Funny but serious by all accounts!!

[daltontrees]

Sod this, I'm getting a MEWP.

 

Seriously though, Dalton explained it comprehensively enough for me to just about wrap my little brain around.

 

Got any explanation for descending on a line to static?(I.e. Abseiling down using your hitch then coming to a stop)

 

Aargh! Yes I suppose so.

 

It is a bit hard to get your head round but when moving at constant speed up or down no additional force is put on the anchor point or rope. So once you have started descending on a static line and have reached a steady, unjerky rate of descent, the load on the rope is the same as when stationary.

 

To calculate what happens when you stop, you either need to know the time it takes you to stop or the distance over which you stop. Time is the easier one. Let's say you are descendign at 1 m/s. And you stop in 2 seconds.

 

The deceleration is 1 m/s divided by 2 seconds = 0.5 m/s/s.

 

The additional force on the rope is therefore F = m a = 100kg x 0.5 = 50 Newtons. The total force on the static line is therefore the dead load of 100kg x 10 m/s/s plus the deceleration load 100kg x 0.5. Total 1050 newtons. This assumes the treee is rigid and the rope does not stretch at all. In reality it's more complex than that, the tree and rope flex and store energy temporarily, reducing the overall rate of deceleration and reducing the load on the anchor point.

 

And I forgot the first bit. As you start to descend you reduce the load. Say you get from o m/s to 1 m/s in 2 seconds. The overall load is reducxed by 50N, the reverse of the stopping calculation

 

So the load in this example goes from standstill 1000N, drops to 950N as you move off, stabilises at 1000N for the descent and then increases to 1050N as you come to the ground. Then when you stand on the ground it becomes 0N. How quickly that happens depends on the gracefulness of the landing. I am assuming stopping at waist height then standing up. The load in your feet then becomes 1000N. 500N each foot.

[daltontrees]

Yesss! Finally killed the thread!

 

That Newton knew his stuff, you english punters should rejoice in his F=ma type stuff. It is as important to understanding as is 'to be or not to be'. No, considerably more so.

[sloth]

Do we have a like button yet?

 

Sent from my GT-I9100 using Arbtalk mobile app

[Joe Newton]

Yesss! Finally killed the thread!

 

That Newton knew his stuff, you english punters should rejoice in his F=ma type stuff. It is as important to understanding as is 'to be or not to be'. No, considerably more so.

 

Thanks for humouring me, it's interesting learning about my namesake!

[Taupotreeman]

Far out Dalton that's a pretty impressive reply.

 

 

Sent using Arbtalk Mobile App

[Dean Lofthouse]

I wouldn't bother highlighting the issue to them Adam, anyone thick enough to believe it should not be in the gene pool anyway, natural selection and all that.

 

Trouble with health and safety nowadays is that it is weakening the said gene pool, danger is natures way of weeding

[Joe Newton]

I wouldn't bother highlighting the issue to them Adam, anyone thick enough to believe it should not be in the gene pool anyway, natural selection and all that.

 

Trouble with health and safety nowadays is that it is weakening the said gene pool, danger is natures way of weeding

 

 

A herd is only as strong as it's weakest link. When the herd is hunted it is the weaker slower members that are picked off. The effect of this is that the herd gets faster as it's slower members are eradicated.

 

Alcohol works in a similar way. It picks off the slower weaker brain cells, which is why you always feel smarter after a drink

[RobArb]

Uh oh, looks like saome basic physics is needed here. Don't run away, it's fairly easy.

 

You need only one equation. F=ma. Force equals mass times acceleration.

 

When you are hanging on a single line the force on the branch equals your mass (and the mass of teh rope and the harness etc.) times the acceleration which if you are static is the gravitational acceleration. it is about 9.8 m/s/s. Call it 10.

 

100kg x 10 m/s/s = 1000 Newtons (the unit of force). Or 1kN.

