# Pulley
## Lever
<div style="text-align: center;">
<img src="https://upload.wikimedia.org/wikipedia/commons/0/0f/Lever_%28PSF%29.png" alt="image"width="600">
</div>

>https://en.wikipedia.org/wiki/Lever

$$\text{IMA} = \frac WF$$
### Class 1 lever
$$\text{IMA} = \frac WF \in R$$
### Class 2 lever
$$\text{IMA} = \frac WF > 1$$
### Class 3 lever
$$\text{IMA} = \frac WF < 1$$
## Pulley type
### Fixed pulley (Class 1 lever)
$\text{IMA} = 1$
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/H1_PEzYwex.png" alt="image"width="150">
</div>

$$\frac WF = \frac{v_F}{v_w} = 1$$
### Movable pulley (Class 2 lever)
$\text{IMA} = 2$
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/SkPKVfFvll.png" alt="image"width="140">
</div>

$$\frac WF = \frac{v_F}{v_w} = 2$$
### Movable pulley (Class 3 lever)
$\text{IMA} = 1/2$
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/rykhNMKvxx.png" alt="image"width="140">
</div>

$$\frac WF = \frac{v_F}{v_w} = \frac12$$
## Block and tackle
### Gun tackle pulleys
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/BkDKBGKDeg.png" alt="image"width="250">
</div>

$$\text{IMA} = \frac WF =\frac {2F}{F} = 2$$

<div style="text-align: center;">
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Tackles.png/570px-Tackles.png" alt="image"width="400">
</div>

>https://en.wikipedia.org/wiki/Block_and_tackle
* Number of line : $n$
$$\text{IMA} = \frac WF =\frac {nF}{F} = n$$
### Spanish burton
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/HkS8J-9Dgl.png" alt="image"width="350">
</div>

$$\text{IMA} = \frac WF =\frac {2F+F}{F} = 3$$
**Multi-spanish burton**
* Number of movable pulleys : $n$
$$M = 2^{(n+1)}-1$$

### Luff upon luff
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/B1WNUGtPxl.png" alt="image"width="380">
</div>

number of line : $m$,$n$
$$M = \frac WF = mn$$
### Differential pulley block
The smaller the difference between $D$ and $d$, the larger $F$
<div style="text-align: center;">
<img src="https://hackmd.io/_uploads/SkAPJW5wle.png" alt="image"width="150">
</div>

$$F(\pi D) = \frac W2(\pi D)-\frac W2(\pi d)$$

$$FD = \frac W2(D-d)$$

$$M = \frac WF = \frac{2D}{D-d}$$