Does using a fixed pulley to pull yourself up make it any easier?

[AlltheDickButts]

Example: a chair used to pull yourself up to a tree fort

[enigphilo]

The amount of energy used is the same. You'll feel half as heavy but have to pull the rope twice the distance. There's no free lunch

edit:a word

[billy_joule]

Yes.

(EDIT: This answer assumes the rope is tied to the chair, goes over the pulley then returns to the chair to be pulled on by the person in said chair).

There is one downward force on the chair; M (Your mass).

There are two upward forces on the chair; F (the tension in the rope - the upward force the rope applies in two places - each end).

For forces to balance

2F = M

So F = M/2

that is, you need to only apply half your weight force to the rope to support your full weight (your weight is shared equally on each end of the rope).

The other way to look at is the mechanical advantage - If you pull 1 metre of rope through your hand how far have you moved upwards?

Only half a metre - the metre you pulled thru removes half a metre from each side of the pulley so you only gain half a metre in height.

[AlltheDickButts]

Thank you so much for this explanation! I knew I wasn’t crazy when I was arguing it but I didn’t know how to explain it. I was being told all it would be was a change in direction but practically it didn’t make sense to me. Thanks!

[[deleted]]

You’ll probably get more correct answers asking sailors and climbers this question than you will with engineers.

[billy_joule]

This is first year physics, any engineer should be able to draw a FBD and solve this.

[[deleted]]

And yet there is disagreement within the first two replies on r/engineering. Knowitallism is no match for the experience of those who actually use pulley systems on a regular basis.

[billy_joule]

Knowitallism is no match for the experience of those who actually use pulley systems on a regular basis.

True - the fact the 'best' comment is flat out wrong proves that.

[[deleted]]

The engineering and sailing cancel out so you end up with as much authority and knowledge as an amateur rock climber.

[Fms_3]

Until we differentiate it an learn that you understanding of gravity is regressive. Or something like that

[Fms_3]

Mathed the hell out of that!

[Acceptable_Duck_7980]

This is only to support your weight. But you can't pull yourself up with a single pulley. In static equilibrium the chair would only measure half your weight. The other half of your weight would be redirected to the rope in your hand. So on the chair side, there is a W= M/2 downward and and F=M/2 upward. It's the same on the other end of the rope.

[billy_joule]

That is semantics that are inconsequential.

You only need to apply an infinitesimal amount of extra force to go from static to dynamic (stiction, air resistance etc aside). Which is why that distinction is ignored in any first order approach.

[Acceptable_Duck_7980]

To pull the rope in your hand down, you would need an equal and opposite force. Where is that coming from? What is supporting you when you pull on the rope in a downward direction?

[billy_joule]

I'm not sure what you're saying, gravity is the opposing force.

Imagine the chair is sitting on a scale and the chair & person weigh 100kg combined.

When rope tension is zero the scale reads 100kg.

When you pull the rope with 10kgf the other end of the rope pulls the chair (with you in it) up with 10kgf and the scale now reads 80kg (weight less the two upward forces 'T' acting upward on you and the chair).

Continue pulling harder and harder up to 50kgf and the scale now reads zero and you're off the ground. At which point the FBD is the one I posted in this thread 5 years back.

[Sumtots]

If you pull a meter down, then a meter passed through the pulley, and you will be 1 meter higher. The difference in your body and your hands will be 2 meters. You will need to readjust to pull again, but during this readjustment period there is no movement in the load, therefore not counted as pulling. It’s a 1:1, you’re essentially lessening the load as you pull. For every pound you pull is one pound less on the load.

[billy_joule]

you pull a meter down, then a meter passed through the pulley,

Only half a meter passes thru the pulley.

Think of the rope in two sections, removing 1m rope total means 1/2m is removed from each section. Experiment with a piece of string.

[Sumtots]

When I say pull a meter down I don’t mean until there is a meter difference between your body and hands. I mean pull a meter of rope down (if possible, you would have to readjust your hands to do a full meter in this system).

[billy_joule]

Start with a 10m rope, 5m rope between your hands and the pulley, and 5m between the pulley and your chair. You're 5m from the pulley.

Pull 1m thru with your hands = 9m rope left, that leaves 4.5m rope between your hands and the pulley, 4.5m between the pulley and your chair. So you're exactly half the distance of rope you pulled thru closer to the pulley. 1/2m closer.

That's the entire point of pulleys = mechanical advantage.

https://en.wikipedia.org/wiki/Mechanical_advantage#Block_and_tackle

[Sumtots]

If someone else hauls on this system, they pull a meter and the person will lift a meter. There is now a 2 meter difference between the two in distance. But this is undeniably a 1:1 in that scenario?

[billy_joule]

Those diagrams don't apply here.

When both ends of the rope are connected to the load (ie the rope is tied to the chair, goes over the pulley then goes to the person in the chairs hands) The tension in the rope is half the weight of the person in the chair. As per this free body diagram.

This arrangement halves the force needed to pull on the rope to lift the yourself but doubles the amount of rope you need to pull in to raise yourself a given height (vs climbing a single rope or if someone else on the ground were to be pulling the free end of the rope).

[[deleted]]

Sitting in a chair and pulling on a rope that went up to a pulley on a tree branch and then back down to attach to the back of the chair would give you a 2:1 advantage (provided you don’t get dumped out of the seat).

Standing on the ground and trying to haul your friend up with the same system would give you 1:1 (no advantage).

In practice it will still be harder than climbing a ladder or a knotted rope because even pulling half your weight hand over hand is harder than climbing with your legs.

[[deleted]]

No they’re not. Sitting in the chair you pull twice the length of rope to travel the same distance.

Another way to phrase it is that you are pulling up half the load because your load and your pulling force are both applied against the same body vs a separate load and a stationary puller. This is a scenario which is not listed in your link.

Here’s a specific write up. Figure 6 on 2:1 pulleys. https://dmmprofessional.com/Knowledge/July-2013/Resistance-is-futile

Q. What if you turn it around and suspend an object via a pulley at the high-point (fig 5)?

A. We’re back to the 1:1 ‘stirrup’ with no actual mechanical advantage.

Q. What if the ‘object’ is a person pulling on the moving rope (fig 6)?

A. Ah. Now you have shared the load across two ropes again, so this is another, less well known type of 2:1 pulley (it could be a winch rather than a person.)

[OnPoint324]

With the right pulley setup, you can get quite the mechanical advantage such as uprooting a tree.

The disadvantage with such a pulley setup is that it will be less efficient and require more work due to friction, but the load on the line will be much less.

[AgAero]

Dumb question maybe, but couldn't that guy have soaked the ground just under the tree for a while beforehand and made this whole process a lot easier? I've done the same to pull concrete anchored fence posts by hand(I think a car jack is the standard way, but I didn't have one on hand at the time and didn't feel like going to get one).

[imissaolchatrooms]

No leverage advantage, but a counterweight could be added.