Rubber Tube Contraction Velocity

The more I thought about my calculations, I came up with a few disclaimers:

In real life, 100% energy transfer is not going to happen. The amount of potential energy that ultimately becomes kinetic energy in the ball is going to be less than 100%. Maybe a lot less. The pocket and rubber bands still have plenty of kinetic energy after the ball is gone, especially if the mass of the rubber band and pocket is large compared to the mass of the ball.

These calculations also assume everything is happening in a vacuum. Air resistance becomes very significant at high velocities.

That being said, I still believe that the longer rubber band will provide a ball with a greater velocity than the shorter one, for equal % elongation.

It is definite that the longer bands will give the higher velocity.

Since we have short range, and really short transit times, I neglected air friction, and also stayed with the unit energy transfer, which is pure bull.

Did you allow for the extra 12 inches of travel to the target from the release point of the longer band?

Distance is measured from the anchor point of the tubes,which are the same distance

from the target.This will not affect velocity,but it will affect time-to-target.

Oops, I forgot to include the elongated travel from loose to free, just the original length. Here are the corrected times below:

The above was copied and pasted from my spreadsheet called "punkinchunkin".

See below. I adjusted the travel distance, the % elongation, and % of the available potential energy transferred to the ball.

It's a spreadsheet (obviously). If anyone would like to tweak any of these assumptions, let me know. It would take about 3 seconds to re-revise the table.

What is missing from your calculation is the mass of the tubing and pouch that get also accelerated. A longer tube will have more mass. This is an unknown but critical parameter. If the projectile was at least five times more massive than the sling then one could ignore the sling mass. With two tubes and only half of each tube is getting accelerated, one can just add the length dependent mass of one tube and one pouch to your calculation. [A more accurate calculation would be to perform all of the correct integrals.] This might have been what HTRN was trying to say but the longer tubes will still provide more velocity.

Yup, that's for sure. After the ball is launched, the rubber band and pouch still have plenty of kinetic energy. If they are more massive than the ball, they will hog proportionally more of the available energy during the acceleration phase, too. Reducing the percentage of available potential energy transmitted to the ball from 100% to 50% was a step in the right direction. That number could be further refined if we knew the mass of the rubber band and pouch. At some point, it would be fun to do a series of experiments to see how close we got.

Redfred is correct. The mass of the rubber band and pouch has to be included in the calculation, especially if they are anywhere near the mass of the ball being shot. I revised my calculations accordingly. I also went back to the assumption that all of the potential energy becomes kinetic energy, but the pouch and rubber band are also accelerated during the process and therefore consume some of the potential energy. In cases 1-3, I assumed the mass of the rubber band and pouch to be equal to the ball. In cases 1A-3A, I assumed the mass of the pouch and rubber band to be 3X the mass of the ball.

A red (natural) rubber pre WWII truck inner tube cut and both free ends nailed to the frame of a hayloft door will send an average sized Macintosh 80 yards down range or in one particular case, into the side of a semi rolling along at that 80 yard distance, whereby the irate driver, unbeknownst to the slingshootests, has ascended the hayloft ladder to knock the noggins of the perpetrators together with a sound akin to two coconuts. Proving every action has a sometimes painful reaction.

That's a great story! You gave me an idea... I'm going to build a big slingshot at my brother-in-law's house on the shores of Lake Erie. We can perfect our aim and technique during the winter. Maybe we will be able to nail some fishing boats or jet skiers with water balloons next summer!

I do not think that the acceleration is constant,or increasing all the way to the end of the contraction of the tubes.

Let's turn the problem 90 degrees and apply a known constant force of acceleration

to the objects.

Lift a 50 pound weight to 10feet,20 feet and 30 feet height.

Release them at the same instant.

No doubt,the highest one will achieve the greatest velocity and energy upon

impact,but which one will strike the ground first?

Not exactly what I was trying to illustrate,but close.

