one, the force is the same. The long one is exerting that force over a longer distance, so the energy is greater. The acceleration is the same in both cases since the force is the same. The longer one is accelerating the ball over a longer distance (and for a longer time), so the final velocity is greater for the longer one.

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#106
In reply to #103

Re: Rubber Tube Contraction Velocity

12/04/2014 11:55 AM

W=1/2k s2 s≠ length, it is displacement elongation. I also used the 14.2 # at 100% rating for the tubing you specified, and I also used 50% elongation is mentioned in the OP, at least I think I did. By now my head is spinning on its axis, and my brain is getting inertial overload.

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