Mechanical advantage, or just a redirection of force?

[garyTheSnail]

TL;DR

A question about leverage

In the following image, does the 4 x 4 post offer a mechanical advantage or does it just redirect force? Thank you in advance.
Reference video:

 

[Baluncore]

It offers both a mechanical advantage and redirects the force. The steeper the post, and the closer its foot is to the stump, the greater is the advantage. The limit is the stretch of the rope.

Once the stump has lifted, the final roots must be pulled, which requires less force, so there is advantage in moving the foot away, to increase the speed, while reducing the advantage.

 

[garyTheSnail]

It offers both a mechanical advantage and redirects the force. The steeper the post, and the closer its foot is to the stump, the greater is the advantage. The limit is the stretch of the rope.

Once the stump has lifted, the final roots must be pulled, which requires less force, so there is advantage in moving the foot away, to increase the speed, while reducing the advantage.

Thank you for the information. Would the top of the post along with its movement give a similar mechanical advantage as a single pulley suspended from above? My thought is the rotational movement of the cable around the pulley is somewhat similar to the arc movement of the post top supporting the cable. Or am I wrong?

 

[renormalize]

Your diagram needs a better looking wench.

 

[garyTheSnail]

Doh!

 

[Baluncore]

Would the top of the post along with its movement give a similar mechanical advantage as a single pulley suspended from above?

No. A pulley would turn freely but remain in position, which will equalise the tension on both sides of the pulley.

As shown, the chain is locked to the top of the pole, so the sum of the forces at the top of the pole gives different tension forces in the chain on either side.

If you had a pulley at the top of the pole, the pole would fall over due to unbalanced forces.

 

[garyTheSnail]

Thank you again.

 

[sophiecentaur]

TL;DR: A question about leverage

does the 4 x 4 post offer a mechanical advantage or does it just redirect force?

It offers both a mechanical advantage and redirects the force.

On a practical note, the angle at which the rope acts on the stump and also where it's fixed will both have a significant effect. The longer the remaining stem, the greater the torque on the root system, which would snap the outside roots first. It could be worth while to use the 4X4 as a lever, with the winch line at the top end and the line to the door. But the bending of the post could be an issue (your way gives no torque on the post, which may be better)

If you have a number of stumps to remove and if you struggles with this one then there are a few 'optimisations' possible - like using a shorter post which would increase the torque (as above).

The M.A. can be adjusted by the relative angles of the rope to the post. A bigger lifting force can act on the root with the post close to the root but the root would be lifted by a shorter distance. I don't know how familiar you are with the (schoolboy) theory of Moments and the expression "vertical distance' between force and lever. The post actually acts as a lever with a fulcrum on the ground. The magnification of the force can be worked out.

If you have many roots to deal with then you may want to follow it up . But don't go there if it's a pain.. . . .