Pulleys and Block-and-Tackle Systems flashcards

A fixed pulley only changes direction: IMA 1, effort equals load. A movable pulley rides with the load and is held by two segments: IMA 2, so effort is half the load.

Count only the rope segments that hold up the moving block (not the wheels). A dead end tied to the moving block counts; ideal effort $F=\frac{W}{n}$.

$d_{rope}=n\times d_{load}$ for n supporting segments. A 3-segment tackle lifting 0.4 m needs 1.2 m of rope. Less force always costs more rope travel.

$\text{AMA}=\frac{F_{load}}{F_{effort}}$ using measured effort; efficiency $\eta =\frac{\text{AMA}}{\text{IMA}}$. 900 N lifted with 400 N on 3 segments: AMA 2.25, η = 75%.

Add the weight of the moving block, hook and sling to the load before dividing by n. 760 N motor plus 40 N block on 4 segments needs 200 N, not 190 N.

$D_1{N}_1=D_2{N}_2$: driver diameter times rpm equals driven diameter times rpm. An 80 mm pulley at 1,800 rpm driving a 240 mm pulley gives 600 rpm. The larger pulley turns slower.

Open belt: both pulleys turn the same direction. Crossed (figure-eight) belt: the driven pulley turns the opposite direction. Pulley sizes never change direction.

$v=\frac{\pi DN}{60}$: pulley diameter D in meters, speed N in rpm, gives m/s. A 0.10 m pulley at 1,500 rpm drives the belt at about 7.85 m/s.