Yes. The force that is provided by rubber bands or springs are not constant, so the acceleration is not constant. If you assume that the change in force per unit of stretch length is linear, you can use the average force for the span to calculate the total acceleration for the span. For example, in the sling shot problem, if the force at maximum stretch is 40 lbs, you can assume the average force during the span is 20 lbs. Then you can calculate the average rate of acceleration during the span as if it was being propelled by a 20 lb force the whole time.

Gravity is different. The gravitational force acting on a falling object is essentially constant, so the acceleration is essentially constant. (Acceleration of gravity is assumed to be constant if object didn't get significantly closer to the center of the earth during the free-fall. Since the distance from sea level to the center of the earth is about 4000 miles, the force gravity would remain essentially constant for a fall of a few miles.)

Assume the 50# weights are directly over the head of a beaten horse.

The first weight will daze the horse, causing it to fall straight to the ground. The second one will partially crush the skull of the dazed horse, although it won't feel it and the third one will mercifully put the horse out of its misery.

James,

It looks like you calculated the times for 10, 20 and 30 meters.

Kroiky! I did it again. If I ever did anything right the first time, Einstein would do cartwheels around a black hole!

RedNek,

I forgot to answer your question about the falling rocks.

Distance -- Time -- Final velocity

10 feet -- 0.788 sec -- 25.4 ft/sec

20 feet -- 1.115 sec -- 35.9 ft/sec

30 feet -- 1.366 sec -- 43.9 ft/sec

(Assuming no wind resistance)

That analogy would work only if the target were zero distance from the slingshot.

Ok,if you insist,place a plate with a hole in it large enough for the weight to pass thru

below each weight.

Place each plate the same distance from the ground.

Let this plate represent the anchor point of the tubing in this analogy.

It will not change the results.

Wrong again, as usual.

By results,I mean that the lower one will still strike first,but with less velocity and energy than the other two.

How is that wrong?

Perhaps you can suggest another,better analogy.

I am open to suggestions.

The gravity case is different from the slingshot case. In gravity, the projectiles continue accelerate even after passing the "zero" point; i.e. ground level.

In the slingshot, the projectiles no longer accelerate after losing contact with the pouch. Although the faster projectile is behind at first, it catches up and passes the slower one.

I suspect that in some combinations of sling characteristics and projectile weight, the catching up can occur even before the projectiles reach the plane if the slingshot; i.e. the zero point. Even if not, the faster projectile soon moves ahead.

After chewing on all the valuable insights and opinions and hard data,I am content to

recognise that at some tube length and distance combinations, the shorter tubes can

get a projectile to the target sooner,but also with increasing distance to target, the

longer tube will eventually pass the shorter one.

An extreme example would be a tube length of 1 mile for the longer tube, and 1 foot

for the shorter tube, and a target at a distance of 10 feet.

The results are very obvious in this case, without the need for calculation or

charts;likewise if the target were moved to 200 yards,the short tube would probably

not even make it to the target.

So it is a case of a specific set of narrow conditions where the shorter tube can make

it of the target first,but always a case of the longer tube having a faster final velocity.

I hope this will bury the poor dead horse.

RIP: Mr. Ed,Trigger, Buttermilk,Silver, Scout,and Flicka

The pull is never evenly balanced between the two tubes. What effect would this have?

The flight of the ball will not be aligned with the aiming point,and the ball will leave

the fork divergent from center of aim point.

It will hit high,low,left,right, or some combination of these errors.

There may also be a spin induced in the sphere,

It will also make it more difficult to calculate the velocity of the ball.

Exit 0!

One last kick for for the poor dead horse... There certainly is an optimum rubber band length for each set of assumptions. (See table below.) If you assume 50% stretch, the pouch having the same mass as the ammo, and a target 10 feet from the sling shot, it appears that a 5 foot (relaxed) rubber band length (2.5 foot stretch length) wins the race to the target (Case 6). The total time to target starts to increase if the rubber band gets longer (because it's in the slingshot longer). For other assumptions, this optimum would be different.