?!

We don't need to *compare* but to *explain* the Poldo

Tackle systems shown in this thread.

--dl*

====

<

**I'm sorry, I made a mistake in this post: **

I'm correcting the original post using red color!

errata corrige:

4L <correct>, 2L <wrong>

F = 1/4 W <correct>, F = 1/2 W <wrong>

and so IMA is 4:1 <correct>, and so IMA is 2:1 <wrong>

we have F_righthand + F_lefthand= 1/4W <correct>, we have F_righthand + F_lefthand= 1/2W <wrong>

and so F_righthand = F_lefthand = 1/8W <correct>, and so F_righthand = F_lefthand = 1/4W <wrong>

please see Reply #19Hi Dan,

you are right, here I am.

The principle of conservation of energy helps us to solve the (ideal) problem (i.e. only conservative forces act).

(for reference see Feynman Lectures on Physics Vol.1,ch.4)

The general principle is:

<change in energy> = <force> x <distance force acts through>

The formula for gravitational potential energy is:

<grav. pot. energy> = <weight> x <height>

Let's consider a rope 6L in length and a load of weight W:

- at its maximum extension Poldo tackle is 3L in length, (we can suppose <grav. pot. energy> = 0, i.e. <height> = 0)

- at its minimum extension, Poldo tackle is 2L in length, (<grav. pot. energy> = W x 1L)

(see figure Poldo_max-min_ext.jpg)

We have gained a change of energy (from 0 to WxL) as "our" force (let's call it F) has been acting on the Poldo tackle, but we have pulled the rope for a displacement of

4L in length (our force F has done a work of Fx

4L) whilst we have lifted the load only by 1L in length (the force of gravity has done a work of Wx1L (remember W is the force of gravity acting on the load)).

Now, F x

4L has to be equal to W x 1L (for the principle of conservation of energy)

and then

F = 1/

4 W

and so IMA is

4:1

Note: if we use both hands (simultaneously and with the same force acting on points RH and LH in the figure (right hand upwards, left hand downwards))

we have F_righthand + F_lefthand= 1/

4 W

and so F_righthand = F_lefthand = 1/

8 W

Curiosity: look at figure Poldo_Super.jpg for a super-min-extension of Poldo tackle!

s.