Physics explanation of a chair trick?

1. Apr 27, 2013

guitarphysics

Today my English teacher told us that we you can't lift a four-legged chair (of avg weight) if you only lift from the bottom of one leg. All the students tried and none of us could. What is the physical explanation of this? I'm guessing it has a lot to do with the moment of inertia of the chair increasing if you only grab the chair from an end at the bottom of one leg, but I'm pretty sure there's more to it than that- maybe something to do with torque?
(Try to attempt this yourself to get what I mean- it's actually really cool).

2. Apr 27, 2013

Simon Bridge

I can lift a 4-legged chair by the bottom of one leg easily by allowing the chair to flop over.
You mean you need to keep the chair with the same orientation ...
:D

you are right, it is about the torques.
The chair wants to fall over with a long lever arm from your wrist to the center of mass of the chair - which is usually just below the middle of the seat depending on the chair. Your wrist muscles have to provide a couple to counteract this to hold the chair steady (opposite forces applied top and bottom of your hand). The lever arm for the couple is just half the width of your palm. This means you need to be able to supply a force much stroger than the weight of the chair to lift it and hold it steady.

It is easier to lift from the back legs (the com is closer to the back than the front), and easier if you first tip the chair until the com is over your hand.

Does the number of legs matter?
Does it matter is if is a stool instead of a chair?

Last edited by a moderator: Sep 25, 2014
3. Apr 27, 2013

Simon Bridge

I can lift a 4-legged chair by the bottom of one leg easily by allowing the chair to flop over.
You mean you need to keep the chair with the same orientation ...
:D

you are right, it is about the torques.
The chair wants to fall over with a long lever arm from your wrist to the center of mass of the chair - which is usually just below the middle of the seat depending on the chair. Your wrist muscles have to provide a couple to counteract this to hold the chair steady (opposite forces applied top and bottom of your hand). The lever arm for the couple is just half the width of your palm. This means you need to be able to supply a force much stroger than the weight of the chair to lift it and hold it steady.

It is easier to lift from the back legs (the com is closer to the back than the front), and easier if you first tip the chair until the com is over your hand.

Does the number of legs matter?
Does it matter is if is a stool instead of a chair?

Last edited by a moderator: Sep 25, 2014
4. Apr 27, 2013

guitarphysics

Oh, that clears it up, thanks very much :)!
As for your questions (which I assume were to make me think a bit more):
I'm pretty sure that the number of legs doesn't matter too much (as long as the mass of the chair doesn't change and the legs are arranged symmetrically)- I think that the center of mass will only move downwards, so I guess it would probably make it a bit easier if there were more legs.
If it's a stool instead of a chair- same thing. The center of mass will be lower. Only other difference I can think of is that the com will actually be in the middle of the chair (not closer to the back legs, as in the previous case).

How did I do?

PS. By arranged symmetrically, I mean that if there are three legs, each leg is positioned at what would be a vertex of an equilateral triangle. If there are four legs, each leg is positioned at a vertex (or corner, or whatever) of the square, and so on... (Basically, what I mean is that each leg must be equidistant from each other and from the center of the chair).

5. Apr 29, 2013

Simon Bridge

Well ... it would work even if you had a chair with just one leg.
It is the horizontal distance to the com that counts. If you think about it, the lower the com, the more of the weight is perpendicular to the moment arm ;)

Experiment: see the the orientation of your write counts. i.e. lie the chair on it's side and pick it up from the end of one leg.

BTW: I used to see weight-lifters do this trick to show off.
They start with their elbow on the ground - which means they get to lever the chair up via arm muscles too.
But it also means that they tip the chair slightly - which puts the com closer, horizontally, to their hand. If you tip the chair so the com is directly over your hand you'll find it's easy.

6. Apr 29, 2013

sophiecentaur

I have done this trick and have found it's easier if you push away as you lift the chair with a bit of a jerk. This tilts the chair as required but isn't quite so obvious. It even looks flashier.
You need to be careful not to dislodge the occupant of the chair though.