 

If you think about it, this is why gear rated to say 30kN can hold 3 tonnes or 3000kg. F = m a.

 

So in the example, the rope is resisting all of this force, so the load on it is 1000N. every action has an equal and opposite reaction. One of Newton's laws of dynamics.

 

But if you pull up on the single line to go up the ways, and you accelerate at 2 m/s/s, you are adding that much to the acceleration of gravity, so the load becomes 100kg x 12 m/s/s = 1200 Newtons.

 

The load on the rope therefore depends on how fast you go up, and is only greater than the static load while you accelerate upwards.

 

It might not be surprising to know then that if you start to descend, the load on the rope decreases.

 

Using a doubled rope is a little more complicated. When static, the load on teh branch is still 1000N, but the load on each half of the rope is 500N.

 

As you ascend, the load on each side is increased by half the additional total load. If you were accelerating upward at 2 m/s/s, the additional load on each side of the rope is equivalent to 1 m/s/s which means each side is loaded 10 + 1 m/s/s = 11 m/s/s times half the deadwweight. Using f=ma again, the load is therefore 11 x 500kg = 600N.

 

With ropes of standard rating 3kN or 3000N, neither SRT nor DdRT will come anywher near breaking strain. To do that you would need to (using our F=ma in reverse now) accelerate at a = F/m = 3000/100 = 30 m/s/s.

That is, your upward speed would need to increase by 30 metres per second per second. After the first second you would have to be travelling at 30 metres per second. Now I don't care how fast SRT is, that aint going to happen unless you're being hoisted by a medieval battle trebuchet.

 

The modest DdRT man would by comparison have to be pulling through 60 metres of rope a second and be body thrusting like Beyonce on speed.

 

Good post Jules but.... (minor correction:lol:)

 

Newton's laws of which you quote are about motion not dynamics. The F=ma is Newton's second law. The popular phrase "for every action there is an equal and opposite reaction" is his third law (for anyone interested his first law was about inertia and mass).

 

And isn't all motion relative anyway:biggrin:

 

 

Queue Einstein retort:001_tt2:

[daltontrees]

Good post Jules but.... (minor correction:lol:)

 

Newton's laws of which you quote are about motion not dynamics. The F=ma is Newton's second law. The popular phrase "for every action there is an equal and opposite reaction" is his third law (for anyone interested his first law was about inertia and mass).

 

And isn't all motion relative anyway:biggrin:

 

Queue Einstein retort:001_tt2:

 

Motion is dynamics! Anyway, I was just rattling stuff off from memory, and as ever I'm delighted that anyone is the slightest bit interested. Well spotted!

 

I don't think Arbtalk is ready for departures from Newtonian physics yet. A smart-ass Einsteinian reply might be able to demonstrate that the climber descending or ascending at a fixed velocity would become heavier or lighter by virtue of that velocity. But the quantum would be so minute that you could lose or gain more weight breathing.

 

Oh what the heck, I'll never get another chance to use E=mc2 on Arbtalk.

 

If you equate the energy of the moving climber E to mc2 where m is climber's mass and c is the speed of light and equate that in turn to the climber's kinetic energy (the energy stored in his momentum) which is 1/2 mv2, the increase in the climber's weight if he is moving at 1 m/s is

 

1/2 (v2/c2) = 1/1.5 x 10 to the 16

 

Which, if the climber weighs 100kg is 0.00000000000000667 kg.

 

Which is not very much.

 

Happily this would be the same whether SRT or DdRT and there is no danger of SRT causing a nuclear holocaust.

[RobArb]

 

I suppose the fact that:

 

a) we, as a climber are not travelling at very fast (light) speeds (S.R.) and;

b) our mass isn't very dense (G.R)

 

Then we don't need to worry:biggrin:

 

 

 

 

 

 

 

 

Unless we cut our single rope........... (sorry, joke)

 

 

I've suddenly rediscovered a love for maths and physics:biggrin: