# Torque with Infinity length can lift anything?

• I
I was always wondering if you can lift anything (no matter how heavy it is) if you just use a really long pipe.
Or does torque increases in a way like ##e^x## , ##a^x## and after some point it barely increases?

Also if this can be explained mathematically, I would love to see it.

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jbriggs444
Homework Helper
2019 Award
I was always wondering if you can lift anything (no matter how heavy it is) if you just use a really long pipe.
Or does torque increases in a way like ##e^x## , ##a^x## and after some point it barely increases?

Also if this can be explained mathematically, I would love to see it.
Torque is given by force times the [perpendicular] length of the moment arm. For example, force from the plumber's hand multiplied by the length of his pipe wrench.

If the wrench is infinitely long, you you cannot rotate it through any finite angle, so you cannot lift anything.

I don't understand it...

Mark44
Mentor
If the wrench is infinitely long, you you cannot rotate it through any finite angle, so you cannot lift anything.
I don't understand it...
Presumably you would have to apply a force to the far end of the wrench, but then again, it's infinitely long...

If we assume that is long enough? For example let's say I want to lift a very heavy rock (100 tons) with just a pipe, if I use a pipe really long (like 1000 km) will it be easy to lift the rock? Or does torque has limits?

jbriggs444
Homework Helper
2019 Award
If we assume that is long enough? For example let's say I want to lift a very heavy rock (100 tons) with just a pipe, if I use a pipe really long (like 1000 km) will it be easy to lift the rock? Or does torque has limits?
How far do you want to lift it? And how far are you willing to push the far end?

[To say nothing of the problem of finding a 1000 km rigid pipe that weighs less than 100 tons]

russ_watters
How far do you want to lift it? And how far are you willing to push the far end?
lets say 1 meter

And how far are you willing to push the far end?
At the very end of the pipe to maximize the length from the spinning point.

[To say nothing of the problem of finding a 1000 km rigid pipe that weighs less than 100 tons]
So, one problem is that the pipe will also weight a lot, making things harder for me?

phinds
Gold Member
2019 Award
If we assume that is long enough? For example let's say I want to lift a very heavy rock (100 tons) with just a pipe, if I use a pipe really long (like 1000 km) will it be easy to lift the rock? Or does torque has limits?
I think you are looking for LEVERAGE, not torque.

Nugatory
Mentor
I think you are looking for LEVERAGE, not torque.
It’s effectively the same thing, as leverage is just the torque around a particular point, namely the fulcrum. And to answer the original and follow up questions:

Yes, the torque/leverage is linear in the distance from the center so in principle you can use an arbitrarily small force just by increasing the distance commensurately. That’s what Archimedes was getting at when he said “Give me a place to stand and I can move the earth”. In practice, if you overdo it your lever will bend and break instead of lifting the object - to lift a mountain with your fingertip you would need a completely rigid rod ten billion kilometers long with the pivot one meter from one end and strong enough to support the entire weight of the mountain hanging from that end.

Vanadium 50, Asymptotic, babaliaris and 1 other person
It’s effectively the same thing, as leverage is just the torque around a particular point, namely the fulcrum. And to answer the original and follow up questions:

Yes, the torque/leverage is linear in the distance from the center so in principle you can use an arbitrarily small force just by increasing the distance commensurately. That’s what Archimedes was getting at when he said “Give me a place to stand and I can move the earth”. In practice, if you overdo it your lever will bend and break instead of lifting the object - to lift a mountain with your fingertip you would need a completely rigid rod ten billion kilometers long with the pivot one meter from one end and strong enough to support the entire weight of the mountain hanging from that end.
This is the answer I was looking for!!! Thank you I get it now!